Mohr-Coulomb Strength Parameters Research Articles

Modified minimum principal stress estimation formula based on Hoek–Brown criterion and equivalent Mohr–Coulomb strength parameters

The most critical parameter for determining equivalent values for the Mohr–Coulomb friction angle and cohesion from the nonlinear Hoek–Brown criterion is the upper limit of confining stress. For rock slopes, this value is the maximum value of the minimum principal stress (sigma_{3,max }^{prime }) on the potential failure surface. The existing problems in the existing research are analyzed and summarized. Using the finite element method (FEM), the location of potential failure surfaces for a wide range of slope geometries and rock mass properties are calculated using the strength reduction method, and a corresponding finite element elastic stress analysis was carried in order to determine sigma_{3,max }^{prime } of the failure surface. Through a systematic analysis of 425 different slopes, it is found that slope angle (β) and geological strength index (GSI) have the most significant influence on sigma_{3,max }^{prime } while the influence of intact rock strength and the material constant m_{i} are relatively small. According to the variation of sigma_{3,max }^{prime } with different factors, two new formulas for estimating sigma_{3,max }^{prime } are proposed. Finally, the proposed two equations were applied to 31 real case studies to illustrate the applicability and validity.

Bearing capacity of foundations resting on rock masses subjected to Rayleigh waves

This study investigates the ultimate bearing capacity of shallow foundations resting on rock masses under earthquakes using upper-bound limit analysis. A modified pseudodynamic method (MPD) that considers the influence of Rayleigh waves is initially used to characterize the spatiotemporal variation in earthquake acceleration. The strength of rock masses is governed by the generalized Hoek‒Brown criterion and the plastic flow at failure is assumed to respect the associated flow rule. The generalized tangential technique is introduced to provide a linear approximation of the strength envelope for capturing the equivalent Mohr‒Coulomb strength parameters. The classic nonsymmetrical multi-block translational mechanism, which is capable of assessing a rock-foundation system under asymmetrical load, is reconstructed to portray the velocity discontinuity of the plastic failure region. Based upon the energy equilibrium theorem of the limit analysis, an analytical solution of seismic bearing capacity is derived and then formulated as a multivariate optimization problem. Comparisons show good agreement with the literature and validate the correctness and rationality of this work. Parametric study indicates that the seismic foundation capacity obtained by MPD tends to be conservative compared to the pseudostatic method with the same seismic coefficients, and that the period of a Rayleigh wave has only a slight effect on the bearing capacity. The failure region is more sensitive to the disturbance coefficient than it is to the other rock strength parameters.

Stress–Strain Strength Characteristics of Undisturbed Granite Residual Soil Considering Different Patterns of Variation of Mean Effective Stress

Granite residual soil is one of the most frequently encountered problem soils in tropical regions, whose mechanical behavior heavily depends on the pattern of variation of mean effective stress (p’) during shearing, which can be classified into three categories: increasing-p’, constant-p’, and decreasing-p’. Unfortunately, so far, the stress–strain strength characteristics of granite residual soils have been studied mainly under increasing-p’ stress paths, although it is very likely to encounter stress paths with decreasing p’ in practice, especially in excavation engineering. Moreover, most pertinent research has focused on remolded granite residual soils, whereas undisturbed specimens have not yet received enough attention. In this paper, stress path triaxial tests considering different patterns of variation of mean effective stress were conducted on an undisturbed granite residual soil. Subsequently, a variable termed loading angle was introduced to quantitatively represent stress path. The influences of stress path on the Mohr–Coulomb strength parameters, deformation characteristics, ductility, and shearing stiffness were analyzed, with an emphasis on the role of pattern of variation of mean effective stress. The experimental results show that friction angle of the soil increases while cohesion decreases with the increase in loading angle. The increase in loading angle leads to less volume contraction and smaller failure strain. During shearing, the soil exhibited a less brittle response under stress paths with smaller loading angles. The initial secant shear modulus first decreased and then increased as the loading angle increased, with the minimum shearing stiffness occurring at a certain loading angle lying between 90° and 123.7°.

