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A Review of Developments in Steel: Implications for Long-Span Structures

• Original Article
• Published: 21 January 2021
• Volume 74 , pages 1055–1064, ( 2021 )

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• Prem Krishna 1  

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Historically, iron in different forms has been known to exist for Architectural and Engineering applications from early periods of civilisation, but in the modern context, it would be best to review the growth of steel, during the last couple of centuries. This paper, first, traces briefly the developments in steel in terms of its various aspects, which are relevant to the design of structures. It is perhaps needless to remind ourselves that humans perpetually endeavour for a better quality of life. To meet the challenge thus created for providing additional and improved infrastructure, and, riding on a number of parallel (or nearly so) developments, the frontiers for Civil and Structural engineers and architects have moved to horizons not easy to imagine. One exciting thrust has been towards increased dimensions, in both height as well as span of structures, which have touched kilometres from tens of metres. One of the important factors responsible for the aforesaid developments is without reservation, the advancements in steel, and, products based upon it, for deployment in structures, besides the related aspects of fabrication, construction and maintenance. There are other factors too, such as, the growth of electronics which has led to enormously increased capabilities in computing. Also, there are the remarkable developments in instrumentation and robotics as tools in structural engineering. This has led to a paradigm shift in the scenario for structural analysis, design and drafting, construction and maintenance. In traversing the journey above, there are different aspects and features that have already become convention through practice and literature, and there is extensive awareness about them. On the other hand, there are issues and areas of comparatively new developments about which the awareness is rather limited. The emphasis in this text is largely on the latter. Since some of these issues can provide for extensive coverage, the attempt herein is to only bring out the salient features.

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Acknowledgements

The author thanks Er. Amitabha Ghoshal and Er. Alok Bhowmick, two eminent structural engineers, for their time in reading through the script and for their valuable inputs. Likewise, thanks are due to Professors Toshio Miyata and Yukio Tamura for information about the Akashi Kaikyo suspension bridge. Permission by Institute for Steel Development and Growth for use of technical material from their archives is thankfully acknowledged. The author is thankful to Mrs. Pratigya Laur helping with the script and illustrations.

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Krishna, P. A Review of Developments in Steel: Implications for Long-Span Structures. Trans Indian Inst Met 74 , 1055–1064 (2021). https://doi.org/10.1007/s12666-020-02173-7

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Received : 20 November 2020

Accepted : 25 December 2020

Published : 21 January 2021

Issue Date : May 2021

DOI : https://doi.org/10.1007/s12666-020-02173-7

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ORIGINAL RESEARCH article

Research on mechanical properties of steel-polypropylene fiber concrete and application of beam structure.

• 1 School of Civil Engineering, Changchun Institute of Technology, Changchun, China
• 2 Shenyang Nonferrous Metallurgy Design and Research Institute Co., LTD., Shenyang, China

Concrete faces the difficulties of low tensile strength and poor crack resistance in building structures. In order to remedy this deficiency. In this paper, steel-polypropylene hybrid fiber reinforced concrete (SPFRC) was prepared by adding steel fiber (SF) and three kinds of polypropylene fiber (PF) to C50-grade concrete. The mechanical properties and microstructure of SPFRC were studied with different fiber combinations and content, obtaining the best hybrid combination. Based on this, the bending resistance and cracking of SPFRC beam members were investigated. The results demonstrate that the addition of fiber improves the compressive strength of ordinary concrete by 0.16% ∼ 17.69%, the splitting tensile strength by 15.18% ∼ 47.45%, and the bending strength by 3.54% ∼ 26.77%. Compared with single-fiber concrete, the hybrid fiber can achieve better internal microstructure, which further enhances the mechanical properties of the material. Hybrid fibers overlap within concrete beams, effectively redistributing stress and inhibiting the formation and propagation of cracks. For the three types of SPFRC beams, the cracking load is increased by 14.29% ∼ 28.57% compared with PC beam, the ultimate bearing capacity is increased by 9.68% ∼ 19.35%. The optimal dosage is determined as 1.0% SF, 0.6% Embossed polypropylene fiber (PBF). It provides reference for the application of SPFRC in flexural members.

1 Introduction

Since its inception, concrete materials have been widely utilized in civil engineering due to their high compressive strength, good plasticity, and ease of availability. However, as concrete applications have expanded, its weaknesses, such as low tensile strength, poor crack resistance, and inadequate durability, have become more pronounced. To meet the increasing demands for concrete performance in engineering, numerous researchers have continuously enhanced concrete performance by modifying aggregates, adjusting mix ratios, using admixtures, and employing various other methods ( Li et al., 2022 ; Sun et al., 2022 ; Li et al., 2024a ). One such method, fiber concrete, involves adding fibers to concrete to restrain and impede crack formation and improve the strength and toughness of the material.

Steel fiber (SF) is a type of metal hard fiber with excellent mechanical properties and a simple production process. These characteristics make it suitable for concrete fiber blending requirements. In 1911, Graham from the United States first experimented with adding SF to concrete, demonstrating the excellent performance of SF concrete through tests. Song and Hwang (2004) research indicated that the participation of SF can increase the compressive strength by 15.3% and the splitting tensile strength by 98.3%. The research of Ramadoss et al. (2023) shows that when the bulk content of SF is 1.5% and the replacement rate of silica ash is 15%, the compressive strength and folding strength increase by 33.41% and 66.67%, respectively. Ahanger and Tiwary (2024) use SF to strengthen recycled aggregate concrete, showing that with 1.5% SF content, compared with PC, the compressive strength increased from 45.5 to 62.6 MPa, and the flexural strength increased by 43.48%. Polypropylene fiber (PF) in the middle of the last century by the Italian Montecatini company took the lead in industrial production. Since its birth, it has attracted scholars to study it. PF density is usually between 0.89 ∼ 0.96 g/cm3, elongation between 15% and 30%, insoluble in water, and good corrosion resistance. In addition, as an organic fiber material, PF is cheaper than other fibers, so it is widely used in engineering fields such as basement floors, parking lot floors, and industrial and civil buildings ( Vedernikov et al., 2022 ; Xian et al., 2024a ). Abousnina et al. (2021) mixed PF into concrete, studied its mechanical properties, working properties, and microstructure, and the results showed that, Although PF reduces the workability of concrete, it significantly increases the toughness of the matrix, which is different from the brittle failure of ordinary concrete. PF concrete shows a progressive failure mode. In addition, under the same volume content, high elastic modulus fiber has a better strengthening effect on concrete, while organic polymer fiber can improve the toughness of concrete materials ( Wang and Wu, 2002 ; Qing et al., 2017 ).

The properties and characteristics of various types of fibers vary, leading to differing effects when added to concrete to improve its working and mechanical properties ( Ding et al., 2022 ; Li et al., 2023a ). When multiple fibers with different properties are mixed into concrete, they can synergistically enhance the performance of concrete in various dimensions ( Abed et al., 2023 ; Awad et al., 2023 ; Kun et al., 2023 ). For instance, Khan et al. (2022) studied the steel-basalt fiber concrete and demonstrated a 43.0% increase in compressive strength compared to regular concrete at specific dosages. Additionally, Muhyaddin (2023) research on ultra-high performance concrete (UHPC) indicated a 6.0% strength improvement when using a composite of steel fiber and glass fiber compared to using either fiber individually. Li et al. (2023b) reinforced concrete matrix with PF and SF to make up for the defects caused by coal gangue aggregate. The test results showed that hybrid fibers could cooperatively improve the microstructure of coal gangue concrete and make it meet the requirements of C30 concrete strength grade. The research of Bhogone and Subramaniam (2022) pointed out that the mixture of SF and PF in concrete can significantly reduce the development of early cracks and improve the fracture pattern. Due to its low elastic modulus, low density, and good ductility, PF can restrain the formation of early micro-cracks in concrete and enhance compactness. In addition, SF has a high elastic modulus, which can act as a skeleton support for the concrete matrix, accept the stress transmitted by PF and cement slurry, and restrain the development of cracks after concrete cracking ( Liu and Han, 2019 ). SF and PF overlap each other to form a complex spatial structure. Under the appropriate dosage, the two kinds of fibers can achieve complementary advantages and produce the “positive hybrid effect”. S.R. Shashikumara applied these two fibers to concrete beams and showed that PF delayed crack formation and reduced crack width before cracking, while SF fibers showed better bearing capacity at yield and ultimate load points ( Shashikumara et al., 2023 ). Abdulrahman Abbadi conducted static load tests on concrete beams with hybrid fiber systems (coarse PF, micro PF and SF). The data show that the cracking load value of hybrid fiber is increased by 14% compared with that of concrete beams doped with SF, which can delay the crack occurrence more effectively and reduce the deflection and reinforcement strain ( Abbadi et al., 2022 ). Dipti Ranjan Sahoo conducted an experimental study on the flexural performance of SF-PF hybrid concrete beams, and the results showed that the addition of hybrid fibers can redistribute tensile stress at cracks, improve ductility and maintain the integrity of the beams. However, when the fiber content is too high, the ultimate load value of the beam decreases instead of increasing ( Sahoo et al., 2015 ). Therefore, finding the right mixture of materials is the basis of SPFRC beam application.

The preliminary study of the research group shows that among the four types of steel fiber (shear type, end hook type, copper plated type, wave type), the shear steel fiber has the most significant strengthening effect on concrete ( JGJ55-2011, 2011 ; Li et al., 2024b ). Therefore, based on C50 concrete, this paper combines shear steel fiber and polypropylene fiber of three different types wavy type (PAF), embossed type (PBF), and monofilament type (PCF) into concrete to prepare steel-polypropylene hybrid fiber reinfored concrete (SPFRC). And conducts mechanical properties tests and analysis to obtain the hybrid fiber combination that improves the mechanical properties of concrete. In addition, the microstructure and strengthening mechanism were analyzed by microscanning test. The beam members were made according to the optimal mixture amount, and the load-bearing properties of different types of SPFRC beams were studied by bending test, which provided a reference for the application of SPFRC in engineering.

2 Experimental summary

2.1 raw materials.

This experiment adopted (42.5) P.O. Portland cement produced by Changchun Yatai Cement Co., LTD. The coarse aggregate selection of granite crushing and screening after the size of 5–12 mm stone, as shown in Figure 1A . The fines is selected from local natural river sand, and after screening and drying, the fineness modulus is 2.7, which belongs to medium sand, as shown in Figure 1B . The selection of a naphthalene superplasticizer (CQJ-NX) can enhance the service behavior of fiber-reinforced concrete. The water that is used in the batch is ordinary tap water.

Figure 1 . Coarse and fine aggregate and fibers appearance. (A) Coarse aggregate (B) Fine aggregate (C) SF (D) PAF (E) PBF (F) PCF.

Based on the previous research basis of the research group ( JGJ55-2011, 2011 ; Li et al., 2024b ), the performance indexes of the selected shear steel fiber are shown in Table 1 , and its appearance is shown in Figure 1C . Three different types of PF, wavy type (PAF), embossed type (PBF), and monofilament type (PCF), were selected for the test. PAF has the longest length, wavy shape and smooth fiber surface. PBF shape is not curved, straight fiber, surface embossed pattern. PCF has the shortest length and is a filamentous shape with a small diameter, smooth surface and soft texture. Their various performance indexes are shown in Table 1 , and their appearance is shown in Figures 1D–F .

Table 1 . Fiber performance index.

2.2 Experimental design

2.2.1 mix ratio design.

The base concrete of this test is C50, and the amount of materials required for C50 common concrete is calculated according to the Design Regulations for Common Concrete Mix Ratio (JGJ55-2011) ( GB/T 50081-2019, 2019 ).

The material properties test was divided into two parts. The selection range of fiber content comes from the research group’s previous research basis ( JGJ55-2011, 2011 ; Li et al., 2024b ). First, the steel fiber (SF) content was 0, 0.4%, 0.6%, 0.8%, 1.0%, and 1.2%, and the cubic compressive strength, splitting tensile strength, and folding strength were tested to obtain the optimal SF content. On this basis, the wave type (PAF), embossed type (PBF), and monofilament type (PCF) polypropylene fiber were mixed with SF respectively, and the three mechanical properties were tested in four groups, and the optimal mixture of hybrid fiber concrete was selected. The specific design is shown in Table 2 .

Table 2 . Experimental group design.

2.2.2 Specimen preparation and curing

According to the specification (GB/T 50081-2019) ( Li et al., 2023d ) and combined with the test indexes. Test blocks with side lengths of 100 mm were utilized for the evaluation of compressive and splitting tensile strength, whereas prismatic test blocks with dimensions of 100 mm × 100 mm × 400 mm were employed for the assessment of flexural strength. Each group consisted of three specimens.

For fiber-reinforced concrete, the mixing process is crucial a factors influencing the performance of concrete. An incorrect mixing process can easily lead to fiber agglomeration and affect the test results. Therefore, the mixing process of fiber concrete was optimized in this experiment. It was necessary to manually disperse the fiber and then add it to the mixer, dry mix it until the fiber was dispersed and evenly mixed with the aggregate, and then add water for mixing. HJW-60 type single-axis horizontal mixer was used for concrete mixing. After the mixing was completed, the mold was filled and vibrated on the shaking table until the bubbles were discharged. After the surface floating slurry was smooth, it was left for 24 h and then molded, and the concrete was put into a standard curing box with a temperature of 20°C and a relative humidity of 95% for 28d.

2.3 Experimental method

2.3.1 compressive strength test.

This material mechanical property test was conducted by the specification (GB/T 50081-2019) ( Li et al., 2023d ). The compressive strength test was carried out by the YAW-2000 pressure testing machine. The test block was positioned at the center of the pressure plate, with the formed side of the test block acting as the pressure surface. The automatic loading was controlled by the computer at a loading rate of 0.5 MPa/s, and the loading was stopped after the specimen was damaged.

The compressive strength of the specimen is calculated by Formula 1 , and the arithmetic average strength of the obtained three test blocks (accurate to 0.1 MPa) is taken as the compressive strength of the cube. As the test block is a non-standard cube, the strength values should be adjusted by the dimensional conversion factor of 0.95.

Type: F ——block breaking load (N);

A ——Section area of test block (mm 2 );

f cu ——Concrete cube compressive strength (MPa).

2.3.2 Splitting tensile strength test

The splitting tensile strength test was conducted using the YAW-2000 pressure testing machine. The pressure surface was the side of the specimen forming surface. Prior to the test, the position of the middle splitting surface was marked on the surface of specimen, and the splitting fixture was aligned with the marked line before loading. The loading rate was 0.05 MPa/s. When the test block is split or the vertical crack in the middle is penetrated, the test is declared to be over.

