Authors: Yiqing Sun, Wei Huang, Lei Gan, Hongwei Zhang, Yan He, Jia’ao Yu, Wenbin Ye, Zhenzhong Shen, Liqun Xu, Lechen Li
Categories: Review, soil science, applied sciences, agricultural science
Source: iScience
Authors: Yiqing Sun, Wei Huang, Lei Gan, Hongwei Zhang, Yan He, Jia’ao Yu, Wenbin Ye, Zhenzhong Shen, Liqun Xu, Lechen Li
Soil tensile strength is often overlooked due to its low magnitude. This review compares testing methods, classifying them as indirect and direct. Indirect methods are simple but rely on unrealistic assumptions, causing inaccuracies and preventing stress-strain curve acquisition. Direct methods obtain the full stress-strain relationship and are divided into triaxial and uniaxial tensile tests. Triaxial tensile tests involve complex failure and end effects, making uniaxial tensile tests preferable. Based on force direction, direct tests are categorized as vertical or horizontal. Vertical uniaxial tensile tests is influenced by soil self-weight, whereas horizontal uniaxial tensile tests offers clear advantages. For specimen fixation, clamping is more efficient and reliable than adhesive, anchorage, or frictional methods. Proposed improvements include using pulleys to reduce base friction, designing dumbbell-shaped molds for effective clamping, extending the tensile section, and scaling up molds for wide-graded soils.
Soil tensile strength serves as a fundamental parameter for evaluating its physical and mechanical properties, alongside compressive and shear strengths. During pedogenesis, the integrity and cohesion of the original rock are progressively diminished, resulting in soils that retain limited compressive and shear strength—significantly lower than that of intact rock—while exhibiting markedly reduced or virtually absent tensile resistance.^1^ Consequently, engineering practice has historically relied predominantly on compressive or shear strength for stability assessment and failure prediction. Owing to its relatively low magnitude and measurement challenges, tensile strength has often been overlooked in geotechnical design.^2^ Nevertheless, tensile failure and crack initiation remain prevalent failure modes in soil structures under various loading conditions.
In geotechnical practice, soil tensile strength serves as the fundamental mechanical parameter controlling tensile crack initiation. This phenomenon is widely observed in various earth structures, including dams, hydraulic barriers, slopes, subgrades, embankments, and riverbanks, particularly under conditions of desiccation, differential settlement, or external loading.^3^^,^^4^ Representative manifestations encompass tensile cracks developing at slope toes,^5^ desiccation and freeze-thaw induced fissures,^6^ and tensile failure zones forming around horizontally loaded structures such as transmission towers and wind turbine foundations.^7^ Crack development substantially compromises soil structural integrity and degrades its mechanical performance. Fractured soils exhibit markedly reduced overall strength and bearing capacity compared to intact materials, thereby inducing various engineering geological hazards.^3^^,^^8^^,^^9^ In hydraulic structures, cracks significantly enhance permeability by forming preferential seepage pathways, which accelerates groundwater infiltration and may impair reservoirs and dam cores. This process simultaneously increases risks of contaminant migration from industrial or agricultural sources.^10^^,^^11^^,^^12^^,^^13^ In earth-rock dams, tensile failure in core walls is primarily induced by two mechanisms. First, the arching effect develops when differential settlement occurs between the rock-fill and clay core, constraining the core wall and generating vertical tensile stresses that initiate horizontal cracks. Second, high hydraulic gradients during rapid impoundment elevate pore water pressure in vulnerable zones, inducing tensile stress at their leading edges and potentially causing hydraulic fracture. The formation of tensile cracks substantially alters both mechanical and hydraulic properties of soils, ultimately compromising dam integrity.^14^ In transportation infrastructure, crack development reduces soil density while increasing compressibility, leading to differential subgrade settlement and superstructure deformation that critically undermine durability and operational safety.^15^^,^^16^ Similarly, slope stability is diminished when rainfall infiltrates through desiccation cracks during precipitation events, elevating collapse potential.^17^^,^^18^^,^^19^ Consequently, soil performance across geotechnical, geological, and environmental engineering disciplines is profoundly affected by crack propagation.^3^^,^^20^^,^^21^^,^^22^ Mechanistically, soil cracking represents structural failure in shear, tension, or combined modes, occurring when stress states exceed the material’s corresponding strength thresholds.^23^ Therefore, systematic characterization of soil tensile strength is essential for elucidating failure mechanisms and developing effective prevention strategies against tensile cracking.
Research on soil tensile properties necessitates the establishment of reliable testing methods.^24^^,^^25^ Due to the historical underestimation of tensile strength in geotechnical engineering, studies in this area remain relatively limited, particularly in China. Most existing tensile testing techniques have been adapted from methodologies developed for rock and concrete. These methods are broadly classified into indirect and direct methods. Indirect testing methods derive tensile strength through theoretical frameworks and assumptions, whereby parameters obtained from compression or bending tests are converted into tensile strength using analytical formulae. Several commonly employed indirect testing methods, namely, the beam bending test,^26^ Brazilian test,^27^^,^^28^ and axial fracture test,^29^ are founded on distinct theoretical elastic bending theory, linear elasticity, and plastic theory, respectively. In contrast, direct testing methods represent the earliest developed techniques for tensile testing of soils.^30^ These methods apply tensile load directly to both ends of the specimen, enabling precise control of both load and displacement, depending on the capability of the testing equipment. Based on the stress conditions, direct testing methods are primarily classified into triaxial tensile tests and uniaxial tensile tests.^31^ In the triaxial tensile test, soil specimens are bonded to the loading heads of a triaxial apparatus, and tensile force is applied directly to the specimen under triaxial stress conditions or in the absence of lateral pressure to determine the tensile strength. The uniaxial tensile test involves fixing the specimen ends and applying axial tension in the absence of lateral pressure to measure the soil’s tensile strength. Furthermore, according to the direction of force application, direct testing methods can be divided into vertical and horizontal methods, while based on the fixation mechanism, they are categorized into adhesive fixation, anchorage fixation, frictional fixation, and clamping fixation.
Li^32^ synthesized the shear and tensile strength characteristics of Malan loess in the Lanzhou region of China through an extensive literature review. The analysis revealed that both the tensile and shear strengths of Malan loess decrease with increasing water content and increase with higher dry density, exhibiting strong multiple regression correlations. The tensile strength of reconstituted samples was found to be significantly lower than that of undisturbed specimens. The shear strength demonstrated directional dependence, reflecting pronounced anisotropy of the loess structure. Furthermore, testing method, specimen dimensions, and loading rate were all identified as factors influencing measured tensile strength values. Venkataramana^22^ critically reviewed methods for determining the tensile strength of fine-grained soils, with particular emphasis on empirical relationships correlating tensile strength with individual parameters, such as suction, plasticity index, liquid limit, cation exchange capacity, clay content, or water content. The study also contributed to developing a generalized relationship incorporating multiple soil properties. Tang et al.^33^ summarized the evolution and characteristics of tensile strength behavior in soils, documented recent advances in tensile testing methodologies, and categorized eight distinct failure modes in rocks and soils. Their analysis further identified persistent challenges in soil tensile behavior research, particularly for unsaturated soils. However, these previous studies have not provided a comprehensive or systematic review of tensile strength testing apparatus and research methodologies, nor have they adequately addressed the limitations inherent in existing experimental devices.
This review provides an updated synthesis of soil tensile strength testing methodologies, building upon decades of research to comprehensively survey both direct and indirect testing methods. It systematically analyzes the advantages and limitations of various methods within these two categories, proposes dual classification frameworks for direct methods based on loading direction and specimen fixation mechanisms, and identifies key factors influencing measurement accuracy in direct testing. This integrated understanding of methodological considerations will enable researchers to make more informed selections of appropriate testing strategies for specific investigation purposes.
This review systematically examines the extensive body of literature on soil tensile strength, drawing upon over 200 referenced works. The paper is structured as The introduction presents a concise introduction to the engineering implications of soil cracking and the fundamental importance of tensile strength characterization. The indirect testing method comprehensively summarizes both historical and contemporary indirect testing methods, including their underlying analytical theories and corresponding experimental investigations. The direct testing method systematically examines direct tensile testing methods, with particular emphasis on uniaxial testing methods. These methodologies are classified according to four distinct specimen fixation adhesive fixation, anchorage fixation, frictional fixation, and clamping fixation. The discussion provides a critical comparison between indirect and direct methods, highlighting their respective advantages and limitations, while discussing crucial factors affecting direct tensile measurements—including soil self-weight, mold-base friction, fixation method, soil type characteristics, and mold dimensional parameters. The concluding section synthesizes key findings and suggests promising avenues for future research.