A Return Mapping Algorithm for Nonlinear Yield Criteria with the Equivalent Mohr–Coulomb Strength Parameters

This paper proposes a modified return mapping algorithm for a series of nonlinear yield criteria. The algorithm is established in the principal stress space and ignores the effect of the intermediate principal stress. Three stress return schemes are derived in this paper: return to the yield surface, return to the curve, and return to the apex point. The conditions used for determining the correct stress return type are also constructed. After the proposed algorithm is programmed in the finite element software, we merely need the equivalent Mohr–Coulomb (M-C) strength parameters, the derivatives of their functions, and the tensile strength of these nonlinear yield criteria. In addition, the Hoek–Brown (H-B) yield criterion is taken as an example to validate the proposed method. The results show that the updated stresses and the final principal stresses obtained by the proposed method are in good agreement with those obtained by other methods. Furthermore, the proposed method is more suitable for the associated plastic-flow rule.

Constitutive models for FE analysis of pile founded buried arch bridge

The paper presents plane strain FE modeling of a pile founded bridge, made from reinforced concrete, by using plate elements for the structure and the soil body. The soil-structure contact is modeled by interface finite elements. The numerical analysis is performed by the Plaxis 2D software. The mechanical behavior of the bridge is approximated by the constitutive models of Hooke and Mohr-Coulomb. Two sets of values of the Mohr-Coulomb strength parameters (cohesion and internal friction angle) for the concrete are obtained - on the basis of the theoretical uniaxial compressive and tensile strengths and on the basis of relationships in the Eurocode 2. The advanced constitutive HSM model is used for the soil. The construction and service periods of the bridge are simulated by a sequence of representative states. The mechanical response of the bridge undergoing backfill and road loads is analysed.

Mobilized Mohr-Coulomb and Hoek-Brown Strength Parameters during Failure of Granite in Alxa Area in China for High-Level Radioactive Waste Disposal

Strength parameters of the host rock is of paramount importance for modelling the behaviors of underground disposal repository of high-level radioactive waste (HLW). Mobilization of strength parameters should be studied for a better understanding and modelling on the mechanical behaviors of the surrounding rock, considering the effect of temperature induced by the nuclear waste. The granite samples cored from NRG01 borehole in Alxa candidate area in China for HLW disposal are treated by different temperatures (T = 20 °C, 100 °C and 200 °C), and then are used to carry out a series of uniaxial and tri-axial compression experiments under various confining pressures (σ3 = 0, 5, 10, 20, and 30 MPa) in this study. With the recorded axial stress—axial strain and axial stress—lateral strain curves, mobilization of both Mohr-Coulomb and Hoek-Brown strength parameters are analyzed with the increasing plastic shear strain. It has been found that NRG01 granite samples show generally similar cohesion weakening and friction strengthening behaviors, as well as the non-simultaneous mobilization of Hoek-Brown strength parameters (mb and s), under the effect of various treatment temperatures. Furthermore, the samples treated by higher temperatures show lower initial values of cohesion, but their initial friction angle and mb values are relatively higher. This should be mainly owing to the thermally induced cracks in the samples. This study should be helpful for a better modelling on the mechanical behaviors of NRG01 granite samples as the host rock of a possible HLW disposal repository.

Determination of Model Parameters for the Hardening Soil Model

The Hardening Soil model, an elasto-plastic second-order hyperbolic isotropic hardening model, in Plaxis has seen many applications in finite element analysis of various earth structures. This technical note presents a protocol for determination of the model parameters of the Hardening Soil model from a set of triaxial compression tests. The technical note also describes details about how to determine the Mohr-Coulomb strength parameters c and ϕ for well-compacted fills (with and without cohesion), of which the failure envelopes are typically curved. The motivation for preparing this technical note came from a study on analysis of field-scale soil–geosynthetic composites in which the soil model and model parameters deduced from triaxial tests were able to predict with very good accuracy “all” measured results of five field-scale soil–geosynthetic composites under increasing applied vertical loads up to 1000 kPa (approximately five times the load level commonly used in design of reinforced soil bridge abutments). The model parameters were determined by a well-defined protocol. The protocol should be of value to researchers and engineers who use the soil model for sophisticated finite element analysis and design of earth structures.

