Mohr-Coulomb Failure Envelope Research Articles

Calibration of Four Nonlinear Failure Envelopes from Triaxial Test Data and Influence of Nonlinearity on Geotechnical Computations

It is now recognized that many geomaterials have nonlinear failure envelopes. This non-linearity is most marked at lower stress levels, the failure envelope being of quasi-parabolic shape. It is not easy to calibrate these nonlinear failure envelopes from triaxial test data. Currently only the power-type failure envelope has been studied with an established formal procedure for its determination from triaxial test data. In this paper, a simplified procedure is evolved for the development of four different types of nonlinear envelopes. These are of invaluable assistance in the evaluation of true factors of safety in problems of slope stability and correct computation of lateral earth pressure and bearing capacity. The use of the Mohr-Coulomb failure envelopes leads to an overestimation of the factors of safety and other geotechnical quantities.

Numerical analysis of coupled thermo-hydro-mechanical behavior in single- and multi-layer repository concepts for high-level radioactive waste disposal

A multi-layer repository concept is proposed as an alternative to the single-layer repository concept to improve the disposal density of high-level radioactive waste (HLW) in Korea. Numerical simulations are performed to compare the coupled thermo-hydro-mechanical (THM) behavior in the existing Korean reference HLW disposal system (KRS) based on the single-layer repository concept to that in the new multi-layer repository concept. The applicability of the multi-layer repository concept, such as double- and triple-layer repositories, for the disposal of HLW is analyzed with respect to a maximum temperature criterion of 100 °C, evolution of saturation and pore pressure, and mechanical stability. Maximum temperatures are below 100 °C in the double- and triple-layer repository concepts, as in the single-layer reference, although two peaks in simulated temperatures are observed during the evolution of the thermal pulse, resulting from superposition of decay heat at different vertical levels in the multi-layer repository concept. There is no significant difference in the evolution of pore pressure and saturation among the three concepts. The evolutions of mean effective stress at the bentonite blocks and backfill materials are also not significantly different between the single-, double-, and triple-layer repository concepts, because the hydraulic behavior is quite similar, resulting in almost the same change in swelling pressure. Stress states in the rock mass near the tunnels and deposition holes remain below the Mohr-Coulomb failure envelopes at the repositories of 500 m depth in the single-, double-, and triple-layer repository concept simulations. However, the stress states exceed the Mohr-Coulomb failure envelopes at the repositories below 500 m depth (beneath the top layer) in the double- and triple-layer repository concepts. Also, mechanical analysis shows high potential for spalling failure around the deposition holes and tunnel roof in the double- and triple-layer repository concepts. Subsidence in the double- and triple-layer concepts due to the construction of repositories is much deeper than that in the single-layer concept, and uplift induced by heating the rock mass due to the decay heat in the double- and triple-layer concepts is much higher than in the single-layer concept. These results indicate that multi-layer repositories with larger depth intervals between layers are a feasible alternative to the KRS to safely achieve higher disposal density.

Shear strength parameters and Mohr-Coulomb failure envelopes for cement stabilised rammed earth

Cement stabilised rammed earth (CSRE) is a stratified layered construction. The technology is predominantly used in the construction of structural walls in buildings, retaining walls, foundations etc. across the world. There is inadequacy in the study on the shear strength parameters of CSRE and there is hardly any information on Mohr-Coulomb failure envelopes for CSRE. Determining the shear strength parameters of CSRE assumes importance in the analysis of CSRE behaviour under compression and in determining the in-plane shear strength walls. The paper presents the experimental studies on characterising the shear strength parameters and generating the Mohr-Coulomb failure envelopes for CSRE. Triaxial compression tests were performed and the shear strength parameters, cohesion and angle of internal friction were determined in dry and wet conditions. Cohesion of CSRE was found to be a function of cement content. Mohr-Coulomb failure envelopes of the form τcsre=c+σtanϕ were generated.