The splitting tensile strength of specimens is determined using Formula 2 , and the average strength of the three test blocks obtained (rounded to 0.1 MPa) is considered as the splitting tensile strength of this group. As the test block is a non-standard cube, the strength values should be adjusted by the dimensional conversion factor of 0.85.

Type: F ——Failure load of test block (N);

A ——Test block splitting surface area (mm 2 );

f ts ——Concrete splitting tensile strength (MPa).

2.3.3 Flexural strength test

The flexural strength test utilized the MW-50D microcomputer-controlled electronic universal testing machine. The bearing surface was formed by the side of the specimen, and the four-point loading method was employed. The load was transferred by the actuator to the loading steel plate, and the loading steel plate was distributed to the specimen through two hard steel cylinders. Before the test starts, position marking lines are drawn at the support position and loading position. The loading rate of the testing machine is 0.08 MPa/s. When the loading rate drops significantly, the specimen is declared damaged and the test ends.

The flexural strength was numeration according to Formula 3 , and the arithmetic average strength of the three specimens (accurate to 0.1 MPa) was taken as the flexural strength of the group of specimens. Since the size of the specimen is non-standard, it is necessary to multiply the dimensional conversion factor by 0.85.

Type: F ——Failure load of specimen (N);

l ——Support spacing (mm);

b ——Section width of sample (mm);

h ——Section height of sample (mm);

f f ——Concrete flexural strength of (MPa).

2.3.4 SEM micromorphology test

The micromorphology scanning test was performed with a HITACHI S-3400 scanning electron microscope. Operation steps: 1) Select the block broken material after the mechanical test as the sample, the sample size is about 8 mm × 8 mm × 5 mm; 2) Fix the sample on the sample bearing table with tape, clean the dust on the surface of the sample and the sample bearing table with the air bag, and invert the sample bearing table to test whether the sample is firmly pasted; 3) Put the sample into the gold spraying equipment for gold spraying treatment. 4) Put the sample bearing table into the electron microscope sample room, and adjust the magnification, color contrast, etc., to obtain the ideal microstructure diagram.

3 Test results and analysis

3.1 compressive strength of cube, 3.1.1 failure pattern.

The failure pattern of the compressive strength test is depicted in Figure 2A , and the progressive loss of effectiveness of a standard concrete test block is illustrated. The outer layer of concrete surrounding the test block has been entirely removed, indicating severe damage. The residual portion exhibits an hourglass shape, characteristic of brittle failure.

Figure 2 . Cube compressive failure pattern. (A) Plain concrete (B) Fiber reinforced concrete SF4 (C) Fiber reinforced concrete SF6.

Figures 2B, C show the failure modes of SF4 and SF6 fiber-reinforced concrete. Compared with ordinary concrete, SF reinforced concrete is relatively complete after failure, with no obvious concrete spalling phenomenon and only a small amount of concrete debris falling, indicating that the addition of fiber improves the failure mode of concrete, from brittle failure to plastic failure. This is because the fibers overlap with each other inside the test block to form a fiber cage structure, which can play a binding role when the specimen is damaged, inhibit the transverse deformation of the concrete, reduce the spalling of the concrete during the failure process, and ensure the integrity of the test block.

By comparing Figures 2B, C , it can also be found that with the increase of fiber content, the spalling phenomenon of concrete compression failure mode is weakened, the crack width is narrower during failure, and the shape of the test block is more complete during failure. Indicate that with the growth of fiber content, the development of cracks can be better restricted and the damage degree of the test block can be reduced. The failure pattern of the hybrid fiber specimen is similar to that of the single doped steel fiber specimen, the whole specimen is relatively complete, only some vertical cracks appear on the surface during failure, and the concrete debris drop is less.

3.1.2 Compressive strength results and analysis

The cube compressive strength test results are drawn as a histogram, as shown in Figure 3 , and analyzed as follows:

Figure 3 . Fiber reinforced concrete cube compressive strength.

For the test group of separately incorporated SF, the cube compressive strength showed a tendency to rise and then diminish. When the SF content is 1.0%, the peak compressive strength reaches 60.82 MPa, which is 17.7% higher than that of PC. However, when the SF content further increases, the compressive strength begins to diminish, indicating that the SF content of 1.0% is the best volume content.

For the test group of SPAF. When the content of PAF is in the range of 0.08% ∼ 0.14%, the compressive strength shows an increasing trend, and the strengthening effect begins to weaken when the content exceeds 0.14%. When PAF content reaches 0.14%, the compressive strength is 58.78 MPa, which is 13.7% higher than that of PC. In summary, when the volume of PAF is 0.14, the compressive strength increases the most, which is the optimal content of PAF.

For the test group of SPBF, the compressive strength is higher than that of PC when the content of PBF is 0.3% ∼ 1.2%. The maximum compressive strength is 57.6 MPa when the PBF content is 0.6%. It is observed that the bar chart, when the slope of the bulk content section of 0.3% ∼ 0.6% is greater than that of the bulk content section of 0 ∼ 0.3%, the former is more effective in improving compressive strength. Therefore, when the bulk of PF is 0.6%, the improvement effect of compressive strength of concrete is the best.

For the SPCF test group, the compressive strength is obviously affected by the volume of PCF. With the increase of PCF content, the compressive strength decreases gradually. When the content reaches 0.17%, the compressive strength drops sharply. At this time, the lifting effect of fiber on concrete is almost 0. Therefore, to ensure the compressive strength of the SPFRC, the content of monofilament PF should be controlled at about 0.11%.

In summary, the improvement of compressive strength of hybrid fiber concrete is about 11%, which is slightly lower than that of pure steel fiber concrete, which is consistent with the results obtained in the literature ( He, 2002 ). However, Irrespective of the fiber type, excessive fiber content can diminish the compactness of the concrete matrix, resulting in a weakened strength enhancement effect. Therefore, it is imperative to determine the optimal fiber content to establish a solid foundation for the application of subsequent beam members.

The fitting function can further express the relationship between the two parameters, and the mechanical properties of SPFRC can be accurately characterized by a quadratic polynomial. Similar to the literature ( Dash et al., 2023 ; Lin et al., 2024 ; Xian et al., 2024b ), this paper uses the origin function plotting tool to fit the test results, and selects polynomial function and exponential function fitting forms to obtain higher fitting accuracy. Figure 4 depicts the correlation between compressive strength and fiber content in fiber concrete.

Figure 4 . Compressive strength fitting curve. (A) SF (B) SPAF (C) SPBF (D) SPCF.

3.2 Splitting tensile strength

3.2.1 failure pattern.

The failure pattern of the tensile strength test is presented in Figure 5A is the failure pattern of the PC specimen. During the loading process, a small crack first appeared near the loading point, but the appearance did not change significantly. After reaching the ultimate load, the small crack near the loading plate suddenly ran through the test block along the splitting line, and the test block split in two, showing typical brittle failure characteristics.

Figure 5 . Cube cleavage damage pattern. (A) PC (B) SF8 (C) SF12.

Taking SF8 and SF12 as examples, the damage patterns of fiber-reinforced concrete are shown in Figures 5B, C . During the loading process, in addition to the microcrack at the loading point, accompanied by the “ding ding” sound of fiber slip. When the ultimate load is reached, the small cracks at the loading point gradually spread to the middle, but unlike PC concrete, the test block is not split in half, indicating that the fiber plays a clear pulling role, showing ductile failure characteristics.

By comparing Figure 5B with Figure 5C , it can be found that the fiber content affects the failure form of the splitting tensile test. As the fiber content increases, the inhibition effect of fiber on crack development is stronger, reflecting that the crack width is smaller and smaller at the macro level, which further indicates that fiber can enhance the tensile failure mode of concrete.

3.2.2 Analysis of splitting tensile strength results

The results of the splitting tensile strength test are drawn as a bar chart, as shown in Figure 6 , and the following analysis is carried out.

Figure 6 . Splitting tensile strength of fiber reinforced concrete.

For the test group of SF, the splitting tensile strength decreased slightly when the volume content was 0.4%. This indicates that it is challenging to achieve a strengthening effect when the SF content is too low, and it can negatively impact the bond between the concrete matrix aggregate and the cementing material. With the increase of fiber content, SF gradually distributes evenly and overlaps with each other in the concrete, forming a complete network structure ( Liu et al., 2021 ), which makes the splitting tensile strength show an increasing trend. The splitting tensile strength of SF10 is 0.32 MPa higher than that of SF8, and the growth rate is 7%. Considering the economic cost factors in the project, 1.0% can be used as the best SF dosage.

Within the SPAF experimental group, a variation in fiber content ranging from 0.08% to 0.14% led to a slight improvement in mechanical properties, resulting in an overall improvement rate of 33% ∼ 40% compared to PC. Notably, at a volume content of 0.14%, the maximum splitting tensile strength reached 5.13 MPa, marking a 10.80% increase compared to the strength of concrete with SF alone. However, an increase in PAF content correlated with a decreasing trend in splitting tensile strength, exhibiting a decrease of 4.09% compared to the highest value, although this decrease was not significant. Therefore, maintaining a dosage within the range of 0.08% ∼ 0.14% can effectively achieve the goal of enhancing tensile strength.

For the SPBF experimental group, when the PBF content is 0.9%, the splitting tensile strength reaches a peak value of 5.41 MPa, which is 47% higher than that of PC splitting tensile strength, and 16.85% higher than that of SF concrete with 1.0%, indicating that the hybrid fiber can enhance the strength of concrete effectively. When the fiber content reached 1.2%, the strength began to decrease to 3.70% of the peak value. Therefore, to improve the splitting tensile strength of concrete, it is recommended that the volume content of embossed PF is 0.9%.

For the experimental group of SPCF, the splitting tensile strength is the maximum value when the volume content is 0.11%, and the minimum value when the bulk content is 0.17%, which are 5.23 MPa and 4.82 MPa, respectively. The strength ratios of the two with plain concrete are 1.43 and 1.31, respectively. As a whole, when the volume content is 0.08% ∼ 0.17%, the effect of this hybrid fiber on the splitting tensile strength of concrete is always maintained at a high level, so to improve the splitting tensile strength of concrete, the volume content should be kept in the range of 0.08% ∼ 0.14%.

In summary, hybrid fibers can improve the splitting tensile strength of concrete matrix better than single-doped SF, and the fiber combination of SPAF14, SPBF09, and SPCF11 has the most significant effect on the gain of splitting tensile strength. The fitting of splitting tensile strength and fiber content of fiber concrete is shown in Figure 7 .

Figure 7 . Split-tensile strength fitting curve. (A) SF (B) SPAF (C) SPBF (D) SPCF.

3.3 Flexural strength

3.3.1 failure pattern.

The failure pattern observed in the flexural strength test is illustrated in Figure 8 . A notable disparity exists between the bending failure modes of ordinary concrete and fiber concrete specimens. When the ordinary concrete specimen reaches its maximum load, a sudden brittle failure occurs without prior warning. The specimen instantaneously fractures into two parts from the middle at the point of failure. In the flexural test of fiber-reinforced concrete, a small crack emerges at the bottom of the span during the loading process, accompanied by a slight fiber fracture sound. With increasing load, the crack width continues to expand, and visible cracks appear on the specimen upon reaching the ultimate load. However, the specimen does not completely disconnect, as depicted in Figure 8B . Even after reaching the ultimate load, the specimen maintains partial bearing capacity with increasing vertical deflection. Upon removal of the specimen after the test, residual fibers of the fracture surface on both sides are discernible from the cracks. These observations indicate that the addition of fiber can effectively mitigate the brittle failure of concrete.

Figure 8 . Bending test failure pattern. (A)Ordinary concrete (B) Fiber reinforced concrete.

3.3.2 Analysis of bending strength results

The data obtained from the flexural test are drawn into the intuitive bar chart shown in Figure 9 , and the following analysis is carried out.

Figure 9 . Flexural strength of fiber reinforced concrete.

For the SF test group, the flexural strength increased first and then decreased when the SF content ranged from 0.4% to 1.2%. When the SF content was 1.0%, the flexural strength reached a peak of 5.98 MPa. Due to the uniform distribution of SF in concrete, the SFs located in the tension area play the role of “micro-reinforcement” ( GB/T50152-2012, 2012 ), and bear part of the load during the generation and development of cracks, limiting the development speed of cracks, and thus improving the bending and cracking resistance of concrete ( Li et al., 2024c ). When the SF content is too high, the densification reduction caused by a large number of fibers is gradually serious, weakening the gain effect, resulting in a gradual slowdown in the growth rate of flexural strength, or even a decline. The optimal SF content is 1.0%.

For the experimental group of SPAF, the increased ratio of the hybrid fiber to the bending strength of concrete is more than 15%, indicating that the mixed fiber has a better effect on the bending strength of concrete in the range of 0.08% ∼ 0.17%. When the volume content is 0.14%, the flexural strength is 6.39 MPa, which is 26% higher than that of plain concrete and 6.86% higher than that of SF concrete with 1.0% volume content. When the volume content reached 0.17%, the strengthening effect began to weaken, and the strength decreased by 7.51% compared with the highest value. Therefore, the recommended dosage range for improving the flexural strength of concrete is 0.08% ∼ 0.14%.

For the experimental group of SPBF, the flexural strength of hybrid fiber concrete showed a trend of first increasing and then slowly decreasing in the range of 0.3% ∼ 1.2% PB fiber volume. When the volume content reaches 0.6%, the bending strength reaches a peak value of 6.44 MPa, which is 1.36 MPa higher than plain concrete and 0.41 MPa higher than SF concrete. When the fiber content exceeds the optimal content, the bending strength decreases at a slow rate. When the fiber content is 1.2%, the flexural strength is reduced by 4.97% compared with the maximum value. Therefore, the optimal content of the hybrid fiber combination to improve the flexural strength of hybrid fiber concrete is 0.6%.

For the SPCF experimental group, the bending strength showed a continuous decreasing trend in the range of 0.08% ∼ 0.17. When the PCF content is 0.08%, the flexural resistance of concrete is the best, the maximum bending strength is 6.03 MPa, and the increase ratio is 19.69% compared with PC. The small diameter and low tensile strength of PCF result in easy clustering between fibers. The higher the dosage, the more noticeable this clustering becomes, which reduces the density of the matrix. To ensure that concrete maintains good bending resistance, the fiber content should be kept within the range of 0.08% ∼ 0.11%.