Laboratory Shear Strength Measurements of Municipal Solid Waste at Room and Simulated In Situ Landfill Temperature, Barmshoor Landfill, Iran

This study was aimed to determine the influence of temperature within the landfill on the shear strength of the MSW samples through the shearing procedure. Different waste samples, i.e., the fresh (C1), 2 years old (C1-2Y) and lab oratory prepared (C2) MSW samples, were heated up, prepared, and placed in the shearing box with the designated temperatures of about 25, 45, and 65 °C (i.e., the range of an anaerobic landfill). The Mohr–Coulomb strength parameters for the warmed-up and room-temperature specimens were separately calculated and compared. The temperature decreases the friction angle from 21 to 17° for T > 45 °C. The cohesion was also decreased by temperature from 19.9 to 13.1 kPa. In addition, two nonlinear envelopes were developed for the specimens tested at room and simulated temperature within the landfill. The test results show a reduction of about 20% for friction angle and shear strength at the temperatures between 45 and 65 °C. Although the warmed-up specimens of fresh MSW were denser under certain normal stress, heating the MSW specimens to temperatures of 45 and 65 °C resulted in loss of the shear strength. Results further indicated that the temperature of the wastes plays an important role when the shear stress is conducted on the MSW specimens. It can be then concluded that temperature of the landfill should be considered as a factor influencing the shear strength of MSW. Considering temperature for site investigation of the shear strength and the correlation of the results with the laboratory tests is important, too.

Interpretation of Geomaterial Behavior during Shearing Aided by PIV Technology

AbstractSeveral researchers have studied the behavior of particles during shearing to have better insight into the Mohr-Coulomb (MC) strength parameters. In most cases, the movements of particles a...

Numerical simulations of triaxial compression tests of cemented sandstone

Three-dimensional DEM simulations of triaxial compression tests of cemented sandstone samples have been performed at different values of confining pressure, initial density and bond strength. The results show that with increase in bond strength, initial density and confining pressure both the initial stiffness and peak strength increase. For a higher bond strength and initial density the samples exhibit a higher rate of dilation. Bond breakage was found to increase with confining pressure and decrease with bond strength and initial density. The Mohr-Coulomb strength parameters c' and φ' were obtained for the numerical samples and correlations between the shear strength parameters and the bond strength were established. The correlations were then used to find the value of the bond strength to be used for comparisons with results of experimental triaxial tests. The stress-strain responses of the numerical samples were found to be in good agreement with the experimental results. The critical state lines (CSL) of triaxial compression tests for both loose and medium dense systems show that the critical void ratio is independent of the initial density but increases with increase in bond strength. Increasing the bond strength increases the dilation, which leads to ahighercriticalstatevoidratio.

Rock Slope Analysis with Nonlinear Hoek–Brown Criterion Incorporating Equivalent Mohr–Coulomb Parameters

In the present work, the results of rock slope analyses incorporating nonlinear Hoek–Brown yield criterion with equivalent Mohr–Coulomb strength parameters to simulate rock mass behaviour are presented. The factor of safety (FOS) of rock slopes are calculated using Morgenstern–Price and Spencer’s method. A simplified method of generating non-circular segmented failure surface is proposed. The search of minimum FOS and associated critical non-circular failure mass for rock slopes is performed by Particle swarm optimization (PSO) technique. A MATLAB code is developed incorporating nonlinear Hoek–Brown criteria with equivalent Mohr–Coulomb strength parameters and coupled with PSO to analyze stability of rock slopes. The efficiency and accuracy of the developed MATLAB code is established by comparing the obtained results with those from existing literatures. Furthermore, the analyses of slopes are performed with varying height and slope angle for an intact rock slope with varying material parameters such as Hoek–Brown constant $$m_{i}$$ and uniaxial compressive strength $$\sigma_{ci}$$ for rock material. It is found that the FOS value follows a decreasing pattern if height and the slope angles are increased.