The beam bending test idealizes the soil specimen as an elastic simply supported beam subjected to concentrated loads at specific locations, inducing tensile stress at its bottom surface and ultimately resulting in tensile failure. This method can be classified into three-point bending^34^^,^^35^^,^^36^^,^^37^ and four-point bending^38^^,^^39^^,^^40^ configurations depending on the number of loading points applied, as illustrated in Figure 1. The underlying analytical theory assumes linear elastic material behavior with identical Young’s modulus in tension and compression, while neglecting the beam’s self-weight.^41^ For the three-point bending test (Figure 1A), the tensile strength σt is calculated (Equation 1)σt=3FmaxL2bh2where Fmax represents the maximum applied fracture load (N), while L, b, and h denote the length, width, and height of the soil specimen (m), respectively.Figure 1Beam bending test(A) Three-point bending configuration.(B) Four-point bending with quarter-span loading.(C) Four-point bending with third-span loading.
In the four-point bending configuration, where loading points are spaced at one-third of the beam span from adjacent supports (Figure 1B), the tensile strength σt is determined by the following (Equation 2)σt=FmaxLbh2In the four-point bending configuration with loading points positioned at quarter-span distances from adjacent supports (Figure 1C), the tensile strength σt is calculated (Equation 3)σt=3FmaxL4bh2
Leonard and Narrain^42^ pioneered the application of beam bending tests to determine the tensile strength of various compacted clays. Their method was subsequently extended to multiple soil types in later studies.^43^^,^^44^^,^^45^^,^^46^^,^^47^^,^^48^ In a comparative investigation, Ajaz and Parry^49^ conducted beam bending tests on two compacted clays, specifically Gault clay and Balderhead clay, to characterize their stress-strain behavior under both tension and compression. Their study also evaluated the ratio of flexural strength to direct tensile strength across varying moisture contents, revealing strength ratios ranging between 1.3 and 1.6 for Gault clay and 1.7 and 1.8 for Balderhead clay. Maher and Ho^35^ demonstrated through beam bending tests on kaolinite clay that fiber reinforcement significantly enhanced tensile strength, with more pronounced improvements observed at lower moisture contents. Wang et al.^50^^,^^51^^,^^52^ introduced a semicircular bending technique using specimens of 100 mm diameter and 65 mm thickness, systematically comparing its performance with conventional three-point bending. Their findings indicated that the semicircular bending method provided superior effectiveness, reliability, and result stability compared to the traditional approach. Quantitatively, the failure load measured in beam bending tests was 1.3–1.6 times greater than that in semicircular bending, while the tensile strength derived from semicircular bending specimens exceeded that of beam specimens by a factor of 2.0–2.4. Thusyanthan et al.^53^ conducted beam bending tests on kaolin clay and employed Hvorslev’s Mohr-Coulomb failure envelope normalization method to analyze the stress state of critical tensile fibers at crack initiation. Their analysis revealed that cracking initiates when the effective stress state reaches the tensile failure line under low mean effective stress conditions, or alternatively attains the “apparent failure line” under elevated mean effective stress conditions. A research team from Tsinghua University^54^ systematically compared four-point bending configurations with uniaxial tensile tests on clay specimens, subsequently developing and patenting an integrated testing apparatus capable of performing both strain-controlled horizontal uniaxial tensile tests and beam bending tests.^55^ In a separate investigation, Thusyanthan et al.^53^ performed four-point beam bending tests on fiber-reinforced soil, with digital image correlation techniques applied to track displacement fields across the beam’s central section. Particle image velocimetry analysis demonstrated that strain distributions maintained linear variation through the beam depth until immediately preceding crack initiation. Viswanadham et al.^41^ enhanced the experimental setup by inserting a 2-mm-thick acrylic plate between the loading transfer bar and soil beam to mitigate stress concentration effects. Employing similar method, Azmatch et al.^56^ investigated parameters governing tensile strength behavior in permafrost soils, establishing that frozen soil tensile strength decreases systematically with increasing temperature, strain rate, and pre-freezing moisture content, with temperature and strain rate exhibiting predominant influence.
The Brazilian test conceptualizes soil specimens as brittle materials subjected to radial compression, which induces tensile stress concentration along the vertical plane and ultimately causes diametrical, median, or diagonal splitting, as schematically represented in Figure 2. This method requires two fundamental first, the material must exhibit linear elastic behavior under biaxial stress conditions; second, it must demonstrate homogeneity and isotropy in both strength and elastic properties.^57^ Test specimens are typically prepared in cylindrical, cubic, or beam geometries, with corresponding analytical expressions provided for tensile strength σt (Equation 4)σt=2FmaxπdLwhere Fmax represents the maximum applied radial load (N), while d and L denote the diameter (or side length) and total length of the soil specimen (m), respectively.Figure 2Brazilian test and different loading methods(A) Brazilian test.(B) Orbicular.(C) Square.(D) Rectangular.(E) Rhombus.
Frydman^58^ pioneered the application of the Brazilian test for soil tensile strength measurement, systematically investigating its suitability across different soil types. Subsequently, Shloido^59^ employed this method on frozen sands, sandy loams, clays, and loamy soils, demonstrating strong agreement between indirect Brazilian test results and direct tensile measurements. Furthermore, the tensile strength values obtained exhibited significantly lower coefficients of variation compared to alternative testing methods. Narain and Rawat^60^ employed the Brazilian test to determine the tensile strength of compacted clay. Through comparison with unconfined compression tests, they established that the compressive strength exceeded the tensile strength by a factor of 6–12. Subsequently, Krishayya et al.^61^ developed an electromechanical measurement system for the Brazilian test, which enabled not only the determination of tensile strength in compacted clay but also the acquisition of complete stress-strain curves. In subsequent investigations, Das et al.^62^ conducted Brazilian tests on fine-grained rounded silica sand, documenting progressive increases in tensile strength with cement admixture incorporation. Furthermore, Chen^63^ performed systematic experiments corresponding to the four fracture modes illustrated in Figure 2, determining the upper and lower bounds of tensile strength based on the maximum and minimum fracture loads, respectively.
Shen et al.^64^ pioneered the application of the Brazilian test in permafrost investigations, establishing that the height-to-diameter ratio of specimens exhibited negligible influence on measured results. Their study recommended avoiding excessively thin specimens when specialized Brazilian test apparatus was unavailable, as such geometries presented handling difficulties and increased susceptibility to eccentric loading, which could substantially compromise measurement accuracy. This foundational work subsequently enabled widespread adoption of Brazilian test for tensile strength characterization in clay, permafrost, and fiber-reinforced soil systems.^62^^,^^64^^,^^65^^,^^66^^,^^67^^,^^68^^,^^69^^,^^70^^,^^71^^,^^72^^,^^73^^,^^74^^,^^75^^,^^76^^,^^77^^,^^78^^,^^79^^,^^80^^,^^81^^,^^82^ Ma^70^ evaluated tensile-to-compressive strength ratios using Brazilian test alongside unconfined compression tests, and demonstrated that the Brazilian test was found to effectively minimize confounding effects from microfractures and other artifacts that frequently complicate frozen soil testing. Consoli et al.^83^ systematically investigated the tensile strength of three distinct soil-cement mixtures, including silty sand, clayey sand, and fine sand, using Brazilian tests. Their experimental results demonstrated that under constant dry density conditions, tensile strength was consistently enhanced with increased cement content or reduced porosity, regardless of variations in moisture content. In a separate experimental program, Olgun^84^ conducted Brazilian tests on polypropylene fiber-reinforced clayey soil, documenting significant tensile strength improvements through fiber and stabilizer incorporation. Following 28 days of curing, the tensile strength increased from 25 to 285 kPa, representing an 11-fold enhancement. Mario Castaneda-Lopez et al.^85^ employed Brazilian testing to evaluate how in situ factors influence the indirect tensile strength (ITS) of cemented stabilized soils. Their analysis established positive correlations between ITS values and both cement content and curing duration, providing quantitative relationships for predicting field performance from laboratory measurements.