In summary, hybrid fibers have a good effect on improving the folding strength of the concrete matrix, among which SPBF14, SPBF06, and SPCF08 are the optimal combination of folding strength, which can provide reference for the subsequent design and calculation of beam members. The fitting of splitting tensile strength and fiber dosage of fiber concrete is displayed in Figure 10 .

Figure 10 . Flexural strength fitting curve. (A) SF (B) SPAF (C) SPBF (D) SPCF.

After a comprehensive analysis of the three mechanical properties, it is concluded that SPAF14, SPBF06, and SPCF11 are the optimal dosage combinations of SPFRC. It can provide a reference for the application of SPFRC in different components.

3.4 Microscopic analysis

3.4.1 micromorphology analysis.

Figure 11 is the microscopic map of the sample under a scanning electron microscope, and the underlying cause of the macroscopic phenomenon of SPFRC is analyzed from a microscopic perspective.

Figure 11 . Microcosmic diagram of specimen. (A) SPBF-Fiber fracture and spalling (B) SPBF-Fiber lapping (C) SPCF-Hybrid fiber combination details (D) SPCF-Fiber agglomeration (E) SF-Fiber fracture (F) SPBF-Fiber extraction.

Figure 11A demonstrates the parallel distribution of PBF and SF. After pretreatment, the surface of PBF has continuous and obviously uneven patterns, which increases the contact area and adhesion between fiber and matrix and is conducive to giving full play to the toughening and strengthening effects of fiber. The water compounds attached to the surface of the fiber in the figure confirm the feasibility and effectiveness of this type of factory treatment method. Macroscopically, the splitting tensile strength of SPBF09 is 16.8% higher than that of SF10.

Figure 11B indicates the overlapping distribution of SF and PAF. Compared with PBF fiber, under the same length-diameter ratio, the unique wavy shape has a larger surface area and significantly increases the surface adhesion, thus increasing the bonding force with the cement matrix. In the process of concrete mixing and vibration, the mutual extrusion between aggregates and fibers will cause the fibers to bend and overlap with each other in a small amplitude. The microstructure enhancement of hybrid fibers is reflected in the increase of the flexural strength of the SPAF14 group by 6.7%.

Figures 11C, D show the hybrid effect of SF and PCF. In Figure 11C , it is evident that the diameter of the PCF differs significantly from that of the SF. In Figure 11C , fibers are observed to be still wrapped in a small amount of slurry material after the specimen has been damaged. Additionally, a substantial amount of hydration product (C-S-H) is attached to the surface of PCF in Figure 11D , providing evidence of the bonding force between such fibers and concrete.

In Figure 11C , the surface of the SF is flat and has a unique brushed metal stripe. Under the electron microscope, it is apparent that there is no gap between the SF and the concrete slurry, and the tight adhesion between the two is strong, which can give full play to the advantages of high elastic modulus and high tensile strength of the SF.

Through the above microscopic graphic analysis, it can be found that SF and PF can realize the synergistic mechanism in SPFRC. This is due to the low elastic modulus, low density, and good ductility of PF, which can restrain the formation of early micro-cracks in concrete and enhance the compactness of the matrix. In addition, SF has high elastic modulus and strong tensile strength, which can play the role of skeleton support for concrete matrix, accept the stress transmitted by PF and cement slurry, and restrain the development of cracks after concrete cracking. SF and PF overlap each other to form a complex spatial structure. Under the appropriate dosage, the two kinds of fibers can complement each other and produce the positive hybrid effect.

3.4.2 Analysis of fiber energy consumption forms

In Figure 11A , the microscopic details of the SF-PAF concrete are presented. This illustration displays two distinct fiber shapes and clearly depicts the failure form of PAF. In comparison to SF, PAF exhibits a smaller elastic modulus, softer texture, and superior ductility. The bond between the fiber and concrete primarily relies on the bite force of the surface pattern. Energy consumption can be categorized into fiber fracture and fiber pulling out, based on the different positions of crack development and fiber space.

When a crack is located near one end of the fiber, the bond between the fiber and the concrete is weakened. Consequently, when the load carried by the fiber surpasses the bond force, slippage between the fiber and the concrete occurs. If the crack is larger, the fiber will be pulled out, leaving obvious grooves in the concrete, as shown in Figure 11F . When the crack appears near the middle of the fiber, both sides of the crack have sufficient contact length to bond with the concrete. At this time, the fiber itself absorbs energy to bear the load, and due to the characteristics of small elastic modulus and large ductility, the internal stress concentration part of the fiber is the first to deform. The fiber appears to shorten between diameters and increase in length until it breaks and fails beyond the tensile strength, as shown in Figure 11E , and the section shape is irregular and rough.

In addition to the above two energy consumption modes, there is an obvious groove in Figure 11A that deserves attention. This phenomenon is not formed by the fiber being pulled out, but by the fiber being located right on the fracture surface, and the fiber is completely removed from the slurry during the stress process, without participating in the process of being subjected to force. At the same time, because the fiber-slurry interface transition zone is often a weak link, the distribution of fibers here will accelerate the development of cracks.

Figure 11E shows the microscopic details of fracture patterns of SF. The shear SF used in this test is a wavy flat strip type, so it can have a larger surface area to enhance the bonding force and reduce the probability of SF slip pulling out. SF has a large elastic modulus and small fracture ductility, which can absorb a lot of energy and delay the crack development during the crack development. In addition, the fracture of SF is a sudden fracture without signs, and the cross-section of SFs is usually more regular and flat.

PCF is very small in diameter, soft, and easy to deform, and the number of fibers is far more than other types of fibers under the same volume content, so fiber clustering is easy to occur. This phenomenon prevents the slurry from entering the interior of the fiber mass, and the fiber cannot be fully mixed with the slurry, becoming a weak link in the interior of the concrete, as shown in Figure 11D , a small part of monofilament PF is pulled out as a whole. This explains the sharp decline in strength caused by high PCF fiber content in SFPC17 test group, and the weakening effect of hybrid fibers is greater than the strengthening effect. In fact, the appropriate PCF content can be evenly distributed inside the concrete. On the one hand, the porosity inside the concrete is reduced and the density is improved. On the other hand, the chaotic distribution of the fibers makes the internal stress distribution more reasonable and enhance the mechanical properties of the concrete.

In summary, surface of the SF is relatively flat, and the energy consumption is mainly pulled out, and some SF breaks after absorbing a lot of energy. PAF and PBF can avoid fiber slippage by increasing the adhesion and biting force with concrete, so it mainly consumes energy for fiber fracture. The length-diameter ratio of PCF is large, and it is packed in concrete, so the energy consumption is mainly fiber fracture and fiber pulling out.

4 Application research of SPFRC beam members

4.1 design and manufacture of test beam.

Based on the analysis results of the mechanical properties and microstructure of SPFRC in Section 3 , the beam members were fabricated by selecting the optimal content of three hybrid fiber combinations (SPAF14, SPBF06, SPCF11). The objective is to investigate the cracking and bending resistance of beams with different SPFRC dosage combinations. The test beam length l = 1,800 mm (calculated span l0 = 1,500 mm), the beam section size b × h = 150 mm × 300 mm, the longitudinal bearing longitudinal reinforcement was selected HRB400 rebar, and the vertical longitudinal reinforcement was selected HPB300 round longitudinal reinforcement. And ordinary concrete beams of the same size and reinforcement are made as a comparison. The size and reinforcement of the component are illustrated in Figure 12A .

Figure 12 . Beam loading test diagram. (A) Section and reinforcement of member (B) Loading diagram (C) The actual loading site diagram.

The components are made of steel molds, and foam glue is used to fill the gap after assembly, and a U-shaped clasp is used to limit the position of the steel mold to prevent mold expansion. Before pouring, a release agent is applied inside the steel mold to facilitate mold release. The optimal dosage is obtained in Chapter 3 of the configuration for composite pouring of the SPFRC beam, and standard cube test blocks are made for maintenance under the same conditions. Preserve the beam in a humid environment for 28d and cover it with plastic film to prevent water loss.

In this test, longitudinal reinforcement and concrete strain gauges of BMB120 type were used. Before pasting, the pasting position was smoothed and smooth and wiped with alcohol. Quick-drying adhesive is used to attach steel strain gauges and epoxy values are used to attach concrete. To ensure the stability and effectiveness of the test data, two longitudinal reinforcement strain gauges are arranged in the middle of the two tensile longitudinal reinforcement spans, denoting L1 (R1) and L2 (R2), and the attaching positions are shown in Figure 12A . Meanwhile, before loading, the concrete strain gauges are arranged in the middle of the beam spans at equal spacing along the beam height, with a spacing of 50 mm, and the distribution mode is shown in Figure 12B . The strain gauge was collected by the DH3821 data acquisition system.

4.2 Loading scheme

The flexural test use the four-point loading method with a support is 150 mm away from the beam end. The loading point is located at the third equal equinox of the effective span length l 0 , and the measuring point of the mid-span displacement and the measuring point of the support is set, as shown in Figure 12B . The hydraulic jack acts the load on the spreader beam and then transmits it to the loading point by the distribution beam. The device diagram is shown in Figure 12C .

Following the steps of the Chinese specification (GB/T 50152-2012) ( Li et al., 2023c ), pre-loading is carried out before formal loading to confirm the normal operation of test devices and measuring equipment such as components, distribution beams, and supports. During the formal loading process, each stage was loaded 5 kN and the load holding time was 3 min. The crack development was observed and marked, and the crack width was recorded and measured by the ZBL-F103 crack width meter. After the loading of each stage is completed and the measurement indicator is stable, the three displacement values and the strain values of the longitudinal reinforcement and concrete are recorded. When the load of concrete beam no longer increases and shows a downward trend, it is declared that the test beam has reached failure and the test is over. The failure pattern and crack width of the component were recorded by photographing.

4.3 Test results and analysis

Table 3 presents the cracking load (Load value of concrete beam at initial crack), ultimate load (The maximum load value that a concrete beam can achieve during loading), and mid-span deflection of the test beam. Both the cracking load and the ultimate load of SPFRC beam are more elevated than that of PC beam, and the hybrid fiber works well together to show a good “positive hybrid effect”. The ultimate load increase of the SPBF beam is the most significant, 8.82% higher than that of the SPBF beam and SPCF, and 19.35% higher than that of the PC beam. The improvement effect is obvious.

Table 3 . Statistical table of crack load, ultimate load, mid-span deflection.

4.3.1 Failure pattern

The failure pattern of the test beam and the first crack at the bottom of the mid-span beam are depicted in Figure 13 .

Figure 13 . Beam failure pattern and initial crack width. (A) PC (B) SPAF (C) SPBF (D) SPCF.

The failure patterns of the four test beams are similar, and they all belong to the bending failure of the normal section, which is in line with the design expectation. The cracking loads of the four test beams are 35, 40, 45, and 40 kN respectively, indicating that hybrid fiber concrete improves the tensile strength of the material, delays the development of cracks, and increases the cracking load. In the course of the test, the main cracks were located in the middle of the span and some surrounding areas, and the new cracks that appeared with the increase of load were axisymmetrically distributed in the middle line of the test beam, and the failure pattern was in line with the expectation on the whole. The concrete in the compression area of the PC beam is crushed when the beam is damaged. On the contrary, the concrete in the compression zone is improved to varying degrees when the hybrid fiber is added to the beam when it reaches the ultimate load.

4.3.2 Load-deflection

The displacement data of the three measuring points during the test loading process are drawn into a line chart, as shown in Figure 14 . To avoid damage to the collection equipment by the test, the displacement meter was removed after the load reached the ultimate load, so the displacement data of the load falling section was not recorded.

Figure 14 . Load-deflection and deflection change curve.

From the overall view of the figure, the mid-span deflection growth of the test beam is mainly divided into two stages. Before the tensile longitudinal reinforcement reaches yield, the deflection increases linearly and slowly. The mid-span deflection of the SPBF test beam changes the most slowly with the increase of load, and the mid-span deflection is the least under the same load. Taking the load of 150 kN as an example, the deflection of SFPB is only 25.8% of PC, which shows that the action of this hybrid fiber has a significant improvement effect on the deflection of the beam. When the load increases to a certain extent, the yield of the tensile longitudinal reinforcement and the bearing capacity of the member do not change obviously, but the mid-span deflection and crack width increase sharply. PC, SPAF, SPCF, and SPBF are listed in the order of the growth inflection point. When the member reaches the ultimate load, the mid-span deflection of the SPBF beam is 35.7 mm, and that of the PC test beam is 27.46 mm, which indicates that PBF raises the ultimate load of the concrete beam while increasing the stiffness of the member and reducing the deformation of the member.

In addition, the deflection at the yield of the longitudinal bar is measured as γ y , and the corresponding deflection at the ultimate load is recorded as γ u , The difference between γ y and γ u is denoted by ∆ γ , As can be seen from the line chart in Figure 14 , SPFRC beams are all larger than PC beams. Among them, the SPBF beam is the highest, reaching 35.7 mm, which is enhanced by 30% compared with PC and 19.6% compared with SPAF group. SPFRC beams have a larger development space for mid-span deflection and better ductility during the process from longitudinal reinforcement yielding to failure. From the microscopic analysis in Section 3.4 , it can be seen that PBF fiber has strong bonding force in concrete, and the energy dissipation effect of the beam is mainly fiber fracture. After the concrete cracking failure in the tensile zone, it can still share load with the longitudinal reinforcement, thus effectively improving the ductility of the beam.

4.3.3 Load-strain

Figure 15 shows the relationship between concrete strain and load. Through the analysis of the figure, it can be deduceed that when the load reaches 100 kN, only the last two effective strain gauges of the PC beam are still working normally, while the number of effective strain gauges of other test beams is 3, 4, and 5 respectively, indicating that the damage of PC beam is relatively serious compared with that of fiber concrete beam. In addition, the measuring points with the same cross-section height of each beam are selected as the research object, and the strain size of each beam under the same load is compared and analyzed. The corresponding strain of the measuring point 150 mm away from the bottom of the beam when the load is 80 kN is taken as an example: The strain of the PC beam is 2594.42με, SPAF beam is 1534.06με, SPBF beam is 1279.22με, and SPCF beam is 882.64με. The strain of hybrid fiber concrete beams is much smaller than that of ordinary concrete beams, which indicates that the elastic modulus and stiffness of the test beams increase and the ability to resist deformation is enhanced.