Assessment of non-linear rock strength parameters for the estimation of pipe-jacking forces. Part 1. Direct shear testing and backanalysis

A method of backanalysis was used for the assessment of pipe-jacking forces from three pipe-jacking drives in laminated shale and interbedded lithological units of metagraywacke, siltstone, greywacke and phyllite found in the highly weathered and fractured lithologies of the Tuang Formation (Malaysia). Direct shear tests were conducted on reconstituted tunneling rock spoils sampled from three pipe-jacking sites. The direct shear test results were initially assessed using the Mohr-Coulomb failure criterion, which demonstrated severe shortcomings in capturing the nonlinear shear strength behavior of the reconstituted tunneling rock spoils. Subsequently, a simple power law function was proposed together with the generalized tangential method to obtain useful equivalent tangential cohesion, c't,p and friction angle, ϕ’t,p for the assessment of pipe-jacking forces in fractured lithologies. The outcomes from this study show that the tangential Mohr-Coulomb strength parameters can be used to backanalyze the frictional coefficient, μavg and the vertical stress at the tunnel crown, σEV. These backanalyzed values were successfully related back to the measured jacking forces and jacking speeds for pipe-jacking drives in various geological conditions and lubrication efforts. The use of the backanalyzed parameters c't,p, ϕ’t,p, μavg and σEV in the assessment of pipe-jacking forces from highly weathered rocks comprising of laminated and interbedded lithological units could lead to the prediction of jacking forces using numerical models. A companion paper to this study has also been produced to evaluate the reliability and suitability of these backanalyzed parameters for assessing pipe-jacking forces using the finite element method.

Upper Bound Solution for Required Supporting Pressure Applied on a Deep Shield Tunnel Face Under Different Groundwater Levels

The construction of shield tunnels is greatly influenced by the presence of groundwater. Based on the upper bound theorem of limit analysis, this paper presents an analytical investigation on the stability of shield tunnel face subjected to the impact of pore water pressure. Considering the nonlinear strength feature of soil mass, the nonlinear failure criterion of power-law type is employed, and the tangential technique is utilized to determine its equivalent Mohr–Coulomb strength parameters. The log-spiral failure mechanism for shield tunnel face is constructed, and three different cases of the relation between groundwater level and this mechanism are summarized. After that, rates of work of external forces and rate of internal energy dissipation are computed and analytical expression for the supporting pressure is deduced. Numerical solution with respect to specified parameters is calculated through optimization. Parametric analysis is performed and the variation of required supporting pressure with increasing height of groundwater level is presented.

Consolidated-undrained triaxial testing of Opalinus Clay: Results and method validation

Specific equipment and procedures developed for geomechanical testing of hydrocarbon caprocks were adopted to conduct truly undrained triaxial tests with Opalinus Clay. The amount of pore pressure development during consolidation, and the resulting effective stress, is managed by equilibrating the samples in vacuum desiccators of different relative humidities (vapor equilibration technique) prior to assembling into the test apparatus. A drained consolidation test was first conducted to determine the appropriate strain rate for consolidated-undrained (CU) triaxial testing. Opalinus Clay samples were then consolidated in the triaxial rig to mean effective stresses in the range from 3 to 52 MPa and eventually sheared. Within the explored stress range elastic and pore pressure coupling parameters were found to be stress dependent. The different stress paths to peak indicate a transition from overconsolidated to rather normally consolidated state, yet failure was in all tests dilatant, i.e. associated with a drop in pore pressure and strain-softening (more so at low effective stress). Accurate pore pressure monitoring enabled the discrimination of different deformation stages during deviatoric loading. In terms of Mohr–Coulomb strength parameters, transition from peak to post-peak strength is manifested by a reduction in the effective cohesion whereas the effective friction angle remains nearly constant. The robustness of the CU testing methodology is demonstrated by (i) diagnostic analyses, (ii) inconsistency of CU tests with two CU tests deliberately loaded faster to explore the effect of strain rate, and (iii) consistency of CU tests with two consolidated-drained tests. Finally, test results of two caprock shales are also shown for comparison. The caprocks are of similar basic properties as the Opalinus Clay and stem from a large data base of tests conducted using the same methodology.