Unloading-induced rock fracture activation and maximum seismic moment prediction

Hundreds of anthropogenic earthquakes have recently occurred worldwide due to underground space creation and energy extraction. The mechanism behind the human-induced geohazards is most likely associated with the reduction of normal stress on pre-existing fractures and faults. This study reports a series of laboratory experiments to investigate the mechanism of unloading-induced fracture activation, and proposes a simple approach to predict the maximum seismic moment for a critically stressed fracture. The unloading-driven shear test results exhibit that the unloading process induces the stress states of the sawcut and natural fractures to approach the Mohr-Coulomb failure envelope, and the normal stress unloading rate influences the peak slip rate. The fracture instability is dependent on the relationship between the stiffness of the system and the slip weakening rate of the fracture, and the shear dilation mainly occurs after the fracture activation. The test results also show that the critical shear stress of the sawcut fracture during the unloading-driven shear test is approximately equal to the residual shear strength after the displacement-driven fracture slip. This relationship inspires us to develop a new approach to estimate the maximum seismic moment. Our data demonstrate that the maximum seismic moments for both the fractures obtained from the unloading-driven shear tests are all below the upper limit lines, indicating that the proposed approach is reasonable. The uncertainty analysis shows that the accurate estimation of fault size can improve the maximum seismic moment prediction.

Experimental Investigation on Shear Strength Parameters of Lime Stabilized Loess

Loess is a typical collapsible soil, which is widely distributed in the upper and middle areas around the Yellow River of China. The stabilization of loess with lime provides a significant improvement in the physical and the mechanical characteristics of the loess and is therefore widely used in the pavement base and subgrade. Therefore, a systematic investigation of Mohr-Coulomb failure envelope of lime stabilized loess needs to be conducted. In this pursuit, the present research envisages the investigation of the effects of the lime content, porosity and curing time on the strength parameters (friction angle (φ) and cohesion (c)), using a series of triaxial tests performed on lime stabilized loess specimens. The experimental results revealed that the friction angle (φ) was independent of the lime content, the porosity and the curing time of the specimen for a given lime stabilized loess, while the factors mentioned above had a significant effect on the cohesion (c) of the lime stabilized loess. For a relatively short curing time (7 days), the change in the lime content did not present an obvious effect on the cohesion (c) of the stabilized loess. However, when the curing time (28, 90 and 180 days) was longer, the increase of the lime content significantly enhanced the cohesion of the stabilized loess. When the lime content was constant, the cohesion (c) of the stabilized loess increased linearly with the decrease in the void ratio. A power function equation was proposed to assess the comprehensive influences of the factors like the lime content, porosity and curing time on cohesion (c). Finally, the Mohr-Coulomb failure envelopes were drawn based on the triaxial test for 47 specimens with various curing time and confining pressure, and the shear strength parameters obtained by the proposed equation were also compared with the experimental results.

Shear behavior of cement stabilized rammed earth assemblages

Adoption of rammed earth technology in building construction has witnessed a surge during the recent times and hence it is essential to understand the mechanical behavior of rammed earth under various loading conditions. In this study, in-plane shear behavior of cement stabilized rammed earth (CSRE) is assessed by conducting two types of tests namely (i) Direct shear test of CSRE causing shearing along two adjacent rammed earth layers similar to triplet shear test of masonry bed joints which is henceforth called as triplet test and (ii) Diagonal tension (shear) test of CSRE panels. Three types of bonding techniques between the rammed layers of CSRE are explored in this study, namely, (i) making conical dents which act as shear connectors between rammed earth layers, (ii) applying a coat of fresh cement slurry along the interfaces of rammed layers and (iii) combination of dents and fresh cement slurry and their influence in enhancing the interface shear strength of CSRE is assessed. The bonding techniques are adopted for both, triplet specimens and diagonal panels. Further, the effect of compressive stress normal to the rammed earth layers on the interface shear behavior of triplet specimens is examined. The different levels of normal pre-compression considered are 0.05 MPa, 0.3 MPa and 0.9 MPa. The triplet and diagonal tension (shear) tests on CSRE assemblages are conducted under both, dry and wet conditions. Shear behavior is assessed in terms of shear strength, shear modulus, strain at peak stress, post-peak behavior and failure patterns. Among the different bonding techniques assessed in this study, CSRE specimens with a coat of fresh cement slurry exhibited higher shear strength in comparison to specimens with other types of bonding techniques or no bonding technique. Further, CSRE triplet specimens exhibited steady increase in interface shear strength with increase in normal pre-compression, both in dry and wet conditions. Also, shear strength of CSRE was found to be lower in wet condition, in comparison to shear strength in dry condition, for all the bonding techniques. A Mohr-Coulomb failure envelope was developed for CSRE under wet and dry conditions based on the results of triplet tests conducted in this study. Overall, the study aims to understand the efficacy of the proposed bonding techniques in enhancing the shear strength of CSRE and the influence of normal pre-compression and moisture content on shear behavior of CSRE.