Figure 15 . Load - concrete strain. (A) PC beam (B) SPAF (C) SPBF (D) SPCF.

Figure 16 shows the relationship between reinforcement strain and load. The last set of data before the failure of the reinforcement strain gauge was selected for drawing and analysis. Among them, the R1 strain gauge in the PC group and the L1 and R1 strain gauge in the SPCF group were not included in the analysis due to the failure caused by damage.

Figure 16 . Load - Strain of reinforcement. (A) PC beam (B) SPAF (C) SPBF (D) SPCF.

As a whole, the strain rise of longitudinal reinforcements of each beam for the test can be roughly divided into three stages. In the first stage, the concrete is in the elastic stage, and the strain growth of the longitudinal reinforcements is not obvious with the load. The second stage is the stage of uniform increase of longitudinal reinforcement strain after concrete cracking, during which the tensile stress is primarily borne by the longitudinal reinforcement. The third stage begins when the longitudinal reinforcement reaches the yield strength. At this time, the cross-section of the longitudinal reinforcement becomes smaller, and load growth is not obvious, but the stress and strain at the weak position of the tensile longitudinal reinforcement increase rapidly. Soon, the longitudinal reinforcement breaks, and the deflection and cracks of the concrete develop rapidly.

The transverse comparison of the data of four test beams can analyze the improvement effect of different hybrid fibers on different levels of concrete properties. First of all, comparing the load corresponding to the turning point of the first and second stages, the index can reflect the level of concrete tensile performance, PC test beam, SPAF beam, SPBF beam, and SPCF beam are 30, 40, 50, and 40 kN respectively, which can preliminarily conclude that SPBF test beam performance is better. Secondly, the load when the tensile longitudinal reinforcement reaches the yield strength can reflect the difference in the energy absorption capacity of hybrid fiber in the process of the test load.

Beam with the lowest index is 140 kN for the PC beam, and the beam with the highest index is 170 kN for the SPBF beam, and the lifting amplitude is 21.4%. In addition, the data of each strain gauge of the load-reinforcement strain curve of the SPBF beam are less discrete, and the transition between the first and second stages is smooth, which further proves the excellent performance of SPFRC and reinforcement working together. In conclusion, the SPBF beam is the best test beam in terms of load-reinforcement strain analysis.

4.3.4 Flat section assumption

The variation of concrete strain with load is verified by the strain data collected by the concrete strain gauge arranged equidistant along the height direction in the beam span. The strain data are collected every 20 kN, and the data are drawn into line charts Figure 17 for easy analysis.

Figure 17 . Strain variation of concrete with different section heights. (A) PC beam (B) SPAF (C) SPBF (D) SPCF.

Through the analysis of the law in the figure, it can be seen that the concrete strain of each group of beams always changes linearly along the height direction before cracking, which accords with the assumption of plain section. With the increase in load, cracks at the bottom of the beam gradually rise. The strain data at the bottom of the PC beam reaches 60 kN, there is a large fluctuation, and the compression zone is basically in line with the assumption of a plain section. Under the same conditions, the SPFRC beam can still maintain a better linear relationship, and the tension zone and the compression zone are in line with the assumption of a plain section.

Consistent with the crack development in Figure 13 , most of the strain gauges of PC beams have been damaged and withdrawn from work when they are about 100 kN, and the data of SPFRC beams under the same load are still in the effective range. It shows that hybrid fibers can share part of the tensile load and alleviate the situation of stress concentration in the tensile area of concrete. Compared with PC beams, SPBF beam has a smaller compression zone height, mainly because the fiber can not only enhance the tensile strength of concrete but also improve the compressive strength of the concrete matrix, which can reduce the strain of the concrete in the compression zone to a certain extent, thereby improving the bending performance of the beam.

5 Conclusion

In this paper, the macroscopic mechanical properties and microstructure of SPFRC materials were tested, and the hybrid effect of fibers and the energy dissipation mode of fibers were analyzed. The strengthening effects of different hybrid fiber combinations on the bearing properties of beam members are also investigated. The main conclusions are as follows:

(1) In the case of single-shear SF reinforced concrete, the compressive strength and flexural strength of concrete at 1.0% are the best, which are 29.9% and 17.7% higher than PC, respectively.

(2) The mechanical properties of SPFRC are better than those of PC and single fiber concrete. The mechanical strength of hybrid fiber concrete with 1.0% SF and 0.14% PAF volume content is the highest. The compressive strength and flexural strength of hybrid fiber concrete with SF content of 1.0% and PBF volume content of 0.6% are the highest. The compressive strength and splitting tensile strength of hybrid fiber concrete with SF content of 1.0% and PCF volume content of 0.11% are the highest.

(3) Through SEM scanning, the SF surface is rough, which can increase the contact area with the concrete matrix. The surface pattern and wavy shape of PF can increase the moisture adhesion on the surface of the fiber per unit length, enhance the bonding effect, and reduce the weakening effect on compactness. In addition, the space skeleton formed by interleaving and overlapping hybrid fibers can improve the strength of concrete. In addition, the energy consumption of SF and PCF is fiber fracture and fiber pull-out, while PAF and PBF are mainly fracture energy consumption.

(4) Compared with PC beams, the initial crack load and ultimate load of SPFRC beams are significantly improved, among which SPBF beams have the most obvious increase, the ultimate load reaches 185 MPa, and the increase rate is 19.35% compared with PC beams. The SPBFRC beams have the best deformation resistance. In addition, the fiber can not only bear part of the tensile stress to delay the yield of the steel bar but also effectively improve the compressive and tensile properties of concrete.

In summary, the hybrid combination of SF with a volume content of 1.0% and embossed PF with a volume content of 0.6% can be used as the optimal scheme for mechanical properties and flexural properties of SPFRC beam members.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

JLi: Resources, Supervision, Writing–review and editing. JLu: Conceptualization, Software, Writing–original draft. LC: Data curation, Investigation, Methodology, Writing–review and editing. XF: Software, Validation, Writing–original draft. YZ: Formal Analysis, Visualization, Writing–original draft. XW: Visualization, Writing–original draft. JG: Project administration, Writing–original draft.

The author(s) declare that financial support was received for the research, authorship, and/or publication of this article. This project is financially supported by the Science and Technology Development Plan of Jilin Province (20210203178SF) and (YDZJ202302CXJD052).

Conflict of interest

Author JG was employed by Shenyang Nonferrous Metallurgy Design and Research Institute Co., LTD.

The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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Keywords: steel fiber, polypropylene fiber, hybrid fiber concrete, mechanical properties, concrete beam

Citation: Li J, Luo J, Chen L, Fan X, Zhu Y, Wang X and Guo J (2024) Research on mechanical properties of steel-polypropylene fiber concrete and application of beam structure. Front. Mater. 11:1440466. doi: 10.3389/fmats.2024.1440466

Received: 29 May 2024; Accepted: 18 July 2024; Published: 06 August 2024.

Reviewed by:

Copyright © 2024 Li, Luo, Chen, Fan, Zhu, Wang and Guo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Jingwei Luo, [email protected]

Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.

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Peer-reviewed

Research Article

On the possible use of hydraulic force to assist with building the step pyramid of saqqara

Roles Conceptualization, Data curation, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected] , [email protected]

Affiliation Paleotechnic., Paris, France

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Software, Validation, Visualization, Writing – original draft, Writing – review & editing

Affiliation Univ. Grenoble Alpes, INRAE, CNRS, IRD, Grenoble INP, IGE, Grenoble, France

Roles Conceptualization, Investigation, Methodology, Software, Visualization

Affiliation Sicame Group, Arnac-Pompadour, France

Roles Conceptualization, Investigation, Methodology, Validation, Writing – review & editing

Affiliation CEDETE—Centre d’études sur le Développement des Territoires et l’Environnement, Université d’Orléans, Orléans, France

Roles Conceptualization, Investigation, Methodology, Validation

Roles Conceptualization, Investigation, Methodology, Visualization

Affiliation AtoutsCarto, Bourges, France

Roles Methodology, Project administration

Affiliation Verilux International, Brienon-sur-Armançon, France

Roles Conceptualization, Investigation, Validation, Writing – review & editing

Roles Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation

Roles Conceptualization, Investigation, Methodology, Supervision, Validation

• Xavier Landreau, 
• Guillaume Piton, 
• Guillaume Morin, 
• Pascal Bartout, 
• Laurent Touchart, 
• Christophe Giraud, 
• Jean-Claude Barre, 
• Cyrielle Guerin, 
• Alexis Alibert, 
• Charly Lallemand

• Published: August 5, 2024
• https://doi.org/10.1371/journal.pone.0306690
• Reader Comments

The Step Pyramid of Djoser in Saqqara, Egypt, is considered the oldest of the seven monumental pyramids built about 4,500 years ago. From transdisciplinary analysis, it was discovered that a hydraulic lift may have been used to build the pyramid. Based on our mapping of the nearby watersheds, we show that one of the unexplained massive Saqqara structures, the Gisr el-Mudir enclosure, has the features of a check dam with the intent to trap sediment and water. The topography beyond the dam suggests a possible ephemeral lake west of the Djoser complex and water flow inside the ’Dry Moat’ surrounding it. In the southern section of the moat, we show that the monumental linear rock-cut structure consisting of successive, deep compartments combines the technical requirements of a water treatment facility: a settling basin, a retention basin, and a purification system. Together, the Gisr el-Mudir and the Dry Moat’s inner south section work as a unified hydraulic system that improves water quality and regulates flow for practical purposes and human needs. Finally, we identified that the Step Pyramid’s internal architecture is consistent with a hydraulic elevation mechanism never reported before. The ancient architects may have raised the stones from the pyramid centre in a volcano fashion using the sediment-free water from the Dry Moat’s south section. Ancient Egyptians are famous for their pioneering and mastery of hydraulics through canals for irrigation purposes and barges to transport huge stones. This work opens a new line of research: the use of hydraulic force to erect the massive structures built by Pharaohs.

Citation: Landreau X, Piton G, Morin G, Bartout P, Touchart L, Giraud C, et al. (2024) On the possible use of hydraulic force to assist with building the step pyramid of saqqara. PLoS ONE 19(8): e0306690. https://doi.org/10.1371/journal.pone.0306690

Editor: Joe Uziel, Israel Antiquities Authority, ISRAEL

Received: December 7, 2023; Accepted: June 22, 2024; Published: August 5, 2024

Copyright: © 2024 Landreau et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: All relevant data are within the manuscript and its Supporting Information files. The computer codes are available upon request.

Funding: The Sicame Group, The Atoutscarto Company and The Verilux Company provided support in the form of salaries for GM, CG and J-CM, respectively. The specific roles of these authors are articulated in the ‘author contributions’ section.

Competing interests: The authors have read the journal’s policy and have the following competing interests: GM, CG and J-CM are paid employees of The Sicame Group, The Atoutscarto Company and The Verilux Company, respectively. There are no patents, products in development or marketed products associated with this research to declare. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

1 Introduction

The funerary complex of King Djoser, built at Saqqara in Egypt around 2680 B.C., is considered a significant milestone in monumental architecture. It is the first to disclose two crucial innovations: a pyramid shape for the pharaoh’s grave and the exclusive use of fully dressed stones for masonry. In practice, it is also revolutionary in the ability to extract and raise stones by millions before stacking them with precision [ 1 ]. Djoser’s complex visible achievements are such that its architect, Vizier, and Great Priest of Ra, Imhotep, was deified by the New Kingdom.

The knowledge and innovations implemented in the Djoser mortuary complex profoundly influenced future developments and were widely perfected throughout the Old Kingdom’s III rd and IV th Dynasties, i . e . circa 2680–2460 B.C. These developments resulted in a substantial increase in the megaliths’ size [ 2 ], leading to pyramids of spectacular dimensions, such as those of the Meidum, Dahshur, and Giza plateaus. In less than 150 years, the average weight of the typical large stones was thus multiplied by ≈8 and went from ≈300 kg for Djoser’s pyramid to more than 2.5 tons for Chephren’s pyramid’s structural blocks [ 3 ]. For the largest lintels, the weight increases by two orders of magnitude, with several blocks of ≈50 – 100 tons for Cheops’ pyramid. On this short timeframe on the scale of human history, Egyptians carried and raised some 25 million tons of stones [ 4 ] to build seven monumental pyramids. Assuming an annual work schedule of 300 days at a rate of 10 hours/day, meaning 450,000 hours spread over less than 150 years, this requires a technical and logistical organization capable, on average, of cutting, moving, and adjusting about 50 tons of stone blocks per hour. Even if one admits that not every pyramid’s blocks are fitted with millimeter precision, the amount of work accomplished is truly remarkable. Interestingly, the pyramids later built in Egypt tended to be smaller with time and never reached the volume of the Old Kingdom’s monumental structures again.

As authentic sources from the working sphere of pyramid architects are currently lacking, no generally accepted wholistic model for pyramid construction exists yet. Although many detailed publications dedicated to pyramid-building procedures have given tangible elements [ 5 , 6 ], they usually explain more recent, better documented, but also smaller pyramids [ 7 ]. These techniques could include ramps, cranes, winches, toggle lifts, hoists, pivots, or a combination of them [ 8 – 10 ]. Studies of the pyramid’s construction sites also revealed a high level of expertise in managing the hydraulic and hydrological environment, such as utilizing waterways to deliver materials, constructing ports and locks, or setting up irrigation systems [ 11 , 12 ]. These achievements have led some scholars to refer to ancient Egypt as an ‘early hydraulic civilization [ 11 ].’ However, there is actually very little multidisciplinary analysis combining the rich archaeological findings on pyramids with other disciplines such as hydrology, hydraulics, geotechnics, paleoclimatology, or civil engineering [ 9 ]. Therefore, the topic of water force in the context of pyramid construction remains insufficiently addressed in the academic literature.

Moreover, a second question accentuates the enigma: the Pharaohs who built these pyramids are missing. Until now, neither written record nor physical evidence reports the discovery of one of the III rd and IV th Dynasties’ Pharaohs. Old Kingdom’s ‘big’ pyramids’ rooms were allegedly plundered [ 13 – 15 ] during the millennia that followed the construction of the pyramids, leaving little evidence behind [ 12 ]. The III rd and IV th Dynasties’ rooms present little or no funerary attributes, such as those observed in other high-dignitary figures’ tombs contemporary to the period [ 16 , 17 ], with no King’s remains found inside. In addition, the walls of the pyramids’ chambers do not exhibit any hieroglyphs, paintings, engravings, or drawings, which would allow us to qualify them as funerary with certainty. Despite this lack of evidence, many authors [ 18 ] still support that these rooms can be attributed to Pharaohs’ burials mainly based on royal cartouches or Kings’ names found elsewhere within the pyramid or nearby temples.