Strength reduction method in Barodesy

Strength reduction analysis are very common in geotechnical engineering to define a factor of safety of structures, e.g. slopes. Usually, the Mohr-Coulomb strength parameters friction angle φ′ and cohesion c′ are reduced until limit equilibrium is reached. This method is only applicable to material models which utilize a Mohr-Coulomb or similar (e.g. Drucker-Prager) failure criterion. In this article a strength reduction method for the barodetic material model is introduced and the results of slope stability calculations compared with the results with an elasto-plastic material model (Mohr-Coulomb) and with the results of an analytical analysis according to Bishop are presented. The strength reduction method for barodesy has been implemented in the Finite Element code Abaqus.

Evaluation of Spalling Fallout on Excavation Disturbed Zone under Deep Hard Rock Tunnel

The prediction of compressive stress-induced failures is of concern when designing and constructing facilities in rock for deep underground excavation. The purpose of this study is to model compressive stress-induced failure and fallouts with appropriate material models and strength parameters for deep hard rock tunnel excavation. Three method of numerical modelling are used, which are Generalised Hoek-Brown; Mohr-Coulomb; and Mohr-Coulomb with Cohesion Softening Friction Hardening (CSFH) material models for capturing the observed rock behaviour. A parametric study was also carried out to verify that the peak friction angle of 10° used in CSFH model. The results show that numerical models used only Generalised Hoek-Brown and Mohr Coulomb strength parameters does not show a good agreement with the observed fallout. The comparison revealed that the numerical models using the Mohr-Coulomb with CSFH provides most realistic to the observation fallout length. This model is valid for prediction of failure and fallouts in hard rock masses with high quality (GSI >65 MPa; intact rock compressive strength >70MPa).

Stability analysis of slope in strain-softening soils using local arc-length solution scheme

Soils with strain-softening behavior — manifesting as a reduction of strength with increasing plastic strain — are commonly found in the natural environment. For slopes in these soils, a progressive failure mechanism can occur due to a reduction of strength with increasing strain. Finite element method based numerical approaches have been widely performed for simulating such failure mechanism, owning to their ability for tracing the formation and development of the localized shear strain. However, the reliability of the currently used approaches are often affected by poor convergence or significant mesh-dependency, and their applicability is limited by the use of complicated soil models. This paper aims to overcome these limitations by developing a finite element approach using a local arc-length controlled iterative algorithm as the solution strategy. In the proposed finite element approach, the soils are simulated with an elastoplastic constitutive model in conjunction with the Mohr-Coulomb yield function. The strain-softening behavior is represented by a piece-wise linear relationship between the Mohr-Coulomb strength parameters and the deviatoric plastic strain. To assess the reliability of the proposed finite element approach, comparisons of the numerical solutions obtained by different finite element methods and meshes with various qualities are presented. Moreover, a landslide triggered by excavation in a real expressway construction project is analyzed by the presented finite element approach to demonstrate its applicability for practical engineering problems.