Shear Properties of Asphalt Mixtures under Triaxial Compression

In order to study the influences of confining pressure and temperature on the shear properties of asphalt mixtures, triaxial tests were conducted at 40 °C, 50 °C, and 60 °C, with the confining pressure ranges from 0 to 1 MPa for the widely used continuous-graded AC (Asphalt Concrete)-13, open-graded OGFC (Open-Graded Friction Course)-13, and gap-graded SMA (Stone Mastic Asphalt)-13 asphalt mixtures in China. A nonlinear regression/prediction model of triaxial strength for asphalt mixtures was proposed. The results show that confining pressure and temperature had a significant effect on the shear resistance of asphalt mixtures. With increasing temperature, the shear strength of the asphalt mixture gradually decreased due to the decreasing of cohesion strength; the shear strength of the asphalt mixture increased with the increase of confining pressure. Meanwhile, the cohesion strength increased and the friction angle decreased gradually with the increase of confining pressure. When the confining pressure was close to 0.6 MPa, the Mohr–Coulomb failure envelope bended down, so the linear Mohr–Coulomb criterion is not suitable to describe the failure behavior of asphalt mixtures. Therefore, a power function failure envelope was put forward to characterize the nonlinear shear properties of asphalt mixtures. The nonlinear evolutional laws of shear parameters, which includes cohesion strength and friction angle, were also proposed for asphalt pavement material and structure design. Among these asphalt mixtures, the gap-graded SMA-13 asphalt mixture exhibited better performance on the resistance to shear failure, and it was recommended as the upper layer material to improve the shear performance of asphalt pavement.

Negative aging of granular materials

Background: Use of abundantly available soft rocks for embankment construction is continuously increasing due to economic reasons. A detailed knowledge on time-dependent deterioration (negative aging) of such weak geomaterial becomes essential for better serviceability of geotechnical structures. Methodology: To explore possible effects of deterioration of soil grains on mechanical properties, a series of consolidated drained torsional shear tests were performed under saturated and dry conditions on crushed soft rocks from Japan and Pakistan. Results: Test results indicated that soils under dry conditions with intact grains exhibited stiffer stress-strain behavior, higher peak stress ratios, and strain softening response after peak shear stress. On the contrary, soils undergoing water-induced deterioration of grain showed enormous loss of strength upon submergence. Mohr-Coulomb failure envelopes elucidated large effects of saturation-induced disintegration of grains on effective angle of internal friction. In addition, peak strength parameters seemed to be relatively more vulnerable to saturated conditions as compared to residual strengths. Conclusion: It is concluded that the observed soil behavior can be crucial to embankments and structural foundations constructed on granular materials obtained from crushed soft rocks.

The Mohr–Coulomb criterion for intact rock strength and friction – a re-evaluation and consideration of failure under polyaxial stresses

Abstract. Darley Dale and Pennant sandstones were tested under conditions of both axisymmetric shortening and extension normal to bedding. These are the two extremes of loading under polyaxial stress conditions. Failure under generalized stress conditions can be predicted from the Mohr–Coulomb failure criterion under axisymmetric shortening conditions, provided the best form of polyaxial failure criterion is known. The sandstone data are best reconciled using the Mogi (1967) empirical criterion. Fault plane orientations produced vary greatly with respect to the maximum compressive stress direction in the two loading configurations. The normals to the Mohr–Coulomb failure envelopes do not predict the orientations of the fault planes eventually produced. Frictional sliding on variously inclined saw cuts and failure surfaces produced in intact rock samples was also investigated. Friction coefficient is not affected by fault plane orientation in a given loading configuration, but friction coefficients in extension were systematically lower than in compression for both rock types. Friction data for these and other porous sandstones accord well with the Byerlee (1978) generalization about rock friction being largely independent of rock type. For engineering and geodynamic modelling purposes, the stress-state-dependent friction coefficient should be used for sandstones, but it is not known to what extent this might apply to other rock types.