Axial fracture test conceptualizes soil specimens as ideal plastic materials. During testing, the specimen is positioned vertically within a cylindrical rigid liner while opposing axial loads are applied at its top and bottom surfaces until tensile fracture occurs, as schematically represented in Figure 3. This method is theoretically founded on perfect plasticity theory for soils, initially developed by Chen and Drucker,^86^ which posits two fundamental first, sufficient local deformability must exist in both tension and compression to validate limit analysis theorems for perfect plastic material behavior; second, the failure surface must conform to a modified Mohr-Coulomb yield criterion specifically adapted for soil materials,^87^ within complete plasticity theory. The corresponding expression for tensile strength σt calculation (Equation 5)σt=Fmaxπ(krh−a2)where F represents the maximum applied axial load (N), k denotes a dimensionless coefficient with a defined value of 1.0, r corresponds to the radius of the soil specimen (m), h indicates the specimen height (m), and a specifies the radius of the cylindrical liner (m).Figure 3Axial fracture test
Fang and Fernandez^88^ established true tensile strength values through failure initiation along the specimen’s weakest plane, demonstrating close correspondence between measurements obtained from the axial fracture test and conventional split-tension methods. Subsequently, Fang et al.^89^ performed a comprehensive assessment of the axial fracture test’s applicability across diverse geomaterials, including soils, concrete, mortar, asphalt, cement-treated highway subgrades, subbase materials, and rock formations. Their comparative analysis with Brazilian test results revealed generally consistent measurements between the two methodologies. Nevertheless, systematic comparisons indicated that the axial fracture test typically produces lower tensile strength measurements than the Brazilian test. This discrepancy originates from their distinct failure in the Brazilian test, failure is predetermined to occur vertically along the loading axis, whereas the axial fracture test permits failure initiation along any radial plane, with rupture occurring specifically at the weakest orientation.^90^ Furthermore, tensile strength determinations via the axial fracture test are influenced by geometric parameters, particularly the specimen’s height-to-diameter ratio and liner dimensions, introducing measurable variability in experimental outcomes. Consequently, reliable characterization of soil tensile strength using this method requires careful consideration of the relationships between testing parameters and resultant strength values.
Subsequently, the axial fracture test gained widespread adoption in geotechnical investigations.^91^^,^^92^^,^^93^^,^^94^^,^^95^^,^^96^^,^^97^ Shen et al.^98^ employed this method to characterize the tensile strength of permafrost, establishing quantitative relationships between tensile strength and critical parameters including height-to-diameter ratio, temperature, and loading rate. Their study further introduced a computational algorithm to derive correction factors for adapting axial splitting test results to in situ permafrost conditions. In their experimental configuration, the liner diameter was maintained at 15 mm, representing one-quarter of the specimen diameter. Similarly, Li^99^ implemented a liner diameter of 20 mm, corresponding to one-third of the specimen diameter. Liu et al.^100^ systematically investigated the coupled effects of liner diameter and height-to-diameter ratio on tensile strength measurements in cohesive soils. Their analysis recommended liner diameters between 20 and 30 mm and a height-to-diameter ratio of 2, while demonstrating the interdependent nature of these parameters on measured strength values. Kim et al.^101^ applied this method to evaluate compacted contaminated sand-bentonite mixtures. Their investigation modified the conventional axial fracture test method^102^ through dual-end liner fixation and the introduction of a controlled gap between the liner and loading chassis. This refinement ensured precise axial alignment of both specimens and applied loads, thereby minimizing weak surface effects and enhancing measurement accuracy. The optimized protocol was employed to assess the influences of plasticity index, liner diameter, loading rate, and specimen dimensions on tensile strength. Their findings identified 254 and 381 mm as optimal liner diameters, while establishing positive correlations between tensile strength and plasticity index, liner diameter, and loading rate in cohesive soils. Liang^103^ conducted a systematic comparison of unconsolidated undrained triaxial compression tests, unconfined compression tests, and axial fracture tests on Q3 loess specimens from the Lanzhou area. The investigation revealed strong correlations between both unconfined compressive strength and cohesion with the measured unconfined tensile strength. Based on experimental results, a modified value of K = 2.19 was proposed for the tensile strength calculation formula. Wu et al.^96^ applied the axial fracture test to loess specimens and demonstrated that both compressive strength and cohesion parameters obtained under tension-shear coupling conditions were substantially lower than those derived from conventional triaxial shear tests. These findings provide critical reference values for selecting appropriate mechanical parameters in geotechnical stability assessments. Li et al.^104^ performed axial fracture tests on remolded loess, revealing that statically compressed specimens developed higher tensile strength compared to compacted samples. Their results further established a linear relationship between tensile strength and loading cylinder diameter, while identifying specimens with height-to-diameter ratios of 1 as producing the most consistent and stable tensile strength measurements.
The hollow cylinder test serves as an indirect method for determining tensile parameters in brittle geomaterials.^105^ A specialized tensile testing apparatus was developed by Al-Hussaini et al.^106^ to apply uniform confining pressures simultaneously to both the interior and exterior surfaces of hollow cylindrical specimens, thereby generating measurable radial compressive and tangential tensile stresses. Their experimental investigation of compacted soils under varied principal stress ratios demonstrated that tensile strengths derived from the hollow cylinder test consistently exceeded those obtained through axial splitting methods. Subsequently, Al-Hussaini and Townsend^107^ implemented the hollow cylinder test on clay specimens, acquiring precise tensile parameters including elastic modulus and Poisson’s ratio through simultaneous radial deformation measurements at both inner and outer specimen surfaces. In a complementary approach, Li et al.^108^ designed an experimental configuration for indirect tensile strength assessment of geomaterials. Their method employed homogeneous radial hydrodynamic pressure applied to the inner wall of hollow cylindrical specimens with inner and outer diameters of 50 and 110 mm, respectively, to induce controlled deformation and failure.
Furthermore, Vomocil et al.^109^ employed centrifuge testing to indirectly evaluate tensile strength variations in five sandy soils, defining tensile strength as the applied tensile stress at specimen failure. In a separate investigation, Snyder^110^ utilized the pneumatic fracture method to determine the tensile strength of a silt material, with comparative analysis revealing statistically equivalent results between this indirect approach and direct tension methods. Wang et al.^111^ systematically investigated the tensile strength of Tibetan plateau silt-clay soils using the hydraulic fracturing method (HFM) at temperatures above −2°C. Their experimental results demonstrated that the relationship between tensile strength of warm frozen soil and temperature followed a power function. Comparative validation among HFM, uniaxial tension tests, and Brazilian tests confirmed HFM’s feasibility as an indirect method for frozen soil tensile strength determination. Consequently, methodological corrections were proposed to enhance the accuracy of indirect tensile measurements.
In direct testing methods, tensile load is applied directly to both ends of the soil specimen, enabling precise control of both load and displacement, which is contingent upon the capability of the testing apparatus.^14^ Consequently, these methods have gained increasing adoption in tensile strength investigations.^112^^,^^113^^,^^114^^,^^115^ Based on stress conditions, direct testing methods are primarily classified into the uniaxial tensile test and the uniaxial tensile test.^116^ Alternatively, according to loading direction, they can be categorized as vertical or horizontal methods, while fixation mechanisms provide another classification into adhesive fixation, anchorage fixation, frictional fixation, and clamping fixation. The tensile strength σt in direct testing is generally determined by the following (Equation 6)σt=FmaxAwhere Fmax represents the maximum tensile load (N) and A denotes the cross-sectional area (m^2^) at the minimum dimension of the necking region in the soil specimen.
The triaxial tensile test is conventionally performed by positioning the soil specimen within a standard or modified triaxial apparatus, where the specimen ends are bonded to the loading heads and tensile force is applied under controlled lateral confinement. This method requires relatively straightforward equipment modifications. As illustrated in Figure 4, tensile failure can be induced through two principal loading paths^117^: first, the specimen is consolidated under a specific confining pressure, followed by maintaining constant axial pressure while progressively increasing the confining pressure until failure occurs (Figure 4B); alternatively, after consolidation under a given confining pressure, the confining pressure is maintained constant while the axial pressure is systematically reduced until specimen failure is achieved (Figure 4C). Both loading paths induce vertical elongation of the specimen, effectively applying tensile stress at its ends. Notably, the magnitude of confining pressure governs the resulting failure mechanism in soil specimen.^118^ Under low confinement conditions, specimens exhibit typical tensile failure patterns (Figure 5A). When subjected to elevated confining pressures, shear failure becomes predominant (Figure 5B). At intermediate confinement levels, combined tensile-shear failure mechanisms are observed (Figure 6C).Figure 4Vertical triaxial tensile test(A) Vertical triaxial tensile test.(B) Constant axial pressure with increasing confining pressure.(C) Constant confining pressure with reduced axial pressure.Figure 5Three failure modes of vertical triaxial tensile test(A) Tensile failure.(B) Shear failure.(C) Tensile-shear failure.Figure 6Horizontal triaxial tensile test
Haefeli^119^ pioneered the direct triaxial tensile test for soils by employing cylindrical saturated clay specimens with cryogenically fixed ends to investigate tensile behavior under varying confining pressures, though the freezing protocol introduced operational complexities. Subsequently, Parry^120^ implemented the triaxial tensile test using a standard triaxial apparatus, systematically examining how confining pressure, overconsolidation ratio, and drainage conditions influence tensile strength development in clayey soils. Further advancing this method, Bishop and Garge^121^ conducted triaxial tensile test on both intact and remolded London Blue Clay by modulating confining pressure to induce axial tension, incorporating a specially contoured neck region at the specimen midsection to control failure localization.