Over the recent years, Dormion & Verd’Hurt [ 19 , 20 ], Hamilton [ 21 – 24 ] or others [ 1 , 25 ] were among the first to consider possible non-funerary functions of pyramids’ internal layouts by pointing out some architectural inconsistencies and highlighting the high degree of complexity of several structures, irrelevant for a burial chamber. Their analysis provided both chambers and gallery systems with a technical dimension, emphasizing a level of engineering on the part of the ancient builders that is quite remarkable and sometimes challenges any apparent explanation. This technical level is at once reflected in the geometry of the rooms and ducts, as well as in the stonework, which includes materials selection, extraction, cutting, and then assembling with exceptional accuracy [ 20 ]. This precision involved several advanced sub-techniques, such as inter-block mortar joint realization [ 26 – 29 ] or stone polishing with flatness and roughness values that reach levels of contemporary know-how. Apart from surfaces and interfaces, the builders’ technical ability is also evident throughout sophisticated mechanical systems set up in the pyramids [ 30 ], as swivel stone flaps’ designs in the Meidum and Bent pyramids [ 21 , 24 ] or tilted portcullises found in the Bent pyramid, as well as at Giza [ 20 ]. These elements suggest that, rather than an aesthetic rendering or a funerary use for these layouts, ancient Egyptians intended technical functions for some walls, tunnels, corridors, shafts, and chambers where more straightforward existing techniques were insufficient.

In summary, the analysis of the pyramids’ construction and the investigation of their internal layouts seem to require more research to provide a wholistic explanation to their purpose. This study aims to provide a fresh look at these topics by applying an alternative, multi-disciplinary, wholistic approach. It revisits the Old Kingdom’s pyramids’ construction methodology and seeks to explain the significance of internal layouts during construction. Based on current archaeological knowledge, we demonstrate that the Saqqara’s topography and the layout of several structures are consistent with the hypothesis that a hydraulic system was used to build the pyramid. The paper is divided into three main sections that analyze the current scientific literature to address the following inquiries: (i) Was the plateau of Saqqara supplied with water? (ii) If so, how was it possibly stored and treated? and (iii) How was it used to build the pyramid? A discussion and some concluding remarks and perspectives follow.

2 The saqqara’s hydrologic network

Our study began with the postulate that the larger Cheops’ and Chephren’s pyramids of Giza plateau were the outcomes of technical progress from previous pyramids, with the Step Pyramid as a technological precursor. While many literature studies focus on the construction of Cheops’ pyramid, we found it more relevant to examine the building techniques used for the Step Pyramid first. This would provide insight into the processes used by ancient builders that were later refined in subsequent pyramids. As a first approach, we analyzed potential reasons for the specific building of King Djoser’s Complex on the Saqqara Plateau.

2.1 Water resource from the desert wadis

Although detailed measurements of the Nile flood levels have been reported since the V th Dynasty (2480 B.C.) [ 31 – 33 ], there is very little information available about the hydrology of its desert tributaries, known as ’wadis’, in ancient Egypt. Sedimentological evidence of heavy rainfalls and flash floods exists [ 31 , 34 ] but little is known beyond that.

Determining the rainfall regime that the Saqqara region experienced about 4,700 years B.P. is challenging and uncertain. Past studies demonstrated that, from about 11,000 to 5,000 B.P, during the so-called ‘Green Sahara’ period, the whole Sahara was much wetter than today, and the landscape was savannah rather than desert [ 35 , 36 ]. Around 4500–4800 years B.P. too, the Eastern Mediterranean region was wetter than it is now, despite drying up later [ 37 – 39 ]. A range of annual precipitation value of 50–150 mm/year is assumed in the following calculation to perform crude computations of water resource. It covers the range between the >150 mm/year suggested by Kuper & Kropelin [ 40 ] for the end of the Green Sahara period, before the subsequent drier period, during which rainfall decreased to <50 mm/year. The range of variability, i . e . 50 to 150 mm/yr is also consistent with the typical inter-annual rainfall variability observed in the region [ 38 ].

Then, current hydrological monitoring on Egyptian wadis located further to the north and experiencing comparable annual rainfall ( i . e ., 100–200 mm/yr) showed that only 1–3% of this mean annual precipitation was measured as runoff, i.e., surface flows [ 41 ]. This average range is hereafter used for conservative, first-order estimations of available water volume, referred hereafter to as the ‘water resource’. Note that the infrequent, most intense events can reach 50 mm of rainfall and trigger devastating flash floods where the runoff coefficients have been measured up to 30%, i . e ., one order of magnitude higher than the mean annual [ 41 – 43 ]. Note that these water resource and flash flood hydrology estimates neglect that the soils were probably richer in clay and silt just after the Green Sahara period, with several millennia of a wetter climate and savannah landscape [ 35 , 36 ], which would increase the runoff coefficient and available surface water resource in the wadis.

2.2 The Saqqara site: a plateau with a water supply

The Saqqara necropolis is located on a limestone plateau on the west bank of the Nile River, about 180 km from the Mediterranean Sea ( Fig 1 ). The entire site lies in the desert, less than two kilometers from the plateau’s edge (elevation 40–55 m ASL— Above Sea Level ), which overlooks the Nile floodplain (height ≈ 20 m ASL). Further to the west, the desert rises gently for about 20 km (hills’ top elevation ≈ 200–300 m ASL).

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

(Satellite image: Airbus Pléiades, 2021-07-02, reprinted from Airbus D&S SAS library under a CC BY license, with permission from Michael Chemouny, original copyright 2021).

https://doi.org/10.1371/journal.pone.0306690.g001

The reasons behind the construction of the Djoser complex at Saqqara remain unclear. The contribution of economic, socio-political, and religious factors was previously highlighted [ 44 , 45 ], but environmental factors were also possibly influential. In 2020, Wong provided evidence that the climate, geology, and hydrology would have influenced building choices and may have contributed to, or perhaps accelerated, the emergence of stone architecture on the Saqqara plateau [ 37 ].

From a geological standpoint, the layered structure of the limestone at Saqqara was indeed stressed as a favorable factor for excavating large amounts of construction stones [ 46 , 47 ]. These layers, which consist of 30–60 cm thick sand-rich calcareous beds alternated with calcareous clay and marl layers, made it easy to extract the limestone blocks from their parent beds by vertical cuttings, the original thickness being reflected in the building stones’ thickness of Djoser’s complex.

From a hydrological standpoint, the Abusir wadi is considered a second environmental factor that strongly influenced the Early Dynastic development of the Saqqara necropolis at least [ 45 , 48 – 50 ]. The Abusir wadi is the ephemeral stream draining the hills west of Saqqara ( Fig 1 ) . Before this study, academic research mainly focused on the downstream part of the wadi [ 45 , 48 – 50 ], namely the Abusir Lake [ 51 ] located north of Saqqara Plateau. However, the upstream portion has remained undocumented.

In order to analyze the relationships between the Abusir wadi and the Step Pyramid’s construction project, the drainage networks west of the Saqqara area were mapped for the first time to the best of our knowledge, using various satellite imagery ( Fig 1 ) and Digital Elevation Models (see S1 Fig in S2 File ).

A paleo-drainage system can be identified upstream of the Gisr el-Mudir structure as the origin of the Abusir wadi ( Fig 1 , pink line). The boundaries of this runoff system form a catchment area never reported so far, although easily recognizable from the geomorphological imprints of surface paleochannels in the desert and on historical maps [ 52 ]. Although it currently has a 15 km 2 surface area, we cannot rule out the possibility that the drainage divides shifted and changed due to land alterations and aeolian sand deposits over the past 4,500 years.

The current catchment summit is about 110 m ASL, giving the Abusir wadi a 1% average slope over its slightly more than 6 km length. In the field of hydrology, a 1% gradient is described as ‘rather steep’. With such steep slopes, transportation of sand and gravel is expected during flashfloods, which can cause severe downstream damage (scouring or burying of structures, filling of excavations and ponding areas). In comparison, irrigation channels are rather at least ten times less steep (about 0.1%), and the Nile slope is less than 0.01% (less than 200m of elevation gain between Aswan and Cairo).

2.3 The Wadi Taflah: A possible complementary water supply

Reported since the early 1800s, a former tributary to the Nile called the Bahr Bela Ma [ 53 , 54 ] or ‘ Wadi Taflah’ flowed parallel to the Abusir wadi catchment, less than two kilometers south of the Saqqara plateau. From satellite imagery, we identified that the Wadi Taflah arises from a drainage area of almost 400 km 2 and consists of three main branches ( Fig 2 , numbered black dots) still visible from the desert’s geomorphological marks. This network is also visible on the radar imagery provided by Paillou [ 55 ] that can penetrate multiple meters of sand ( S2 Fig in S2 File ). The similarity of the optical and radar drainage patterns confirms the existence and old age of this hydrological network.

https://doi.org/10.1371/journal.pone.0306690.g002

Although no canal was detected from the satellite data, the close proximity of Abusir wadi with the Wadi Taflah ( Fig 2 ) is intriguing and raises the question about a potential ancient, artificial connection between them. According to the 18 th -century maps published by Savary [ 54 ], the Wadi Taflah was ‘closed by an ancient King of Egypt.’ Such a testimony, although imprecise, could suggest the construction of a water diversion by a former ruler. A geophysical investigation could help to find such a structure if existing. The drainage area of Wadi Taflah covers nearly 400 km 2 at an elevation >58 m ASL. This elevation is high enough to allow the diversion of the drainage area toward the Abusir wadi. This would result in an increase in the drained area and associated availability of water resources by a factor of >25 times. Based on the hydrological conditions described in section 2.1, the estimated water resource from Abusir wadi and Wadi Taflah is crudely between 7,500 to 68,000 m 3 /year and 200,000 to 1,800,000 m 3 /year, respectively.

2.4 The Abusir wadi: A structural element in the early dynastic Saqqara’s development

According to the Saqqara topography ( Fig 3 ), the Abusir wadi flowed through the Gisr el-Mudir enclosure before heading north towards the Nile floodplain, where it used to feed an oxbow lake, the Abusir Lake [ 51 ]. With such a localization, the Gisr el-Mudir walls literally dam the Abusir wadi valley’s entire width. The sparse vegetation only growing in the valley bottom upstream of Gisr el-Mudir and not elsewhere in the area evidences this damming and interception of surface and subsurface flows ( Fig 4A , green line). This slight moist area is dominated by plants commonly found in desert margins and wadis, such as Panicum thurgidum and Alhagi graecorum [ 56 ], and is typical of hypodermal flows.

Contour lines extracted from the 1:5,000 topographical map [ 52 ] “Le Caire, sheet H22”.

https://doi.org/10.1371/journal.pone.0306690.g003

a. The Gisr el-Mudir check dam (Satellite image: Airbus Pléiades, 2021-07-02, reprinted from Airbus D&S SAS library under a CC BY license, with permission from Michael Chemouny, original copyright 2021); b.: Digital Elevation Model generated from the 1:5,000 topographical map “Le Caire, sheet H22”.

https://doi.org/10.1371/journal.pone.0306690.g004

Downstream of the Gisr el-Mudir, the Abusir wadi joins the Saqqara Plateau. Its boundaries are defined to the south by an outcropping limestone ridge and to the east by the Sekhemkhet and Djoser’s enclosures ( Fig 3 ).

The landform of this area seems inconsistent with a pure fluvial formation. Instead, the very flat topography on about 2–2.5 km 2 , according to the Saqqara Geophysics Survey Project (SGSP) [ 57 – 60 ] and possibly allowed some ephemeral ponding water which may have resulted in an episodic upper Abusir lake after the most intense rainfalls. However, due to the several-meter deep wind-blown and alluvial sand cover accumulated over the past millennia [ 57 ], the riverbed altitudes during Djoser’s reign are challenging to establish without further investigations, and only broad patterns can be determined from the local topography [ 52 ].

As with many other small wadis, the Early Dynastic hydrology of the Abusir wadi remains largely unknown. According to fluvial sediment analysis in the Abusir Lake area, the Abusir wadi was probably a perennial stream during the Old Kingdom period [ 51 ]. Although the climate is hot and arid nowadays, several studies support a more humid environment during the Old Kingdom [ 34 ] . Multiple strands of evidence indeed suggest that Egypt experienced considerable rainfalls around the reign of Djoser, resulting in frequent flooding and heavy runoffs on the Saqqara Plateau. This climatic feature is supported by sedimentary deposits resulting from flowing water of ‘considerable kinetic force’ contemporary to Djoser’s reign [ 61 , 62 ] . According to Trzciński et al.[ 34 ], the strongly cemented structure L3 found in the Great Trench surrounding the Djoser Complex was due to cyclical watering while the high content of Fe3+ indicates that the region experienced intensive weathering in a warm and humid environment. In 2020, Wong concluded that the ‘ intriguing possibility that the Great Trench that surrounds the Djoser complex may have been filled with water ’ during Djoser’s reign [ 37 ]. If so, this might explain why tombs were built on the northern part of the Saqqara plateau which has a higher altitude [ 45 ] and nothing was constructed inside the Trench until the reign of Userkaf and Unas (V th Dynasty).

3. The saqqara’s water management system

3.1 the gisr el-mudir check dam.

Reported at least since the 18 th century [ 63 ] and extensively described within a decade of a geophysical survey by Mathieson et al ., see also [ 45 ] for a summary, the Gisr el-Mudir is a rectangular enclosure located a few hundred meters west of the Djoser’s complex ( Fig 3 , Fig 4A & 4B ). This monumental structure has a footprint of about 360 m x 620 m, i . e ., larger than the Djoser complex (545 m x 277 m). The walls have an estimated volume of >100,000 m 3 (SGSP, 1992–1993 report), meaning about one-third of the Step Pyramid’s volume. Field inspection and geophysical results from the SGSP [ 57 ] found no construction inside except for a couple of more recent, small graves, thus confirming that the enclosure is mainly empty. Moreover, several elements in the building suggest that this structure predated the Step Pyramid’s complex and was tentatively dated to the late II nd or early III rd Dynasty [ 57 , 64 ], which might turn it into the oldest substantial stone structure in Egypt discovered so far.