Range of confining pressures for the Hoek–Brown criterion

Engineering in weak rock using modern, computer-based design techniques is notoriously challenging because the laboratory tests and classification methods routinely carried out on such materials yield rock parameters. Such parameters are not directly compatible with the most widely used constitutive model of those computer-based methods – that is, the Mohr–Coulomb failure envelope. There is no direct relationship between Mohr–Coulomb (linear) and Hoek–Brown (non-linear) parameters, and marrying those two failure envelopes is notoriously difficult. When formulating a failure criterion for rock materials, based on rock and rock mass parameters, a correlation with the Mohr–Coulomb failure criterion has been proposed, which can be obtained from the computer program RocLab. One of the essential input parameters for such correlation is called the maximum confining pressure. This parameter directly affects the correlated shear strength parameters on the Mohr–Coulomb failure envelope and hence choosing it with care is the key to producing a safe, yet economic design. The present paper discusses the use of several methods for determining the maximum confining pressure to derive Mohr–Coulomb parameters for weak rock in slope and retaining wall applications. The suitability of each method considered is discussed against the results of back analyses, and design recommendations are proposed.

Mohr–Coulomb failure envelopes of lime-treated soils

Mohr–Coulomb failure envelopes of lime-treated soils

Mohr–Coulomb failure envelopes of lime-treated soils

The aim of this study is to quantify the influence of amount of lime and porosity in the assessment of the Mohr–Coulomb failure envelope of lime-treated soils based on unconfined compressive strength (σc) and splitting tensile strength (σt) of such materials, without the necessity of carrying out triaxial testing. Based on a previously established concept that the σt/σc relationship is unique for each specific fine-grained soil and lime blend, it is shown that the effective angle of shearing resistance of a given lime-treated soil is independent of the porosity and the amount of lime of the specimen and that effective cohesion intercept is a direct function of σc (or σt) of the improved soil; this in turn depends on the porosity and volumetric amount of lime in the soil–lime blends. Finally, the concepts are successfully tested for clayey sand treated with lime at two distinct curing time periods, considering weak to moderate cementation levels.

INTERFACE SHEAR STRENGTH OF CONCRETE-TO-CONCRETE BOND WITH AND WITHOUT PROJECTING STEEL REINFORCEMENT

Composite concrete consists of two elements cast at different times which are the concrete base and concrete topping. To achieve composite action, interface shear strength must be sufficient to resist the sliding motion between the two concrete surfaces in contact. The interface shear strength is mainly depended on concrete cohesion, friction and dowel action. A total of 36 “push-off” tests were performed to study the interface shear strength and to assess the influence of surface texture and steel reinforcement crossing the interface. Three different concrete base surfaces are prepared which include smooth or “left as-cast”, roughened by wire-brushing in the transverse direction and steel reinforcement projecting from the concrete base. Eurocode 2 provides design equations for determining the interface shear strength with different surface textures and also the one where projecting steel reinforcement crosses the interface. The experimental results show that the transverse roughened surface produced the highest interface shear strength of 1.89 N/mm2 (σn = 0 N/mm2), 4.69 N/mm2 (σn = 0.5 N/mm2), 5.97 N/mm2 (σn = 1.0 N/mm2) and 6.42 N/mm2 (σn = 1.5 N/mm2) compared with the other surface textures. This proves that the increase in the degree of roughness contributes to higher concrete cohesion and friction coefficient. However, for the surface with projecting steel reinforcement, the failure is not sudden as experienced by the surface without one. This is due to the contribution of the clamping stress from the dowel action of the steel reinforcements. Meanwhile, for specimens without any projecting steel reinforcements, the interface shear strength depended solely on friction and concrete cohesion of the surface textures. The interface shear strength of surface with and without the projecting steel reinforcement can be predicted using the Mohr-Coulomb failure envelope. This paper also proposed design expressions for concrete-to-concrete bond on surfaces provided with and without projecting steel reinforcement that can be adopted in Eurocode 2.