Zhou^122^ systematically investigated soil behavior through triaxial tensile tests, establishing an inverse relationship between tensile strength and confining pressure. Their analysis categorized failure mechanisms into three distinct pure tensile rupture, shear elongation progressing to tensile failure, and pure shear failure. Specifically, three characteristic confinement thresholds were (1) when confining pressure remains below critical value ccot(45°-φ/2), specimens undergo predominantly tensile failure with minimal confinement influence on tensile strength; (2) at confining pressures between thresholds ccot(45°-φ/2) and σ3tan^2^(45°+φ/2) + 2cot(45°+φ/2), failure transitions to shear-induced elongation followed by tensile rupture; (3) when confinement exceeds threshold σ3tan^2^(45°+φ/2) + 2cot(45°+φ/2), complete shear failure occurs without tensile rupture. Based on these observations, Zhou emphasized the critical importance of maintaining appropriate confining pressure ranges during triaxial tensile testing. Subsequently, Zhu et al.^1^ further examined tensile-shear strength relationships in soils using triaxial testing methodologies, obtaining results that substantiate Zhou’s original conclusions.
Lawton et al.^123^ performed triaxial tensile tests on both fiber-reinforced and unreinforced sandy soils to evaluate strengthening effects. Additionally, Yu et al.^124^ documented characteristic brittle fracture patterns in tested specimens, while Zhang et al.^125^ developed specialized instrumentation for monitoring pore pressure evolution during specimen extension. In comparative studies, Hu et al.^126^ demonstrated that the lightweight impact compaction method yielded systematically higher tensile strength values than standard compaction techniques. Concurrently, Li^127^ systematically investigated how moisture content, confining pressure, and fissure development influence tensile strength degradation in loess. Siripun^128^ further examined tensile strength enhancement in crushed stone pavement bedding materials through fiber reinforcement.
To eliminate gravitational artifacts inherent in vertical configurations, Zhang et al.^30^^,^^129^ developed an innovative horizontal triaxial tensile test apparatus (Figure 6). This design incorporates specimen-end bonding to loading heads and employs standardized specimens (50 mm diameter × 100 mm length) for tension testing, providing experimental validation for the failure modes originally proposed by Zhou.^122^
The uniaxial tensile test is conducted by fixing the specimen ends and applying direct axial tension, representing the most straightforward and effective approach for determining soil tensile strength under unconfined conditions.^130^ This method has been formally adopted as the standard testing procedure by China’s water conservancy administration.^131^ Based on fixation mechanisms, the uniaxial tensile test can be classified into four principal adhesive fixation, anchorage fixation, frictional fixation, and clamping fixation.^31^^,^^116^
In adhesive fixation, soil specimens are bonded to loading heads by chemical or physical methods, and tensile force is subsequently applied through these heads.
Dash^132^ and the Tsinghua University Earth-Rock Dam Fracture Resistance Research Group^54^ employed chemical adhesives to bond rectangular soil specimens under tension. Their investigations revealed that both tensile strength and tensile deformation modulus exhibited negative correlations with moisture content while demonstrating positive correlations with dry density. Subsequently, Lee et al.,^133^ Zhu,^1^ and Farrell et al.^113^ conducted analogous experimental investigations using rectangular and cylindrical specimens respectively, all implementing adhesive fixation methodologies as schematically represented in Figure 7A. Notably, Plé et al.^134^ and Mesbah et al.^135^ incorporated polypropylene fibers and sisal fibers respectively as soil reinforcements. Mesbah et al. further prepared rectangular specimens (100 × 140 × 295 mm) featuring pre-fabricated notches (6 mm width × 25 mm depth) for controlled fracture testing.Figure 7Vertical uniaxial tensile test with adhesive fixation(A) Plé et al.^133^(B) Tang and Graham.^2^
Tang and Graham^2^ positioned cylindrical soil specimens horizontally within a mold, where chemical adhesives were employed to bond the specimens to both the upper and lower interior surfaces of the cylindrical fixture. Axial tensile force was subsequently applied to the assembly, as illustrated in Figure 7B. This configuration significantly increased the contact area between the cylindrical mold and soil specimen, thereby enhancing the adhesive bond strength. The tensile strength σt was subsequently determined using the following (Equation 7)σt=FmaxA=Nmax−WAwhere Fmax represents the maximum tensile force at specimen failure (N), A denotes the cross-sectional area at the most severely damaged section (m^2^), Nmax corresponds to the maximum applied tensile load (N), and W indicates the combined weight of the upper cylinder section and its contained soil mass after fracture (N).
Hu et al.^126^ modified a conventional triaxial apparatus to enable both triaxial and vertical uniaxial tensile tests. Their initial setup, which used cyanoacrylate adhesive (502 glue) to bond specimens to upper and lower plexiglass plates, induced tilting. To address this, the adhesive fixation protocol was plexiglass components were first bonded to the specimen ends, and these assemblies were then connected to the loading platens using a combination of petroleum jelly and cyanoacrylate. This modified fixation method effectively minimized misalignment and disturbance. The refined apparatus was subsequently used to systematically investigate how preparation methods affect the tensile strength of remolded loess.
To mitigate the influence of gravitational effects inherent in vertical configurations, researchers developed horizontal testing methodologies. Li et al.^136^ and Zhang et al.^129^^,^^137^ fabricated rectangular specimens (160 × 140 × 70 mm and 160 × 70 × 70 mm, respectively) and employed adhesive fixation on the end faces, as shown in Figure 8A, using ball bearings to reduce friction.Figure 8Horizontal uniaxial tensile test with adhesive fixation (mm)(A) Zhang et al.^137^(B) He et al.^138^
Sun et al.^139^ and Wang et al.^140^ adopted similar configurations, their tests were sometimes compromised by poor adhesive bond integrity.^138^ In response, He et al.^138^^,^^141^ developed an innovative three-side adhesively-bonded tensile mold (Figure 8B). It featured deployable side panels and 2-mm-thick replaceable rubber sheets on the grip surfaces to prevent adhesive contamination. This apparatus, which incorporates a 75 × 30 × 30 mm tensile section and ball bearings, was designed to minimize friction. In a parallel development, Murray et al.^142^ also used adhesive fixation at the ends but employed dog-bone-shaped specimens with narrowed centers to control failure location.
Following comparative analysis of international soil classification standards,^143^ soil materials were systematically classified according to established specifications.^144^ The historical development of horizontal uniaxial tensile test apparatus employing adhesive fixation is chronologically summarized in Table 1.Table 1Comparison of horizontal uniaxial tensile test apparatus with adhesive fixationSoil sample fixationResearch scholarParticular yearSpecific fixing methodEarthworkSoil typeLength of tensile section(mm)Ways to eliminate frictionAdhesive fixationSun et al.^139^2009one-sidedloessfine grained soil (CL)–smooth glassZhang et al.^145^2014one-sidedsilty clayfine grained soil (CL)160bearPang^129^2014one-sidedartificial gravel soilfine grained soil (CLG)160bearMurray et al.^142^2014one-sidedsilty clayfine grained soil (−)30ball bearingWang et al.^140^2019one-sidedloessfine grained soil (CL)–sliding platformHe et al.^138^^,^^141^20182019three-sidedloessfine grained soil (CL)75ballsCL, liquid limit clay; CLG, low liquid limit clay.
Anchorage fixation involves embedding structural components within both ends of a soil specimen during preparation, or anchoring components into the specimen ends post-preparation, thereby applying tensile force to the specimen via these embedded elements.
Heibrock et al.^146^ and Zeh et al.^147^ implemented this technique by drilling an 8-mm diameter axial hole through a cylindrical specimen (90 mm height × 24 mm diameter), inserting a filter cloth liner into the resulting cavity, anchoring tension hooks within the borehole, and subsequently backfilling with epoxy resin. Tensile loading was then applied through the embedded hooks as illustrated in Figure 9.Figure 9Vertical uniaxial tensile test with anchorage fixation(Heibrock et al.^146^ and Zeh et al.^147^).