Effects of nonlinear strength parameters on stability of 3D soil slopes

Actual slope stability problems have three-dimensional (3D) characteristics and the soils of slopes have curved failure envelopes. This incorporates a power-law nonlinear failure criterion into the kinematic approach of limit analysis to conduct the evaluation of the stability of 3D slopes. A tangential technique is adopted to simplify the nonlinear failure criterion in the form of equivalent Mohr-Coulomb strength parameters. A class of 3D admissible rotational failure mechanisms is selected for soil slopes including three types of failure mechanisms: face failure, base failure, and toe failure. The upper-bound solutions and corresponding critical slip surfaces can be obtained by an efficient optimization method. The results indicate that the nonlinear parameters have significant influences on the assessment of slope stability, especially on the type of failure mechanism. The effects of nonlinear parameters appear to be pronounced for gentle slopes constrained to a narrow width. Compared with the solutions derived from plane-strain analysis, the 3D solutions are more sensitive to the values of nonlinear parameters.

정수압에 의존하는 항복기준의 강도정수 비교연구

이론적 연구를 통하여 정수압의 영향을 받는 항복기준인 Mohr-Coulomb 항복기준과 Drucker-Prager 항복기준의 강도정수를 <TEX>${\pi}$</TEX>-평면에 대해 일치시킴으로써 강도정수간의 상관관계를 분석해 보았다. Drucker-Prager 강도정수 <TEX>${\alpha}$</TEX>와 k를 Mohr-Coulomb 강도정수인 c와 <TEX>${\phi}$</TEX>를 이용하여 표현하였는데 k는 c, <TEX>${\phi}$</TEX>의 함수로 표현되었고 <TEX>${\alpha}$</TEX>는 <TEX>${\phi}$</TEX>만의 함수로 표현되었다. Drucker-Prager 강도정수 <TEX>${\alpha}$</TEX>값은 흙의 내부마찰각이 커짐에 따라 증가함을 알 수 있었는데 Drucker-Prager 항복기준을 나타내는 원이 Mohr-Coulomb 항복기준에 외접 및 내접하는 경우의 <TEX>${\alpha}$</TEX>값을 나타내는 <TEX>${\alpha}_c$</TEX>와 <TEX>${\alpha}_i$</TEX>값에 대하여 평균값인 <TEX>${\alpha}_{av}$</TEX>의 값은 내부마찰각에 비례하였는데 내부마찰각이 <TEX>$10^{\circ}$</TEX>인 경우 약 0.07이었으며 내부마찰각이 <TEX>$45^{\circ}$</TEX>인 경우 약 0.29이었다. 또한, <TEX>${\alpha}_c/{\alpha}_i$</TEX>값은 내부마찰각에 비례하였는데 내부마찰각이 <TEX>$10^{\circ}$</TEX>인 경우 약 1.12이었으며 내부마찰각이 <TEX>$45^{\circ}$</TEX>인 경우 약 1.62이었다. Mohr-Coulomb 강도정수가 Drucker-Prager 강도정수 k에 미치는 영향을 살펴보았는데 본 연구에서 가정한 흙의 점착력 중 최소값이 10kPa인 경우를 제외하고 흙의 내부마찰각의 영향을 거의 받지 않고 전체적으로 흙의 점착력에 영향을 받음을 알 수 있었다. 일정한 점착력에 대하여 내부마찰각이 증가함에 따라 일축압축시 및 일축인장시의 Mohr-Coulomb 항복기준에 의한 축차응력인 <TEX>$S_{c0}$</TEX>와 <TEX>$S_{t0}$</TEX> 그리고 두 값의 평균값인 <TEX>$S_{0(ave)}$</TEX>값은 감소하였다. 또한 내부마찰각이 증가할수록 Mohr-Coulomb 항복궤적을 나타내는 육각형이 더욱 불규칙해져 <TEX>$S_{0(ave)}$</TEX>로부터 <TEX>$S_{c0}$</TEX>와 <TEX>$S_{t0}$</TEX> 사이의 편차가 내부마찰각이 증가함에 따라 커짐을 알 수 있었다. In this theoretical study, the strength parameters of the Drucker-Prager yield criterion and Mohr-Coulomb yield criterion were set to equal values, in order to analyze the correlation among the parameters. The Drucker-Prager strength parameters <TEX>${\alpha}$</TEX> and k were represented by the Mohr-Coulomb strength parameters c and <TEX>${\phi}$</TEX>. Specifically it can be seen that k is function of c, <TEX>${\phi}$</TEX> and <TEX>${\alpha}$</TEX> is function of <TEX>${\phi}$</TEX> alone. Drucker-Prager strength parameter <TEX>${\alpha}$</TEX> increases as the internal friction angle of soil increases. <TEX>${\alpha}_{av}$</TEX> which is the average of <TEX>${\alpha}_c$</TEX> and <TEX>${\alpha}_i$</TEX> was proportional to internal friction angle in which <TEX>${\alpha}_c$</TEX> and <TEX>${\alpha}_i$</TEX> are <TEX>${\alpha}$</TEX> values corresponding to the circles of the Drucker-Prager yield cirteria circumscribes and inscribes the Mohr-Coulomb yield criterion respectively. The values of the <TEX>${\alpha}_{av}$</TEX> was 0.07 and 0.29 which correspond to the internal friction angle of <TEX>$10^{\circ}$</TEX> and <TEX>$45^{\circ}$</TEX> respectively. In addition, value of <TEX>${\alpha}_c/{\alpha}_i$</TEX> was proportional to internal friction angle of soil and the values of <TEX>${\alpha}_c/{\alpha}_i$</TEX> 1.12 and 1.62 which corresponds to internal friction angle of <TEX>$10^{\circ}$</TEX> and <TEX>$45^</TEX><TEX>{\circ}$</TEX> respectively.The influence of the Mohr-Coulomb strength parameters on the Drucker-Prager strength parameter k was investigated and it was found that k was mainly influenced by the cohesion of the soil, except in the case of the minimum assumed value of c of 10kPa. The deviator stresses, <TEX>$S_{c0}$</TEX> and <TEX>$S_{t0}$</TEX>, which correspond to the cases of the Mohr-Coulomb yield criterion under uniaxial compression and uniaxial tension, respectively, and <TEX>$S_{0(ave)}$</TEX>, which is the average value of <TEX>$S_{c0}$</TEX> and <TEX>$S_{t0}$</TEX>, decrease as the internal friction angle increases. Furthermore, the hexagon, which represents the Mohr-Coulomb yield locus, becomes more irregular, and the deviations of <TEX>$S_{c0}$</TEX> and <TEX>$S_{t0}$</TEX> from <TEX>$S_{0(ave)}$</TEX> also increase, as the internal friction angle increases.