Before this study, several conflicting theories about the Gisr el-Mudir’s purpose were put forward [ 59 ]: e . g ., an unfinished pyramid complex (but the lack of a central structure made it improbable to be a funerary monument), a guarded fortress [ 65 ] protecting the Saqqara necropolis from nomadic Bedouin incursions, an embankment to raise a monument to a higher level [ 66 ], a celebration arena [ 64 , 67 ], or even a cattle enclosure. However, given the low level of exploratory work afforded to the structure, no generally accepted explanation exists yet, and its purpose has remained more conjectural than substantiated.

In light of the upstream watershed and its transversal position across the Abusir River, the Gisr el-Mudir’s western wall meets the essential criteria of a check dam, i . e ., a dam intending to manage sediment and water fluxes [ 68 , 69 ]. This comparison is particularly striking regarding its cross-section ( Fig 5 ). According to Mathieson et al . [ 59 ], the basic structure of this wall consists of a hollow construction of two rough-hewn limestone masonry skin-walls, ≈3.2 m high, separated by a 15 m interspace filled with three layers of materials extracted from the surrounding desert bedrock [ 70 ] and cunningly arranged. The first layer ( Fig 5 , ‘ A ’ dot) is made of roughly laid local limestone blocks forming a buttress against the inside of the facing blocks. The secondary fill ( B ) comprises coarse sand and medium to large limestone fragments. Then, the third fill ( C ) consists of rough to fine sand and silt, small limestone fragments, and chippings with pebble and flint nodules. Finally, these A, B, and C backfill layers are positioned symmetrically to the median axis of the wall.

Figure adapted from [ 58 ].

https://doi.org/10.1371/journal.pone.0306690.g005

Civil engineering was used during the Old Kingdom to protect settlements from flash floods, such as the Heit el-Ghurab (’Wall of the Crow’) safeguarding the village of the pyramid builders at Giza [ 71 ]. Regarding the Gisr el-Mudir structure, the abovementioned elements strikingly echo the transversal profile and slope protection of another famous Old Kingdom structure: the Sadd el-Kafara dam built on the Wadi al-Garawi , a colossal building found to be contemporary to that of the Gisr el-Mudir [ 72 – 74 ]. Both structures present the technical signature of zoned earthen dams: a wide embankment made of a central impervious core surrounded by transition filters, i . e ., filling material with coarser grain size, preventing erosion, migration, and potential piping of the core fine material due to seepage. The semi-dressed limestone walls stabilized the inner material and protected it against erosion when water flowed against and above the dam. Both dams have much broader profiles than modern dams. This oversizing could be due to the unavailability of contemporary compaction systems or an empirical and conservative structural design. They both have narrower cores of fine material at the bottom of the dam than at their crest, contradicting modern design [ 75 ]. This can be attributed to the construction phasing that would have started by raising the sidewalls buttressed against the coarse and intermediate filling ( B and C fills in Fig 5 ), followed by a phase of filling the wide core with finer, compacted material [ 72 ].

Finally, the eastern wall’s north-south profile ( Fig 6 , line A-B ) presents a parabolic profile relevant to guide the flows to the basin’s center formed by Gisr el-Mudir. This guidance would have prevented the dam failure by outflanking during flooding events when the dam outlet was saturated. We estimate that the accumulated water crossed the dam through an outlet likely located at the valley’s lowest elevation, i . e ., near 48.7 m ASL ( G1 in Figs 4B and Fig 6 ). In summary, the Gisr el-Mudir’s western wall likely acted as a first check dam to the Abusir wadi flows.

https://doi.org/10.1371/journal.pone.0306690.g006

The excavations performed on the eastern wall of the Gisr el-Mudir highlighted a lower structural quality [ 45 ]. Its shape is similar to that of the western wall, with a distinctive parabolic profile ( Fig 6 , line C-D ). Furthermore, it discloses two topographical singularities: first, its overall altitude is a few meters lower than the western wall ( Fig 7A ). Then, in the southern part of the eastern wall, a geophysics anomaly ( G2 in Figs 4B and Fig 6 ) was found to be a series of massive, roughly cut, ‘L’-shaped megaliths [ 45 , 66 ]. Before our study, these megaliths were thought to possibly be the remains of a monumental gateway–due to their similarities with the Djoser’s complex enclosure’s entrance–but their purpose was not specified [ 66 ]. According to our analysis, these megaliths could be the side elements of the water outlets, possibly slit openings [ 76 ] that were likely closed off by wood beams but could be opened to drain the basin. They are consistently found near a trench that is 2.2 m deep [ 45 ], which we believe is possibly the canal that guided outflowing water. In a nutshell, the eastern wall likely acted as a second check dam to the Abusir flows.

a. West-east elevation profile of the Gisr el-Mudir structure. b: Schematic reconstitution of the profile with water flow.

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In addition to the two dams formed by the western and eastern walls, the Gisr el-Mudir enclosure forms a basin ( Fig 4 ). It is closed to the north by another wall made of limestone blocks, though not very tall (likely <2m) because it is built on a natural ridge [ 45 ]. The basin’s southern boundary is also mostly made of a natural ridge. The possible absence of a masonry wall on certain portions on this side was unexplained by previous analyses [ 45 ]. However, it makes perfect sense when considering a reservoir function. Anchoring dams against side slopes is indeed the standard approach to guide flows and prevent outflanking [ 68 ].

In essence, the Gisr el-Mudir enclosure exhibits the defining features of a check dam ( Fig 7B ). The catchment it intercepts is large enough (15 km 2 ), plus eventual water derivation from the Wadi Taflah to produce flash floods transporting significant amounts of gravel, sand, mud, and debris due to its slope during intense rainfalls. The valley upstream of the western wall likely served as a first reservoir where the coarsest gravels tended to deposit. The overflowing water then filled the inner basin of the Gisr el-Mudir, where coarse sand would again deposit. Assuming a storage depth between 1 and 2 meters, the retention capacity of the basin would be approximately 220,000–440,000 m 3 . This volume is in line with the overall water volume of a flash flood that could be produced by the Abusir wadi, which is estimated to be about 75,000–225,000 m 3 , assuming 50 mm of rainfall and a 0.30 runoff coefficient. This key, first structure of the Saqqara hydraulic system would have then delivered clear water downstream in normal time, as well as muddy water with an eventually suspended load of fine sand and clay during rainfall events.

3.2 The deep Trench’s water treatment system

3.2.1 general configuration..

The Djoser’s Complex is surrounded by a vast excavation area, commonly referred to as the ’Dry Moat’ since Swelim spotted its outlines [ 77 , 78 ] ( Fig 3 , blue strip). The Dry Moat is alleged to be a continuous trench cut in the bedrock, up to 50 m wide and ≈3 km long, enclosing an area of ≈600 m by ≈750 m around the Djoser complex [ 77 , 79 , 80 ]. When considering an average depth of 20 m for the four sides of the trench [ 61 ], the total excavated volume is estimated at ≈3.5 Mm 3 , approximately ten times the Step Pyramid‘s volume. Due to the thick cover of sand and debris [ 61 ] accumulated over the past millennia, its precise geometry is incompletely characterized. The moat’s east and south channels are particularly debated [ 61 ].

According to Swelim, the moat’s south channel probably split into two parts, known as the Inner and Outer south channels [ 78 ] ( Fig 8 , blue strips). The Inner south channel is relatively shallow (5–7 m deep), 25–30 m wide, and spans approximately 350 m parallel to the southern wall of Djoser’s complex.

Water from the Abusir Lake can follow two parallel circuits.

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The ‘Deep Trench’ [ 81 ] ( Fig 8 , red rectangles and dotted lines) is built inside the Inner south channel, along its south wall. It is a ≈27 m-deep, 3 m-wide, and hundreds of meter-long rock-cut channel with several ‘compartments’. So far, only about 240 m [ 78 ] of its probable 410 m length have been subject to archaeological excavations in 1937–1938 [ 78 ], 1937–1945 [ 81 ], and 1975 [ 82 ]. Consequently, approximately 170 m remains unexplored, mainly due to the presence of the later Old Kingdom two groups of mastabas built above the trench and at risk of collapse if submitted to underground excavation (transparent grey parts in Fig 8 ).

Generally, two leading theories are highlighted in the literature to explain the purpose of the trench: (i) a quarry for the Djoser’s complex [ 47 , 83 ], or (ii) a spiritual function [ 78 , 84 , 85 ]. However, over recent years, authors have pointed out several specificities in the trench’s architectural layout, which seem irrelevant in a religious or mining context [ 1 , 86 , 87 ]. In particular, on the mining aspect, several authors estimate [ 45 , 86 ] that the form of the track suggests that the extraction of stones was not its sole or even primary function, as it does not match with the ancient Egyptian quarrying methods. Reader also considers that some parts of the trench which are ~27 m deep and covered with a rocky ceiling, are wholly unrealistic for quarrying operations and unlikely to have required the paving found near the trench’s bottom [ 45 ]. This point is further emphasized by the narrow width of the excavated Deep Trench (3m), which is impractical in a mining scenario.

On the spiritual aspect, Kuraszkiewicz suggests that the trench may have developed a ritual significance as a gathering place for the souls of the nobles to serve the dead King [ 86 ]. Monnier [ 1 ] considers that the discovery of several niches in the channel does not fully demonstrate the moat’s religious purpose and considers it secondary. The trench’s ritual significance is also regarded as secondary by Reader [ 45 ], who suggests the ritual aspects developed only after the complex’s construction and do not reflect the original function of the structure.

In 2020, based on the archaeological, geological, and climatic evidence, Wong was the first to introduce the idea that the trench may have had a completely different function, being filled with runoff water following downpours [ 37 ]. If so, this would explain why it was not until the reigns of Unas and Userkaf (V th Dynasty) that new graves occupied the moat. The onset of drier climatic conditions [ 31 , 88 ] around the end of the IV th Dynasty would have created more favorable conditions for new constructions inside the moat. Despite the potential impact of Wong’s assumption, it did not receive much attention in the literature. Nonetheless, the current authors believe that Wong’s conclusions make sense when considering Saqqara’s downstream localization of a watershed.

3.2.2 The deep Trench: A series of rock-cut compartments built in a hydrological corridor.

The Inner south channel and the Deep Trench are built inside the Unas Valley, a hydrological corridor connecting the Abusir wadi plain to the Nile floodplain ( Fig 3 ). Both were thus possibly submitted to (un)controlled flooding [ 34 , 61 ] from the Abusir wadi plain.

The Deep Trench connects at least three massive subterranean compartments [ 45 , 47 ] ( Fig 8 , red parts) meticulously carved out with precisely cut surfaces [ 78 ] ( Fig 9 ) and joined by a tunnel [ 77 ] . A fourth compartment, retroactively named compartment-0 ( Fig 10 ), likely exists [ 45 , 78 ]. On a large scale, the perfect geometric alignment of these compartments is remarkable, as well as their parallelism with the Djoser’s complex and their bottom level similar to those of the southern and northern shafts (≈27 m ASL). These spatial relationships have led some authors to consider that the trench was created as a part of Djoser’s Complex [ 86 , 89 , 90 ]. This assumption has been reinforced by Deslandes’ discoveries of at least two east-west pipes, about 80 m long, connecting the Djoser’s Complex’s subterranean layouts to the Dry Moat’s eastern side [ 91 ].

a: View from the west; b: View from the east. The workers in the background provide a sense of the structure’s immense scale and technicity.

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View of the south face.

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Taken together, the Deep Trench architecture highlights technical proficiency and suggests that the ancient Egyptians intended a technical function rather than a spiritual one. Surprisingly, despite the available clues, the Deep Trench has never undergone detailed engineering studies to analyze its features and identify its purpose. The following sections suggest a hydraulic rationale behind the trench’s internal layout (more details in the Supplement ).

3.2.3 Consistency of the Deep Trench architecture with a water treatment system.

Being largely described in the literature [ 77 , 86 , 92 ] , the compartments’ layouts are presented in detail in the Supplement . Considering its architecture and geographical location, the Dry Moat’s southern section combines the technical requirements of a water treatment system, including sedimentation, retention, and purification. Fig 10 illustrates a comprehensive outline of the installation’s functioning process. Similarly to the Gisr el-Mudir, we found that the Deep Trench compartments likely served to transfer water with low suspended sediment concentration to the downstream compartments by overflowing. The process of using a series of connected tanks to filter water and remove sediment is an ancient technique that has been extensively documented in archaeological and scientific literature [ 93 – 96 ]. This method has been employed for centuries to clean water and has played a significant role in the development of water treatment practices.

Compartment-0 presents the minimum requirements of a settling basin (considerable length and width, low entry slope, position at the entry of Unas hydrological corridor) whose purpose is to facilitate the coarse particles’ settling that would overflow from Gisr el-Mudir during heavy rainfalls. The descending ramp along the south wall identified by Swelim [ 97 ] may have permitted workers to dredge the basin and remove the accumulated sediments along the east wall ( Fig 10 ) . The very probable connection [ 45 , 97 ] between compartment-0 and compartment-1, blocked with rough masonry ( Fig 9B and S3 Fig in S2 File ), is consistent with an outlet overflowing structure. Additionally, when the flow rate in compartment-0 was too high, the tunnel or even the northern portion of the trench may have been used as a spillway bypass to evacuate excess water toward the eastern portion of the Unas wadi valley ( Fig 8 , safety circuit).

Compartment-1 is then consistent with a retention basin with > 3000 m 3 capacity ( Fig 10 , left part). The bottom stone paving with mortar joints probably limited water seepage through the bedrock. Its eastern end could go until the compartment-2 [ 45 ] to form a single compartment, but this point remains debated [ 78 , 97 ] .

Compartment-2’s is, unfortunately, largely unexplored ( Fig 10 ). Its downstream position might indicate a second retention basin or possibly an extension [ 45 ] of the first one. The western part of this compartment (stairs area) perfectly aligns with the base levels of the Djoser’s complex south and north shafts, which points towards a connection between the three [ 86 ] . If so, it would be aligned with the recently discovered pipe of a 200 m-long tunnel linking the bottom of Djoser’s Complex’s southern and northern shafts [ 91 ] (see next section, Fig 11 ). Compartment-2 would then be another, or an extended, retention basin equipped with a water outlet toward the north.