To mitigate the influence of specimen self-weight in vertical configurations, researchers have increasingly adopted horizontal testing arrangements. Zhang et al.^148^ and Nearing et al.^149^^,^^150^ employed an anchorage fixation approach analogous to the method developed by Heibrock and Zeh but implemented two critical specimens were positioned horizontally, and ball bearings were incorporated beneath the specimens to minimize frictional resistance, as depicted in Figure 10A. In an alternative configuration, Varsei et al.^151^ installed multiple screws along the interior surface of tensile molds, which became embedded during specimen preparation to provide mechanical interlock, as illustrated in Figure 10B. Furthermore, their study incorporated theoretical prediction of uniaxial tensile strength σt through the Moore-Cullen model based on effective stress principles, expressed (Equation 8)σt=2c′cosφ′+2Sre(ua−uw)tanφ′cosφ′1+sinφ′where c′ and φ′ are defined as the effective cohesion and effective internal friction angle, respectively, Sre represents the effective saturation, ua denotes the pore gas pressure, uw indicates the pore water pressure, and ua-uw corresponds to the matric suction.Figure 10Horizontal uniaxial tensile test with anchorage fixation(A) Zhang et al.^148^(B) Varsei et al.^151^
Furthermore, soil materials were systematically classified according to established specifications,^144^ enabling the chronological organization of horizontal uniaxial tensile test apparatus utilizing anchorage fixation in Table 2.Table 2Comparison of horizontal uniaxial tensile test apparatus with anchorage fixationSoil sample fixationResearch scholarParticular yearSpecific fixing methodEarthworkSoil typeLength of tensile section(mm)Ways to eliminate frictionAnchorage fixationZhang et al.^148^1997wood screwclay/fiber reinforced soilfine grained soil (CL)–bearVarsei et al.^151^2016boltsloamfine grained soil (CL)–ball bearingCL, low liquid limit clay; CH, high liquid limit clay.
Frictional fixation is characterized by the clamping of tensile molds around both ends of a soil specimen, whereby tensile load is transferred through the interfacial friction developed between the mold interior and the specimen surface.
Zhang et al.^152^ and Zhu et al.^152^^,^^153^ developed a dual-fixture apparatus in which compacted soil specimens were radially constrained, with specimen fixation achieved through bolt-adjusted circumferential compression for subsequent tensile loading, as illustrated in Figure 11. This configuration was implemented using a universal testing machine. Similar frictional fixation methodologies were subsequently employed by Ibarra et al.^154^ and Ni et al.^155^ Notably, Conlon^156^ enhanced the interfacial friction by incorporating a fine-grit sandpaper interface between the fixture and specimen surfaces, while simultaneously introducing a geometrically constrained neck region at the specimen center to promote controlled failure localization within this reduced section.Figure 11Vertical uniaxial tensile test with frictional fixation(Zhang et al.^152^ and Zhu et al.^153^).
To mitigate gravitational artifacts in vertical testing configurations, researchers have developed horizontal testing methods. Lu et al.^157^^,^^158^ inclined the specimen-mold assembly at an angle to the loading platform, utilizing the gravitational component to offset frictional forces. Specimen fixation was achieved through radial compression applied via a shrink-fitted sleeve, as schematically represented in Figure 12. According to the Mohr-Coulomb shear failure criterion, failure initiates not when applied stress reaches bond strength, but rather when the shear-to-normal stress ratio at any point attains a critical value tanφ.^159^ Since the tensile apparatus lacked suction control or measurement capabilities, tensile strength σt was predicted using the total stress approach under these (Equation 9)σt=2ccosφ1+sinφwhere c and φ represent the cohesion and internal friction angle, respectively, of unsaturated loess under total stress conditions.Figure 12Horizontal uniaxial tensile test with frictional fixation(Lu et al.^160^).
Meanwhile, Lu^159^^,^^161^^,^^162^ established an analytical expression for the uniaxial tensile strength σt of unsaturated sandy soils as a function of soil suction and equivalent σt=2tanφttan(π4−φt2)(ua−uw){+[α(ua−uw)]n}1/(n−1)(Equation 10)σt=2tanφttan(π4−φt2)Seα[Sen/(1−n)−1]1/nwhere φt denotes the internal friction angle under low normal stress conditions (below 1 kPa), ua represents the pore gas pressure, uw indicates the pore water pressure, α corresponds to the inverse of the air-entry pressure, n is the pore size distribution index, and Se defines the equivalent saturation.
Lv et al.^163^ employed an analogous frictional fixation method to test soil specimens measuring 800 mm in height and 39.1 mm in diameter. Similar to the approach by Conlon,^156^ a lubricated rosin-coated non-slip textile interface was inserted between the mold interior and specimen surface, thereby enhancing frictional resistance while preventing specimen damage during mold tightening procedures.
Furthermore, soil materials were systematically classified according to specification,^144^ enabling the chronological organization of horizontal uniaxial tensile test apparatus utilizing frictional fixation in Table 3.Table 3Comparison of horizontal uniaxial tensile test apparatus with frictional fixationSoil sample fixationResearch scholarParticular yearSpecific fixing methodEarthworkSoil typeLength of tensile section (mm)Ways to eliminate frictionFrictional fixationLu et al.^157^^,^^158^20052007a tube for wrappingshotcoarse soil (SM)–leangritcoarse soil (SP)medium sandcoarse soil (SP)Lv et al.^163^2013Boltred clayfine grained soil (CH)–glass paneexpansive soilfine grained soil (CH)SM, silty sand; SP, poorly graded sand; and CH, high liquid limit clay.
Clamping fixation is defined as a method where specimens are secured through a mold designed with narrowed central sections and widened ends, utilizing the mold’s opposing inclined surfaces to provide mechanical restraint.
Towner^164^ developed a C-shaped mold design for vertical uniaxial tensile tests, incorporating top and bottom clamping mechanisms with a dedicated tensile section as illustrated in Figure 13A. Subsequently, Volkan et al.^165^ investigated compacted fine-grained soils using a modified C-shaped configuration featuring reduced transition angle inclination. Multiple research groups have employed hourglass-shaped molds for specimen clamping in tensile testing. Tang et al.,^14^^,^^166^^,^^167^ Li et al.,^168^ Tran et al.,^169^ Ji et al.,^112^^,^^170^^,^^171^^,^^172^^,^^173^ and Zhang et al.^174^ all adopted this symmetrical clamping configuration, as demonstrated in Figure 13B, for soil tensile characterization across various experimental programs.Figure 13Vertical uniaxial tensile test with clamping fixation(A) Towner^164^(B) Tang et al.^14^
To mitigate the influence of specimen self-weight inherent in vertical configurations, researchers have progressively adopted horizontal testing methods. Based on structural distinctions among clamping molds, these methods can also be categorized into several primary types, including hourglass-shaped, C-shaped, dumbbell-shaped, and other specialized geometries.
Perkins et al.^175^ implemented an hourglass-shaped clamping configuration by inserting wedge elements into a rectangular mold, creating a tensile section with effectively zero length. Frictional interference between the mold base and loading platform was eliminated through integrated guide rails, as depicted in Figure 14A. This experimental configuration was subsequently adopted by Kim et al.,^176^^,^^177^^,^^178^ Arslan et al.,^179^ and Divya et al.^180^ for their uniaxial tensile investigations. Building on the Perkins experimental framework, Jhuo et al.^181^ systematically evaluated specimen clamping performance using triangular (10°, 20°, 30°), trapezoidal (30°), and rectangular wedge profiles. Their analysis determined that trapezoidal and rectangular geometries were unsuitable for uniaxial tensile testing, while triangular wedges demonstrated viable performance, with tensile strength exhibiting a hyperbolic decrease as the wedge angle diminished.Figure 14Horizontal uniaxial tensile test with hourglass-shaped clamping fixation (mm)(A) Perkins et al.^175^(B) Mikulitsch et al.^182^(C) Ziegler et al.^183^(D) Cai et al.^116^
Mikulitsch et al.,^182^ Stirling et al.,^57^ and Tang et al.^167^ eliminated wedge components by directly fabricating hourglass-shaped tensile molds featuring widened ends and a constricted central region. This integrated design utilized the mold’s inherent geometry to provide specimen constraint, as presented in Figure 14B. Ziegler et al.^183^ extended the tensile section to 25 mm in molds derived from the Mikulitsch design to improve stress distribution uniformity (Figure 14C), though frictional effects between the mold base and platform were not addressed. Subsequently, Tollenaar et al.^184^ incorporated ball bearings beneath similar molds to reduce basal friction while implementing a 24 × 24 × 80 mm tensile section geometry, achieving significant mitigation of stress concentration effects. This experimental paradigm has been further employed by Rodríguez et al.,^185^ Prat et al.,^186^ Chebbi et al.,^187^ Lakshmikantha et al.,^188^ Trabelsi et al.,^189^^,^^190^^,^^191^ and Cai et al.^116^ Notable implementations include Trabelsi’s 20 mm tensile section with rail-guided friction reduction, and Cai’s configuration featuring a 20 × 26 × 52 mm tensile section, base-mounted guide rails, and 20° clamping inclination (Figure 14D). The optimal inclination angle of 18.4° was determined analytically through the following (Equation 11)tan[arctan(1/μ)−α]tanα≥tanψwhere α represents the sidewall inclination angle relative to the horizontal plane, μ denotes the coefficient of friction (0.45), and ψ indicates the dilation angle (20°) for the fine sand tested.