Shear strength of unsaturated granular soils: three-dimensional discrete element analyses

To investigate the shear strength behavior of unsaturated granular soils, the three-dimensional discrete element method has been used to model soils in triaxial compression tests. A simple but effective contact model with an attractive capillary force was implemented. The effects of matric suction and packing density on shear strength of unsaturated granular assemblies were examined. The Mohr–Coulomb strength parameters (apparent cohesion and friction angle) were fitted for each matric suction examined. The results show that matric suction can increase the strength and modulus of granular soils and lead to increased dilation. The peak friction angle depends on the packing density but seems independent of matric suction. The apparent cohesion increases with matric suction non-linearly at a decreasing rate. Similar values of cohesion were observed for both dense and loose assemblies, which can be explained by the anisotropic distribution of capillary force network. Based on the microscopic observations, the stress-induced anisotropy of contact distributions leads to an anisotropic distribution of capillary water and, as a consequence, the capillary stress is anisotropic, imposing a shear effect on an assembly in parallel with that imposed by the externally applied loading. Consequently, the strength of unsaturated granular soil is controlled by the combined effects of packing density, and the magnitude and degree of anisotropy of the capillary stress. A new shear strength function for unsaturated soils, considering the anisotropic effects of matric suction, is proposed and validated using experimental data in the literature.