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Compartment-3 ( Fig 10 , right part) is likely a side purification basin for drinking water. Its position as an appendix of the primary water circuit connecting Gisr el-Mudir to Djoser’s complex seems optimal to minimize water circulation and maximize water-settling time, thus increasing its purification. The second and third sections likely allowed further settling of particles and would have served as reservoirs during dry periods. The relatively smooth walls of the whole structure would have hindered the growth of microbes, plants, and other contaminants, thereby helping maintain the water’s cleanliness [ 98 ] . Four surface wells allowed access to the end of the last compartment where the water, kept clear and fresh in the shadow of this subterranean monumental cistern, could be used by the building site workforce [ 99 ] .

The excavated volume of the Deep Trench is greater than 14,000 m 3 [ 77 , 86 , 92 ]. If we assume that most of the water available in the Wadi Taflah was diverted toward Saqqara, this volume could be filled about a dozen to more than one hundred times per year on average. We hypothesize a typical filling level of 45 m ASL in the Deep Trench, but an accurate topographical survey is lacking, and the maximum water level could vary between 40–52 m ASL, according to the surrounding terrain elevation.

In essence, we discovered and highlighted for the first time that the Deep Trench’s position and design are consistent with possible use as a water treatment and storage system capable of cleaning and storing thousands of cubic meters of water.

4. The central hydraulic lift system

4.1 overview of the djoser’s complex’ substructure.

The internal and external architecture of the Djoser’s Complex is thoroughly documented [ 1 , 3 , 100 , 101 ]. The Supplement provides an overview of this structure. Basically, the six-step Step Pyramid itself stands slightly off-center in a rectangular enclosure toward the south and reaches a height of approximately 60 m ( Fig 11 ). The pyramid consists of more than 2.3 million limestone blocks, each weighing, on average [ 2 ], 300 kg, resulting in a total estimated weight of 0.69 million tons and a volume of ≈330,400 m 3 .

The substructure features at least 13 shafts, including two significantly sizeable twin shafts located at the north and south of the complex ( Fig 11 , insets 3&4), and an extensive and well-organized network of galleries descending up to 45 m below ground level [ 102 ]. The north shaft is surrounded by four comb-shaped structures distributed on each side and angled 90° apart. Ground Penetrating Radar (GPR) revealed that the twin shaft layouts are connected [ 91 , 102 ] by a 200 m-long tunnel. Moreover, at least two of the twelve shafts on the pyramid’s east side are connected to the supposed eastern section of the Dry Moat by two 80 m long pipes ( Fig 11 and Supplement ).

From our 3D models, we estimate that ancient architects extracted more than 30,000 tons of limestone from the bedrock to dig the whole underground structure. The total length of the tunnels and subterranean rooms combined is ~6.8 km. However, its layout and purpose remain primarily poorly known and debated [ 6 ].

4.2 The connected twin shafts

The ‘north shaft’ is located under the pyramid of Djoser and is almost aligned with its summit. This shaft is ≈28 m deep and has a square shape with 7 m sides. Its bottom part widens to ≈10 m on the last, deepest 6 m, forming a chamber ( Fig 12 and S6 Fig in S2 File ). On its upper part, the shaft extends above the ground level by at least four meters inside the Step Pyramid in the shape of a hemispherical vault that was recently reinforced ( Fig 11 , inset 5 ). This upper part inside the pyramid body remains unexplored. However, as noticed by Lauer, the shaft sides above ground level display comparable masonry to that of the southern shaft, indicating a possible upward extension [ 3 ]. On the pyramid’s north side, a steep trench with stairs provides access to the shaft.

a.: Granite box of Djoser’s complex north shaft serving as an opening-closing system for the water flow coming from side tunnels -source: [ 113 ]. b.: Limestone piles supporting the box - source: [ 3 ]. c: Diagram of the North Shaft plug system. Redrawn from Lauer sketches [ 108 ].

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The ‘south shaft’ is located ~200 m south of the north shaft, close to the Deep Trench ( Fig 11 , inset 1 ). Its dimensions and internal layout are broadly similar to the north shaft’s. The substructure of the south shaft is entered through a west-facing tunnel-like corridor with a staircase that descends about 30 m before opening up inside the shaft. The staircase then continues east and leads to a network of galleries whose layout imitates the blue chambers below the Step Pyramid. As mentioned earlier, a 200 m-long tunnel connects the lower part of the north and south shafts ( Fig 11 , orange pipe). A series of deep niches located on the south face of the south shaft [ 97 ], the shape of which resembles that of the Deep Trench’s compartments 1 and 2, might indicate a former connection between both. This point remains to be confirmed by additional investigation.

The south shaft is connected to a rectangular shaft to the west via a tunnel-like corridor with a staircase that descends approximately 30 meters before opening up into the south shaft ( Fig 11 , inset 2 ). At the corridor level, a chamber has been cut into the bedrock parallel to the descending passage [ 3 ], towards the south. This chamber features several incompletely excavated niches on its south wall, which could extend under the south wall of the Djoser complex ( Fig 8 ). Pending further excavations, they might indicate a connection with the Deep Trench.

4.3 The twin shafts’ internal layout: two plug-systems topped with maneuvering chambers

The initial purpose of the twin shafts’ granite boxes has been largely debated [ 15 , 100 ]. The presence of two shafts with two similar granite boxes and almost identical substructures was previously explained as a separation of the body and spirit of Djoser [ 100 ]. However, the Pharaoh’s body is actually missing and was not found during modern excavations. Several authors and explorers excluded the possibility of King Djoser’s burial in the north shaft [ 15 , 103 ]. Vyse claimed [ 15 ] that the box’s internal volume was too narrow for moving a coffin without breaking the body. Firth and Quibell considered [ 103 ] the fragments found by Gunn and Lauer [ 104 ] to be of mummies of ‘late date’, possibly belonging to the Middle or New Kingdom. Finally, a thorough radiocarbon dating [ 105 ] on almost all retrieved remains [ 104 , 106 , 107 ] located near the granite box excluded the possibility that ‘ even a single one of them ’[ 105 ] could have belonged to King Djoser. Therefore, although the northern shaft had clear funerary significance much later, its original purpose during the time of Djoser may have been different.

Unfortunately, the main part of the materials that filled the twin shafts was removed during past archaeological excavations, mainly in the 1930s [ 108 ], leaving only the two granite boxes at their bottom ( Fig 11 , insets 3 and 4 ). Therefore, the shafts’ internal layout description is mainly based on the explorers’ archaeological reports and testimonies[ 109 – 111 ].

The two granite boxes are broadly similar in shape and dimensions. Both are made of four layers of granite blocks and present top orifices closed by plugs that weigh several tons ( Fig 12A ). The southern box is slightly smaller, with a plug made of several pieces, making it less versatile. The north box does not lay directly on the underlying bedrock but is perched on several piles of limestone blocks supporting the lower granite beams ( Fig 12B ), tentatively attributed to robbers by Lauer [ 3 ]. The space around the box is connected with four tunnels arranged perpendicularly on each side of the shaft (see Supplement ). This space was filled with several successive layers [ 108 ] ( Fig 12C , grey parts). The lowermost layer consisted of coarse fragments of limestone waste and alabaster, making it permeable. Meanwhile, the upper layer, going up to the box ceiling’s level, was made of limestone jointed with clay mortar [ 108 ], i . e ., less permeable [ 112 ]. This ceiling was itself covered by a 1.50 m thick layer of alabaster and limestone fragments plus overlying filling ( Fig 12C , blue part), except around the plug hole, which was encircled by a diorite lining, a particularly solid rock ( Fig 12C , green part).

Directly above the granite boxes were ‘maneuvering chambers [ 108 ]’ that enabled the plug to be lifted. The plug closing the north shaft’s box has four vertical side grooves, 15 cm in diameter, intended for lifting ropes ( Fig 12C ) and a horizontal one, possibly for sealing. Below the chamber ceiling and just above the orifice, an unsheathed wooden beam was anchored in the east and west walls ( Fig 12C ). This beam likely supported ropes to lift the plug, similar to those found in the south shaft with friction traces [ 108 ].

Interestingly, the granite stones forming the granite box ceiling were bounded by mortar ( Fig 12A ), creating an impermeable barrier with the shaft’s lower part and leaving the plug’s hole as the only possible connection between the shaft and the inside of the box. Conversely, most joints between the box’s side and bottom stones, connected with the permeable bottom layer, were free from mortar.

These details, thoroughly documented during Lauer’s excavation [ 3 , 108 ] and visible on pictures ( Fig 12A and 12B ), clearly point to technical rather than symbolic application. Taken together, the granite box’s architecture and its removable plug surrounded by limestone clay-bound blocks present the technical signature of a water outlet mechanism.

When opened, such a plug system would have allowed the north shaft to be filled with water from the Deep Trench or, in another scenario, from the Dry Moat’s eastern section. The permeable surrounding filling would have permitted water discharge control from the four side tunnels. Then, the water could only seep through the granite box’s lower joints. This design would have prevented water from rushing through the system at high speed and with pressure shocks.

Considering water coming from the Deep Trench (elevation delta: 10–20 m), the retaining walls and the many layers’ cumulated weight stacked over the granite box acted as a lateral blockage and would have prevented the box ceiling from being lifted due to the underlying water pressure.

4.4 Consistency of the internal architecture of the Djoser’s complex with a hydraulic lift mechanism

After gathering all the elements of this study, we deduce that the northern shaft’s layout is consistent with a hydraulic lift mechanism to transport materials and build the pyramid. Elements at our disposal indicate that the south and north shafts could be filled with water from the Dry Moat. A massive float inside the north shaft could then raise stones, allowing the pyramid’s construction from its center in a ‘volcano’ fashion ( Fig 13 ).

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Although a connection between the Compartment -2 and the Djoser shafts has yet to be identified, it is highly probable that sediment-free water from the Deep Trench was used in this system ( Fig 13 , disk ‘ 1 ’). This water quality would have reduced the risk of fouling and malfunction because it minimizes the presence of sand and clay that feed into the north shaft. This would prevent the deposition and progressive filling in the tunnels and connections, as well as the clogging of the joints between the bottom and side granite blocks of the box. The 200 m-long underground pipe [ 91 ] that connects the north and south shafts is then consistent with the transfer of water from the Deep Trench’s water treatment system to the north shaft, possibly via the south shaft.

Furthermore, there is a proven connection between the tunnels surrounding the north shaft and the Dry Moat through the Deslandes’ pipes [ 91 ] on the eastern side of the complex ( Figs 11 and 13 ). Pending further investigation, we hypothesize that the water inlet was located to the south ( Fig 13 , disk ‘ 1 ’), with the outlet(s) sending water toward the east through two juxtaposed pipes (disk ‘ 2 ’). Several horizontal galleries connected to these two pipes were acacia-cased [ 3 ], a technique commonly used to safeguard the walls in hydraulic works in ancient Egypt. A large stone portcullis [ 108 ] found in one of these galleries may have served as a versatile gate closed during the water filling of the north shaft.

In another scenario, the Deslandes’ juxtaposed pipes ( Fig 13 , disk ‘ 2 ’) could be considered as a water inlet for unfiltered water.

Finally, we hypothesize that a hydraulic lift, a massive float that was possibly made of wood and weighed several tons (see Supplement ), should run slowly inside the shaft to prevent instabilities and friction with the sides. The stones could have been elevated by filling and emptying cycles, allowing the lift to move up and down with stones ( Fig 13 ). These stones could have passed along the northern entrance until the central shaft. Recent discoveries have shown that this gallery was kept open until the very end of the pyramid’s construction, after which it was closed [ 1 , 91 ]. In our scenario, the stones could have been transported directly at ground level, corresponding to the pyramid’s first course, or slightly higher through a ramp penetrating in a (currently sealed) corridor some meters above the ground level. This configuration would have had the particular advantage of minimizing the elevation gain for which the hydraulic lift would be required. The stones could have been transported via the so-called ‘Saite gallery [ 114 ]’ in a final scenario. Although Firth [ 114 ] considers this gallery to postdate the III rd Dynasty, it remains possible that it was recut on the basis of an earlier gallery.

4.5 Modelling the hydraulic lift mechanism

We developed a simple numerical model of the hydraulic lift to study its water consumption and loading capacity (see Supplement ). The model was kept as simple as possible to be easily checked and only intended to give relevant orders of magnitudes.

The hydraulic lift is modelled as a float loaded with stones to build the pyramid and with a vertical extension to raise this material at the necessary level. Based on the initial altitude of the lift, Z m , which cannot be below 17m from ground level (the bottom of the shaft was filled with the box and overlying rocks, see Fig 12C ), and assuming a loading of the material on the lift at the ground level, the maximum height that can be reached in one cycle is <17m. To achieve greater heights, we hypothesize that the lift platform was blocked during the float descent, e . g ., using beams (see Fig 14 ). This modification would have allowed the platform to reach higher altitudes by adding or unfolding an extension. For the top of the pyramid, the float could be conversely used as a counterweight when descending, pulling on ropes that would haul the platform after passing over pulleys above the shaft head. A dual-use method involving hauling during shaft draining and elevating during water filling would have been the optimal management approach.

The lift platform (red line), and extension support (orange line) during the unfolding of the lower element are represented. The associated holes are to be localized in further excavation of the upper part of the shaft.

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The beginning of the pyramid building was most probably performed using ramps prolonging the path from the local quarry, possibly the Dry Moat [ 44 ]. To provide an upper bound of water consumption, we modelled the pyramid building using the hydraulic lift from the first layer at ground level. Our model suggests that this upper bound value is 18 Mm 3 of water required to build the whole pyramid using the float to lift stones only when the shaft is filled (see Supplement ). A few million were required to build the first 20 m and could be saved if ramps were used instead. The total amount of water needed would have been reduced by about one-third if the float had been used as a counterweight, pulling on ropes to haul stones on a platform suspended in the top part of the shaft rather than being located on a wooden frame extension attached to the float. Finally, if both lifting (when filling the shaft) and hauling (when draining the shaft) were used, the water consumption would decrease by two-thirds. If the loading was not performed at ground level but rather through a ramp and gallery above ground level, about one-quarter of the water would be saved if, for instance, using a 5 m-high ramp and 43% for a 10 m-high ramp. Further investigation above the vault and on the pyramid sides could help to identify such an eventual gallery. If, conversely, the loading was performed about 13 m below ground level in the top part of the northern gallery ( S6 Fig in S2 File ), the water consumption would typically increase by two-thirds.