Tamrakar et al.^192^^,^^193^^,^^194^^,^^195^ and Akagawa et al.^196^ reconfigured the conventional hourglass-shaped mold into dual C-shaped components incorporating ball bearings at their base, as presented in Figure 15A. Subsequently, Xiang et al.^197^ employed a similar mold design with slotted interfaces replacing ball bearings, although the zero-length tensile section in this configuration failed to improve tensile stress distribution and induced stress concentration at the grip interfaces.^138^ To address these limitations, Cui et al.^198^^,^^199^^,^^200^ developed an advanced apparatus featuring interchangeable tensile segments of four distinct lengths (10, 20, 40, and 80 mm). Concurrently, Vesga et al.^201^ and Wang et al.^202^ reduced the clamping inclination angle in C-shaped configurations to mitigate stress concentration effects, as demonstrated in Figure 15B.Figure 15Horizontal uniaxial tensile test with C-shaped clamping fixation(A) Tamrakar et al.^197^(B) Vesga et al.^203^ and Wang et al.^204^
To address persistent challenges of non-uniform stress distribution and localized stress concentration, Zhang et al.^205^ introduced a dumbbell-shaped mold design incorporating smooth bidirectional curvature transitions, replacing conventional hourglass-shaped linear and C-shaped transitions. This configuration featured a 100 × 50 × 50 mm tensile section and integrated sliding guides beneath the mold assembly, as illustrated in Figure 16A. Concurrently, Fan et al.^206^ developed an adjustable dumbbell-shaped mold system permitting tensile section lengths from 80 to 110 mm, incorporating roller mechanisms for friction reduction as demonstrated in Figure 16B.Figure 16Horizontal uniaxial tensile test with dumbbell-shaped clamping fixation (mm)(A) Zhang et al.^205^(B) Fan et al.^206^
Nahlawi et al.^25^ introduced an innovative clamping mold design featuring a square configuration with integrated serrated grip surfaces, significantly enhancing clamping effectiveness while incorporating ball bearings for friction mitigation as shown Figure 17A. Frías-Guzmán et al.^203^ developed an alternative fixation method by positioning two separation plates within a pre-formed specimen seam, creating a 90° interlocking structure with side plates. Tensile loading was achieved through controlled platform retraction that progressively separated these embedded plates, as illustrated in Figure 17B.Figure 17Horizontal uniaxial tensile test with clamping fixation of other shapes(A) Nahlawi et al.^27^(B) Frías-Guzmán et al.^207^
Furthermore, soil materials were systematically classified according to specification^144^ enabling the chronological organization of horizontal uniaxial tensile test apparatus utilizing clamping fixation in Table 4.Table 4Comparison of horizontal uniaxial tensile test apparatus with clamping fixationSoil sample fixationResearch scholarParticular yearSpecific fixing methodEarthworkSoil typeLength of tensile section (mm)Ways to eliminate frictionClamping fixationPerkins et al.^175^1991hourglass-shaped (triangular wedge-shaped block)moon soil simulation material MLS-1–0slidewayKim et al.^176^^,^^177^^,^^178^200320042008hourglass-shaped (triangular wedge-shaped block)sandy soil F-75coarse soil(SP)0slidewayArslan et al.^179^2008hourglass-shaped (triangular wedge-shaped block)moon soil simulation material JSC-1coarse soil (SM)0slidewayPrat et al.^186^2008hourglass-shaped (triangular wedge-shaped block)silty claycoarse soil (CL)0slidewayDivya et al.^180^2014hourglass-shaped (triangular wedge-shaped block)natural soilfine grained soil (CL)0slidewaybentonite-natural clay mixturesfine grained soil (CH)Jhuo et al.^181^2019hourglass-shaped (triangular, trapezoidal, rectangular wedge blocks)sand-clay mixturescoarse soil (SC)0slidewayMikulitsch et al.^182^1995hourglass-shapedloess–––Ziegler et al.^183^1998hourglass-shapedfiber reinforced soil–25–Rodríguez et al.^185^2007hourglass-shapedLow plasticity sludgefine grained soil (ML)20ball bearingTrabelsi et al.^189^^,^^190^^,^^191^201020122018hourglass-shapedloamfine grained soil (CH)20slidewayLakshmikantha et al.^188^2012hourglass-shapedsilty clayfine grained soil (CL)20ball bearingStirling et al.^57^2015hourglass-shapedkaolin-bentonite-sand mixturesmodified glacial claycemented silty sandcoarse soil (SP)0Restraint Bracketcoarse soil (SC)coarse soil (SM)Tollenaar et al.^184^2017hourglass-shapedloamfine grained soil (CH)24ball bearingTang et al.^167^2019hourglass-shapedloamfine grained soil (CL)0slidewayCai et al.^116^2020hourglass-shapedunsaturated sandy soilcoarse soil (−)20slidewayChebbi et al.^187^2020hourglass-shapedloamfine grained soil (CH)140–Tamrakar et al.^192^^,^^193^^,^^194^^,^^195^20052007C-shapedloamfine grained soil (CH)0linear slide rollersandfine grained soil (−)sandy soilcoarse soil (SP)hetian sandcoarse soil (SP)kantō loamfine grained soil (CH)Vesga et al.^201^2006C-shapedloamfine grained soil (−)0–Cui et al.^198^^,^^199^^,^^200^2016C-shapedloamfine grained soil (CL)10/20/40/80ballsWang et al.^202^2020C-shapedsandy clayfine grained soil (CLS)0bearXiangwei et al.^197^2021C-shapedReinventing the Loessfine grained soil (−)0slotsZhang et al.^205^2014dumbbell-shapedloamfine grained soil (CL)100slidewayFan et al.^206^2014dumbbell-shapeddispersed soilfine grained soil (CL)80∼110tirenon-dispersed soiltransitional soilNahlawi et al.^25^2004dentate projectionloamfine grained soil(CH)50ball bearingFrías-Guzmán et al.^203^2019separator platefive types of sandy soilcoarse soil (−)0bearSP, poorly graded sand; SC, clayey sand; SM, silty sand; CH, high liquid limit clay; CL, low liquid limit clay; ML, low liquid limit silty sand; CLG, gravelly low liquid limit clay; CLS, sandy low liquid limit clay.
Indirect testing methods derive tensile strength through theoretical frameworks that presuppose linear-elastic or elastic-perfectly plastic soil behavior, thereby circumventing direct tensile loading. These approaches employ compressive or flexural loading configurations, with subsequent calculation of tensile strength via analytical solutions. The comparative advantages and limitations of indirect tensile tests are systematically summarized in Figure 18.Figure 18Summary of indirect testing methods
The beam bending test offers operational simplicity and loading conditions that effectively simulate field scenarios. However, its analytical framework neglects beam self-weight effects, potentially compromising measurement accuracy. Conversely, the Brazilian test provides exceptional efficiency and represents the most prevalent method for tensile strength determination, though its theoretical basis demands material homogeneity and isotropy in both strength and elastic properties—conditions predominantly satisfied only in brittle soils.
The axial fracture test eliminates common experimental artifacts including stress concentration and grip misalignment while accommodating multi-directional testing capabilities. Nevertheless, constraints in loading mechanisms and boundary conditions restrict its capacity to determine in situ stress states. Similarly, the hollow cylinder test and other indirect methodologies presuppose either perfectly elastic or ideal plastic material responses with uniform tensile stress distribution across failure surfaces, consequently exhibiting optimal suitability for brittle, elastic materials.
In direct testing methods, tensile load is applied directly to both ends of soil specimens, enabling precise control of both load and displacement parameters. Consequently, these methods have gained increasing adoption in tensile strength research. The triaxial tensile test offers minimal apparatus requirements while enabling simulation of soil tensile behavior under complex three-dimensional stress states at specific depths, thereby providing more realistic approximations of engineering conditions. However, the triaxial tensile test involves complex loading conditions and failure mechanisms, where the axial stress at specimen failure transitions progressively from tensile to compressive as confining pressure increases. Furthermore, end effects and constraint conditions significantly influence measurement accuracy in triaxial tension configurations. For the uniaxial tensile test, systematic evaluation of existing apparatus and methodologies reveals several persistent factors that continue to affect measurement reliability in direct testing approaches.