On the other hand, through our research and calculations, we have determined that the Wadi Taflah catchment had the capacity to supply 4–54 Mm 3 over 20–30 years of construction, therefore not enough when assuming only pessimistic values (lower bound for rainfall and runoff coefficient, fast construction and sub-optimal use of the lift just using it when water rose), but sufficient when assuming intermediate values, and eight-times enough water to meet this demand when assuming optimistic values (upper bounds of parameters and dual lifting-hauling functioning). If further research demonstrates that the higher clay and silt content possibly present at that time shortly after the Green Sahara period probably led to increased runoff coefficients by a factor of 2–3 or even more, the resource would be increased by the same factor.

The climatological conditions on the Saqqara plateau during the III rd Dynasty are still not well understood [ 37 ]. As a first assumption, we estimate that the water supply may have been continuous even without an upper Abusir lake’s permanent existence, thanks to the flow from the wadi Abusir and, more significantly, through a probable derivation system from the nearby Wadi Taflah, assuming this large catchment had a more perennial runoff regime. Pedological investigations would be worthwhile in the plateau area and in the talweg of both wadis to look for evidence of more frequent water flow.

As a result, the hydraulic mechanism may have only been usable when sufficient water supply was available, so it may have only been used periodically. Other techniques, such as ramps and levees, were likely used to bring the stones from the quarries and adjust their positions around the lifting mechanism or when it was not in operation.

5. Discussion

A unified hydraulic system.

Based on a transdisciplinary analysis, this study provides for the first time an explanation of the function and building process of several colossal structures found at the Saqqara site. It is unique in that it aligns with the research results previously published in the scientific literature in several research areas: hydrology, geology, geotechnics, geophysics, and archaeology. In summary, the results show that the Gisr el-Mudir enclosure has the feature of a check dam intended to trap sediment and water, while the Deep Trench combines the technical requirements of a water treatment facility to remove sediments and turbidity. Together, these two structures form a unified hydraulic system that enhances water purity and regulates flow for practical uses and vital needs. Among the possible uses, our analysis shows that this sediment-free water could be used to build the pyramid by a hydraulic elevator system.

By its scale and level of engineering, this work is so significant that it seems beyond just building the Step Pyramid. The architects’ geographical choices reflect their foresight in meeting various civil needs, making the Saqqara site suitable for settling down and engaging in sedentary activities, such as agriculture, with access to water resources and shelter from extreme weather conditions. This included ensuring adequate water quality and quantity for both consumption and irrigation purposes and for transportation, navigation, or construction. Additionally, after its construction, the moat may have represented a major defensive asset, particularly if filled with water, ensuring the security of the Saqqara complex [ 115 ].

The hydraulic lift mechanism seems to be revolutionary for building stone structures and finds no parallel in our civilization. This technology showcases excellent energy management and efficient logistics, which may have provided significant construction opportunities while reducing the need for human labor. Furthermore, it raises the question of whether the other Old Kingdom pyramids, besides the Step Pyramid, were constructed using similar, potentially upgraded processes, a point deserving further investigation.

Overall, the hydraulic lift could have been a complementary construction technique to those in the literature for the Old Kingdom [ 8 , 10 ]. Indeed, it is unlikely that a single, exclusive building technique was used by the ancient architects but that a variety of methods were employed in order to adapt to the various constraints or unforeseen circumstances of a civil engineering site, such as a dry spell. Therefore, the beginning of the pyramid building was most probably performed using ramps prolonging the path from the local quarry. According to petrographic studies [ 47 ], the main limestone quarry of the Saqqara site could correspond to the Dry Moat that encircles the Djoser Complex, providing access on the four sides of the pyramid for the extracted blocks and reducing the average length of the ramps.

An advanced technical and technological level

By their technical level and sheer scale, the Saqqara engineering projects are truly impressive. When considering the technical implications of constructing a dam, water treatment facility, and lift, it is clear that such work results from a long-standing technical tradition. Beyond the technical aspects, it reflects modernity through the interactions between various professions and expertise. Even though basic knowledge in the hydraulics field existed during the early Dynastic period, this work seems to exceed the technical accomplishments mentioned in the literature of that time, like the Foggaras or smaller dams. Moreover, the designs of these technologies, such as the Gisr el-Mudir check-dam, indicate that well-considered choices were made in anticipation of their construction. They suggest that the ancient architects had some empirical and theoretical understanding of the phenomena occurring within these structures.

…questioning the historical line

The level of technological advancement displayed in Saqqara also raises questions about its place in history. When these structures were built remains the priority question to answer . Were all the observed technologies developed during the time of Djoser, or were they present even earlier? Without absolute dating of these works, it is essential to approach their attribution and construction period with caution. Because of the significant range of techniques used to build the Gisr el-Mudir, Reader estimates [ 70 ] that the enclosure may have been a long-term project developed and maintained over several subsequent reigns, a point also supported by the current authors. The water treatment facility follows a similar pattern, with the neatly cut stones being covered and filled with rougher later masonry. Finally, the Djoser Step Pyramid also presents a superposition of perfectly cut stones, sometimes arranged without joints with great precision and covered by other rougher and angular stones [ 3 ]. Some of these elements led some authors [ 6 , 100 ] to claim that Djoser’s pyramid had reused a pre-existing structure.

Some remaining questions

The Deep Trench was intentionally sealed off at some point in history, as evidenced by the pipe blockage between Compartment-0 and Compartment-1. The reasons are unknown and speculative, ranging from a desire to construct buildings (such as the Khenut, Nebet, or Kairer mastabas) above the trench to a technical malfunction or shutdown due to a water shortage. This sealing might also have been done for other cultural or religious purposes.

The current topography of the land around the Djoser complex, although uncertain given the natural or anthropogenic changes that have occurred over the last five millennia, does not support the existence of a trench to the east side. Therefore, our observations join those of Welc et al. [ 61 ] and some of the first explorers [ 63 ], reasonably attributing only three sections to the Dry Moat.

6 Materials and methods

• High-resolution commercial satellite images (Airbus PLEIADES, 50 cm resolution) and digital elevation models (DEM) were computed and analyzed to identify Abusir wadi’s palaeohydrological network impact on Djoser’s construction project. The processing sequence to generate DEM was mainly achieved using the Micmac software [ 116 ] developed by the French National Geographic Institute (IGN) and the open-source cross-platform geographic information system QGIS 3 . 24 . 3 . Tisler .
• Geospatial data analysis was performed using the open-source WebGL-based point cloud renderer Potree 1.8.1 and QGIS 3 . 24 . 3 . Tisler .
• The 2D CAD profiles of the Step Pyramid Complex presented throughout this article were produced using Solidworks 2020 SP5 (Dassault Systems) , Sketchup Pro 2021 (Trimble) , Blender (Blender Foundation) , and Unreal Engine 5 (Epic Games) , mainly based on dimensions collected by successive archaeological missions during the last two centuries reported in the literature.
• The Wadi Taflah watershed and the catchment area west of Gisr el-Mudir have been identified and characterized using QGIS 3 . 24 . 3 . This was done with the help of the Geomeletitiki Basin Analysis Toolbox plugin, developed by Lymperis Efstathios for Geomeletitiki Consulting Engineers S . A . based in Greece.
• The modeling of the hydraulic lift mechanism was performed using the open-source programming software RStudio 2022 . 07 . 2 .

7. Concluding remarks and perspectives

This article discloses several discoveries related to the construction of the Djoser complex, never reported before:

• The authors presented evidence suggesting that the Saqqara site and the Step Pyramid complex have been built downstream of a watershed. This watershed, located west of the Gisr el-Mudir enclosure, drains a total area of about 15 km 2 . It is probable that this basin was connected to a larger one with an estimated area of approximately 400 km 2 . This larger basin once formed the Bahr Bela Ma River , also known as Wadi Taflah , a Nile tributary.
• Thorough technical analysis demonstrates that the Gisr el-Mudir enclosure seems to be a massive sediment trap (360 m x 620 m, with a wall thickness of ~15 m, 2 km long) featuring an open check dam. Given its advanced geotechnical design, we estimate that such work results from a technical tradition that largely predates this dam construction. To gain an accurate understanding of the dam’s operating period, the current authors consider it a top priority to conduct geological sampling and analysis both inside and outside the sediment trap. This process would also provide valuable information about the chronological construction sequence of the main structures found on the Saqqara plateau.
• The hydrological and topographical analysis of the dam’s downstream area reveals the potential presence of a dried-up, likely ephemeral lake, which we call Upper Abusir Lake, located west of the Djoser complex. The findings suggest a possible link between this lake and the Unas hydrological corridor, as well as with the ‘Dry Moat’ surrounding the Djoser complex.
• The ‘Dry Moat’ surrounding the Djoser complex is likely to have been filled with water from the Upper Abusir Lake, making it suitable for navigation and material transportation. Our first topographical analysis attributes only three sections to this moat (West, North, and South).
• The Dry Moat’s inner south section is located within the Unas hydrological corridor. The linear rock-cut structure built inside this area, called ‘Deep Trench,’ consisting of successive compartments connected by a rock conduit, combines the technical requirements of a water treatment system: a settling basin, a retention basin, and a purification system.
• Taken as a whole, the Gisr el-Mudir and the Deep Trench form a unified hydraulic system that enhances water purity and regulates flow for practical uses and vital needs.
• We have uncovered a possible explanation for how the pyramids were built involving hydraulic force. The internal architecture of the Step Pyramid is consistent with a hydraulic elevation device never reported before. The current authors hypothesize that the ancient architects could have raised the stones from inside the pyramid, in a volcano fashion. The granite stone boxes at the bottom of the north and south shafts above the Step Pyramid, previously considered as two Djoser’s graves, have the technical signature of an inlet/outlet system for water flow ( Fig 15 ). A simple modeling of the mechanical system was developed to study its water consumption and loading capacity. Considering the estimated water resources of the Wadi Taflah catchment area during the Old Kingdom, the results indicate orders of magnitude consistent with the construction needs for the Step Pyramid.

Graphical conclusion

North Saqqara map showing the relation between the Abusir water course and the Step Pyramid construction process (Inset). The arrows figuring the flow directions are approximate and given for illustrative purposes based on the Franco-Egyptian SFS/IGN survey [ 52 ]. Satellite image: Airbus Pléiades, 2021-07-02, reprinted from Airbus D&S SAS library under a CC BY license, with permission from Michael Chemouny, original copyright 2021.

https://doi.org/10.1371/journal.pone.0306690.g015

Supporting information

https://doi.org/10.1371/journal.pone.0306690.s001

https://doi.org/10.1371/journal.pone.0306690.s002

https://doi.org/10.1371/journal.pone.0306690.s003

The application and research progress of steel structures in construction industrialization

Published under licence by IOP Publishing Ltd IOP Conference Series: Earth and Environmental Science , Volume 330 , Issue 2 Citation Yi Peng 2019 IOP Conf. Ser.: Earth Environ. Sci. 330 022003 DOI 10.1088/1755-1315/330/2/022003

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Building industrialization is the trend for future building industry. The development prospect is promising because of the many advantages of fabricated steel structure. This paper presents an introduction to the fabricated steel structures, including its concept, advantage and main forms in domestic and overseas areas. Besides, the latest researches on the fabricated steel structures were reviewed. Typical cases of assembled buildings with steel-structure were also introduced. The questions and difficulties concerning this issue are also discussed in this paper.

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Research on the optimal trajectory planning method for the dual-attitude adjustment mechanism based on an improved multi-objective salp swarm algorithm.

1. Introduction

2. system structure and kinematic modeling, 2.1. system structure, 2.2. kinematic model, 2.3. motion trajectory planning, 2.3.1. optimization of terminal trajectory based on b-spline curve, 2.3.2. multi-objective optimization model for trajectory planning, 2.3.3. multi-objective trajectory optimization based on improved salp swarm algorithm.

• Population initialization:

3. Simulation Experiment and Analysis

3.1. algorithm comparison, 3.2. simulation analysis, 3.3. experimental analysis, 4. conclusions, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Liu, X.; Wang, L.; Shen, C.; Ma, W.; Liu, S.; Han, Y.; Wang, Z. Research on the Optimal Trajectory Planning Method for the Dual-Attitude Adjustment Mechanism Based on an Improved Multi-Objective Salp Swarm Algorithm. Symmetry 2024 , 16 , 1028. https://doi.org/10.3390/sym16081028

Liu X, Wang L, Shen C, Ma W, Liu S, Han Y, Wang Z. Research on the Optimal Trajectory Planning Method for the Dual-Attitude Adjustment Mechanism Based on an Improved Multi-Objective Salp Swarm Algorithm. Symmetry . 2024; 16(8):1028. https://doi.org/10.3390/sym16081028

Liu, Xu, Lei Wang, Chengwu Shen, Wenjia Ma, Shaojin Liu, Yan Han, and Zhiqian Wang. 2024. "Research on the Optimal Trajectory Planning Method for the Dual-Attitude Adjustment Mechanism Based on an Improved Multi-Objective Salp Swarm Algorithm" Symmetry 16, no. 8: 1028. https://doi.org/10.3390/sym16081028

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A Review on Behaviour of Columns of Steel Framed Structure with Various Steel Sections

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China's steel industry speeds up optimization of steel variety structure

BEIJING - China's steel industry has been accelerating the optimization of steel variety structure in pace with the adjustment and optimization of national industrial structures, the China Iron and Steel Industry Association (CISA) said Wednesday.

Data showed that in the first half of this year, the output of steel mostly used in construction, bridges and machinery dropped year-on-year, while that in areas including auto and ship manufacturing continued to grow.

Yao Lin, head of the association, said at a CISA council meeting that since the beginning of the year, China's steel sector has been coping with challenges, including an imbalance between market supply and demand, falling steel prices, high raw material prices and low economic efficiency.

The overall production and operation of the industry have remained generally stable, Yao said, adding that with the transformation and upgrading continuing to advance and the constantly optimized variety structure, the higher demand for steel products in the downstream industry was effectively met.

The steel industry's pace of green transformation has accelerated significantly, and intelligent manufacturing has been upgraded, he said.

Currently, the number of enterprises that use industrial internet technology to achieve smart production process control accounted for 79.6 percent of the total.

Yao said that the manufacturing industry will be the main driving force to support the steel sector.

The rapid development of new energy vehicles, the increase in orders for new energy-powered ships, and the accelerated renewal of old ships will support the demand for steel, and large-scale equipment renewal will also bring development opportunities for the equipment manufacturing industry, according to Yao.

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