The uniaxial tensile test can be classified into vertical and horizontal configurations based on loading direction. In vertical testing, the self-weight of the upper soil section above the fracture plane introduces measurement artifacts. Although this effect can be mathematically compensated by measuring the combined mass of the upper specimen segment and its mold attachment, such correction procedures increase computational complexity. Furthermore, vertical orientation presents practical challenges for large-scale specimens typically prepared in horizontal configurations.
In contrast, the horizontal uniaxial tensile test provides significant advantages, including direct acquisition of stress-strain relationships and inherent elimination of gravitational effects, making it the predominant methodology in contemporary research. However, frictional resistance between specimen molds and testing platforms remains a persistent challenge. Conventional mitigation approaches employ guide rails, bearing systems, or roller mechanisms to transform sliding friction into rolling friction, though residual frictional interference continues to affect measurement precision.
Complete elimination of frictional artifacts would substantially improve tensile stress measurement accuracy. An innovative solution proposed by Yu et al.^204^ utilizes magnetic levitation to achieve frictionless suspension of both mold and platform assemblies in horizontal three-point bending configurations, potentially resolving this fundamental experimental limitation.
The secure immobilization of soil specimens in uniaxial tensile test apparatus, specifically the effective application of tensile force, has long represented a fundamental challenge in experimental soil mechanics. Since the late 20th century, specimen fixation techniques have undergone continuous discussion and refinement.^24^ Four primary fixation methods are currently employed in uniaxial tensile adhesive fixation, anchorage fixation, frictional fixation, and clamping fixation.^31^ Figure 19 systematically summarizes the limitations associated with these different fixation approaches.Figure 19Summary of uniaxial tensile test with different fixation methods
Specifically, adhesive fixation necessitates not only cumbersome procedures but also meticulous surface preparation to ensure bonding integrity between the mold and soil specimen. Inadequate adhesion compromises force transmission reliability and frequently induces stress concentration or premature failure at the interface. Furthermore, prolonged adhesive curing durations may alter the soil’s moisture content.
Anchorage fixation introduces distinct when anchors are installed after specimen completion, the specimen ends are damaged. When they are pre-embedded during the preparation process, the procedure, particularly layered compaction, is hindered.
Frictional fixation requires circumferential clamping around the specimen exterior. Precise bolt tightness control presents critical operational difficulties—excessive compression risks specimen damage while insufficient force permits slippage. Moreover, enhancing frictional resistance necessitates expanded mold-soil contact area, which inherently shortens the tensile section and potentially generates stress concentration.
In contrast, clamping fixation converts the specimen mold into a tensile fixture through simple disassembly, leaving the soil specimen intact within the mold and utilizing its inherent structure for fixation. This approach reduces operational time and specimen damage while improving success rates. Because the geometry of the mold remains constant, the clamping force and initial stress state of the specimen are reproducible and unaffected by variations in soil moisture content or dry density. This consistency eliminates the clamping uncertainties introduced in conventional methods that require specimen transfer. It should be noted, however, that the tensile force transmitted through the interlocking of the device and the specimen inevitably produces uneven stress distribution. This effect is particularly pronounced in hourglass-shaped or C-shaped fixtures—as shown in Figure 20, such geometries generate localized stress concentrations along the inner jaw edges due to abrupt sectional changes. Severe concentrations can induce localized permanent deformation or fracture. While serrated jaw surfaces (Figure 17A) and dumbbell-shaped (Figure 16) clamping fixation methods partially alleviate this issue, the former increases preparation complexity. A more practical path for future device development may involve implementing jaw structures with smoothly curved, dumbbell-shaped transitions (Figure 16).Figure 20Stress concentration occurs at the gripping jaws(Lakshmikantha^188^).
Analysis of soil types employed in uniaxial tensile tests, as summarized in Tables 1, 2, 3, and 4, indicates a predominant use of fine-grained soils, with coarse-grained soils representing a minor proportion. These materials encompass multiple poorly graded sand, clayey sand, silty sand, high-plasticity clay, low-plasticity clay, low-plasticity silty clay, gravelly low-plasticity clay, and sandy low-plasticity clay. When categorized by fixation methodology, adhesive and anchorage fixation techniques are primarily applied to fine-grained soils, particularly high- and low-plasticity clays. In contrast, frictional and clamping fixation demonstrates compatibility with both fine- and coarse-grained soil types. Soil composition significantly influences tensile measurement outcomes, as variations in soil properties directly affect mechanical responses. Notably, clamping fixation exhibits superior versatility across diverse soil classifications, suggesting broader applicability in experimental geomechanics.
(1)Soil specimens are frequently compromised during transfer from molding to tensile apparatus due to handling during demolding and disassembly, resulting in premature test termination. Consequently, development of integrated molding-tensile apparatus is recommended to enable direct testing following specimen formation, requiring only minimal disassembly steps.(2)Current tensile strength investigations are predominantly confined to homogeneous soil types (e.g., clays and loess), while mold dimensions remain generally insufficient for testing wide-graded soils. Many such geomaterials contain particles exceeding 100 mm in maximum dimension, necessitating gradation scaling through particle size reduction prior to testing. However, this process alters original aggregate distribution characteristics, introducing systematic deviations between experimental results and actual mechanical behavior that may engender significant engineering risks.^208^ To minimize these artifacts, scaled gradations should closely approximate the original soil structure without exceeding mold capacity constraints. According to standardized Geotechnical Test Methods (GB/T 50123–2019)^209^ and Geotechnical Test Procedures (SL 237–1999),^131^ maximum particle dimensions must be maintained within 1/6–1/4 of specimen height for consolidation testing and below 1/5 of specimen diameter for triaxial compression testing. Current mold configurations typically provide maximum tensile section lengths of approximately 160 mm,^112^^,^^129^^,^^152^^,^^153^^,^^170^^,^^171^^,^^172^^,^^173^^,^^174^ thereby restricting testable particle sizes to below 32 mm. This limitation presents fundamental constraints for wide-graded soil characterization. Consequently, modest increases in minimum mold dimensions should be considered, though device upscaling may introduce operational complexities. Numerical simulation of larger scale specimens represents a promising complementary approach for advancing research in this domain.(3)A further limitation concerns the frequently abbreviated length of specimen tensile sections, which induces non-uniform stress distributions. In their investigation of gravelly soils, Zhu et al.^153^ and Zhang et al.^152^^,^^153^ designed specimens with 150 mm total length and 61.8 mm diameter, incorporating 40-mm long clamping segments at both ends to establish an effective 70 mm tensile section. This configuration partially alleviated stress concentration issues. However, the elongation of the tensile section introduces significant vertical shear stresses from increased self-weight in horizontal configurations. Consequently, bearing supports or similar stabilization mechanisms should be implemented beneath extended tensile sections to counterbalance gravitational effects.
Consequently, standardized methodologies and procedures for the horizontal uniaxial tensile test should be established to unify experimental apparatus specifications and dimensional parameters, thereby minimizing the influence of mold configuration on test results.
Both indirect and direct tensile testing methods necessitate that soil specimens sustain tensile forces until failure at their ultimate limit. Extensive comparative analyses of these methods have been conducted by numerous researchers. For instance, Li et al.^207^ evaluated the tensile strength of cohesive soils using beam bending tests, Brazilian tests, axial fracture tests, and uniaxial tensile tests, establishing functional correlations among them. Their findings indicate that the Brazilian test and axial fracture test provide the simplest and most efficient methods for determining tensile strength, whereas uniaxial tensile tests enable explicit observation of soil deformation. Furthermore, studies by Kezdi^210^^,^^211^ and Ajaz et al.^49^^,^^212^^,^^213^ compared uniaxial tensile test and uniaxial compression with beam bending tests, confirming distinct characteristics between tensile and compressive stress-strain responses. These investigations demonstrated that the tensile modulus substantially exceeds the compressive modulus, with the tensile stress-strain relationship transitioning from linear to nonlinear behavior under increasing load. In a separate comparative study, Zhu^117^ performed beam bending tests, Brazilian tests, axial fracture tests, and uniaxial tensile tests on various clay types. The results revealed that the beam bending test consistently yielded higher tensile strength values, whereas the Brazilian and axial fracture tests produced comparatively lower measurements. Similarly, Yoginder^214^ performed parallel comparisons between triaxial tensile tests and horizontal uniaxial tensile tests on cohesive soils, documenting superior tensile strength in horizontal configurations under identical stress path conditions. Notably, the Tsinghua University Rock-Fill Dam Crack Resistance Research Group^54^ contrasted beam bending tests with uniaxial tensile tests on clay specimens. Their analysis confirmed that the former method generates higher tensile strength values than the latter, while also revealing a nonlinear stress-strain relationship for the tested soil material.
Indirect testing methods are generally characterized by simpler apparatus and more straightforward operation than their direct counterparts. These methods facilitate the determination of soil tensile strength while effectively circumventing common experimental challenges such as specimen misalignment, fixation complexities, and stress concentration.^106^ The fundamental principle underlying indirect testing methods involves calculating tensile strength based on specific theoretical assumptions, primarily the presumption of uniformly distributed tensile stress across the failure plane. However, significant discrepancies exist between these theoretical foundations and actual soil mechanical behavior. Soils typically exhibit lower tensile strength and higher ductility than brittle materials such as concrete or rock. Consequently, the uniform stress distribution assumption inherent in indirect testing methods contradicts the genuine mechanical properties of soils, resulting in non-uniform stress fields across the failure surface. The derived tensile strength values may therefore deviate substantially from actual measurements, failing to accurately represent the material’s true tensile capacity while precluding direct acquisition of stress-strain relationships or tensile force-displacement curves. The beam bending test presupposes that plane sections remain planar during bending and that material response follows Hooke’s law. This method calculates tensile stress and strain at the tension-bearing edge through deflection measurements using formulae from material mechanics. Nevertheless, this elastic framework contradicts actual soil mechanical behavior. Similarly, the Brazilian test postulates a linear elastic stress-strain relationship, deriving tensile strength from the specimen’s ultimate load—an assumption that substantially diverges from realistic soil characteristics. The axial fracture test, while methodologically analogous to the Brazilian test, incorporates plastic theory to compute tensile strength from the maximum failure load. Beyond sharing limitations with the Brazilian test regarding drainage control and confining pressure application, this method introduces additional complications including unconstrained aspect ratios and arbitrary liner dimension selection. Therefore, tensile strength values obtained through indirect testing methods consistently demonstrate systematic deviations from actual measurements. Furthermore, these methods demonstrate superior suitability for brittle, elastic materials such as rigid, highly compacted, or chemically stabilized soils compared to ductile geomaterials including soft and moist clays.^14^ Given these fundamental limitations in accuracy and applicability, the research community increasingly favors direct testing methods, particularly triaxial and uniaxial tensile tests, for rigorous investigation of soil tensile properties.
In direct testing methods, the triaxial tensile test offers the distinct advantage of requiring minimal specialized apparatus, as it can be conducted using conventional triaxial apparatus. However, specialized fixation methods are required for the specimen ends. During testing, confining pressure and axial load can be precisely controlled according to in situ stress conditions, enabling simulation of soil tensile behavior at specific depths under complex three-dimensional stress states, thereby providing a more realistic approximation of actual engineering scenarios. This method provides direct measurements of stress-strain curves under lateral confinement, tensile strength, ultimate tensile strain, and tensile modulus. Furthermore, by controlling drainage conditions during testing, the determination of Poisson’s ratio is enabled. Consequently, this method was among the earliest methods adopted for investigating soil tensile strength.^119^ During the early 21st century, triaxial testing remained extensively employed in soil tensile strength research.^87^^,^^88^^,^^89^^,^^90^^,^^91^^,^^92^^,^^93^^,^^94^^,^^95^^,^^96^^,^^97^^,^^98^^,^^99^^,^^100^ Subsequent investigations, driven by advanced understanding of soil behavior, progressively shifted focus toward tensile failure mechanisms. Triaxial tests encompass diverse failure modes, including pure shear, shear-elongation progressing to tensile failure, and pure tensile failure. The axial stress at specimen failure systematically transitions from tensile to compressive as confining pressure increases. Notably, end effects and constraint conditions in triaxial tensile testing introduce significant discrepancies between measured and actual tensile strength values. In contrast, the uniaxial tensile test represents the most straightforward and effective method for determining soil tensile strength,^130^^,^^215^ while offering superior capability for simulating and analyzing failure mechanisms. This approach effectively simulates the tensile state of surface soils in geotechnical structures. Although specimen end fixation still necessitates specialized techniques, the well-defined loading conditions yield stable and reproducible results. The method provides complete characterization including stress-strain relationships under tensile loading, tensile strength, ultimate tensile strain, and tensile modulus, establishing it as a comprehensive method for soil tensile strength measurement.
Experimental evidence indicates that numerous soil deposits, including laboratory-prepared specimens, exhibit cross-anisotropic behavior. This inherent cross-anisotropy represents a fundamental characteristic of particulate assemblies deposited under gravitational fields with a single vertical axis of symmetry, even in assemblies comprising perfectly spherical particles.^216^^,^^217^^,^^218^ The distinction between inherent anisotropy, which describes the material’s anisotropic state before loading, and induced anisotropy, developing through loading history, was first articulated by Casagrande,^219^ highlighting the crucial role of anisotropy in soil mechanics. When investigating soil mechanical properties under anisotropic conditions, the true triaxial test represents the most rigorous experimental approach. This method enables independent application of confining pressures along three orthogonal axes, thereby accurately capturing the soil’s anisotropic response. Its implementation proves particularly essential for examining soil behavior under complex stress states. However, the true triaxial apparatus demonstrates inherent complexity and substantial costs, requiring significant investment in both specialized equipment design and operational procedures. The test demands sophisticated loading systems and precise pressure control mechanisms, consequently elevating equipment design, maintenance, and operational expenditures.
This review systematically summarizes advancements in soil tensile testing methods, encompassing experimental investigations, theoretical frameworks, and influencing factors for soil tensile strength through both indirect and direct testing methods. Existing studies demonstrate that comprehensive understanding of soil tensile cracking mechanisms relies on accurate and reliable measurement techniques. This section concludes with synthesizing remarks and future research directions.
Among experimental apparatus for soil tensile strength measurement, indirect testing methods are characterized by operational simplicity and enable tensile strength derivation through analytical formulas. However, these methods necessitate the assumption of linear elastic material behavior, a theoretical premise inconsistent with actual soil mechanical properties. This fundamental discrepancy leads to potential deviations between derived tensile strength values and actual measurements. Furthermore, indirect testing methods cannot directly acquire stress-strain relationships or tensile force-displacement curves, whereas direct testing methods effectively overcome these limitations. Direct testing methods are categorized into triaxial and uniaxial tests based on confinement conditions. Notably, end effects and constraint conditions during triaxial testing significantly influence measurement accuracy, leading to increased research preference for uniaxial testing configurations.
Several critical factors continue to affect direct method measurements. In vertical loading configurations, stress measurements incorporate the self-weight of soil above the fracture plane. Similarly, horizontal loading methods introduce frictional interference between mold bases and loading platforms. Regarding specimen fixation, adhesive, anchorage, and frictional fixation methods all present varying limitations that may compromise test validity. Additional challenges include soil disturbance during demolding and transfer to tensile apparatus following specimen preparation. Current apparatus designs show insufficient addressing of excessive tensile segment shortening and non-uniform stress distribution. Furthermore, dimensional constraints of existing equipment limit their applicability for characterizing wide-graded soils.
Future research on soil tensile cracking should prioritize minimization of specimen disturbance during preparation, demolding, and installation processes. An integrated sample-tensile mold design enabling direct testing through simplified disassembly represents a promising approach. For horizontal testing methods, frictional effects between mold and platform require rigorous mitigation. Clamping fixation demonstrates superior operational feasibility compared to adhesive, anchorage, or frictional alternatives. For coarse-grained wide-graded soils, non-uniform stress distribution can be ameliorated through dumbbell-shaped curved transitions in mold jaw design or by extending tensile segments beyond 200 mm. Ensuring the minimum tensioned dimension exceeds four times the maximum particle size in wide-graded soils will improve particle-mold compatibility and reduce particle size effects. Additionally, numerical simulations on larger-scale specimens enable detailed analysis of tensile characteristics in coarse-grained materials, driving novel advancements in this research domain.
The findings of this review should be interpreted with the recognition that they are based solely on the accessible body of literature.
This work was supported by 10.13039/501100002858China Postdoctoral Science Foundation (grant nos. 2025T180860, 2025M783180 and 2024M760736), 10.13039/501100010855Department of Human Resources And Social Security of Jiangsu Province, Jiangsu Funding Program for Excellent Postdoctoral Talent (grant no. 2025ZB625), 10.13039/501100001809National Natural Science Foundation of China (grant no. 52409155), and 10.13039/501100004608Natural Science Foundation of Jiangsu Province (grant no. BK20241522).
Y.S., writing – review and editing and writing – original draft; W.H., supervision; Y.H., investigation; H.Z. and L.G., funding acquisition; J.Y., data curation; W.Y., project administration; Z.S., conceptualization; L.X. and L.L., review and editing and data curation.
The authors declare no competing interests.