The effects of normal and shear stress wave phasing on coseismic landslide displacement

Predictive models used to assess the magnitude of coseismic landslide strain accumulation in response to earthquake ground shaking typically consider slope-parallel ground accelerations only and ignore both the influence of coseismic slope-normal ground accelerations and the phase relationship between dynamic slope-normal and slope-parallel accelerations. We present results of a laboratory study designed to assess the significance of the phase offset between slope-normal and slope-parallel cyclic stresses on the generation of coseismic landslide displacements. Using a dynamic back-pressured shearbox that is capable of simulating variably phased slope-normal and slope-parallel dynamic loads, we subjected sediment samples to a range of dynamic loading scenarios indicative of earthquake-induced ground shaking. We detail the variations in strain accumulation observed when slope-normal and slope-parallel stresses occur independently and simultaneously, both in and out of phase, using a range of dynamic stress amplitudes. Our results show that the instantaneous phasing of dynamic stresses is critical in determining the amount of coseismic landslide displacement, which may vary by up to an order of magnitude based solely on wave-phasing effects. Instantaneous strain rate is an exponential function of the distance normal to the Mohr Coulomb failure envelope in plots of shear stress against normal effective stress. This distance is strongly controlled by the phase offset between dynamic normal and shear stresses. Our results demonstrate that conditions considered by conventional coseismic slope stability models can either overestimate or underestimate earthquake-induced landslide displacement by up to an order of magnitude. This has important implications for accurate assessment of coseismic landslide hazard.

Assessing Failure Envelopes of Soil–Fly Ash–Lime Blends

AbstractThis study aims to establish the influence of curing time and the amount of lime and porosity in the assessment of the Mohr-Coulomb failure envelope of fly ash–lime-treated soils based on unconfined compressive strength (σc) and splitting tensile strength (σt) of such materials. Founded on the concept that the σt/σc relationship is unique for each specific fine-grained soil, fly ash, and lime blends, it is shown that the angle of shearing resistance of a given lime-treated soil is independent of the porosity and the amount of lime of the specimen and that cohesion intercept is a direct function of σc (or σt) of the improved soil, which depends of the porosity and volumetric amount of lime of the soil–fly ash–lime blends. Finally, the concepts are tested with success for a sandy soil treated with fly ash and lime at distinct curing time periods, considering moderate to strong cementation levels.

Hyperbolic models for a 2-D backfill and reinforcement pullout

ABSTRACT: A series of direct shear tests were performed using an idealised two-dimensional test medium consisting of rhombically stacked steel rods to facilitate displacement computations for reinforced slopes using a force-equilibrium-based finite-displacement method. A series of pullout tests using extensible and stiff reinforcement with various embedment lengths (Lt) were also performed. Modelling for the non-linear behaviour of shear stress–displacement and pullout force–displacement relationships was performed using hyperbolic models. In modelling shear stress–displacement relationships for the steel rod backfill, a linear Mohr–Coulomb failure envelope was assumed for the investigated range of confining pressures. It was found that model parameters for the initial shear stiffness, namely K and n, are significantly different from those for ordinary soils because of the regular and dense packing of the steel rods, but are advantageous as a backfill material for model tests because of its consistency and repeatability. Results of hyperbolic curve fitting for the pullout force–displacement relationship indicate that the model parameters describing non-linear and pressure-dependent behaviour of reinforcement pullout, namely Kt, m, and Rt, are functions of Lt. The modelled hyperbolic shear stress–displacement relationships and the pullout force–displacement relationships are in good agreement with the experimental ones and are applicable for simulating the behaviour of model slopes consisting of steel rod assemblies.

Mohr–Coulomb failure envelopes of lime-treated soils

The aim of this study is to quantify the influence of amount of lime and porosity in the assessment of the Mohr–Coulomb failure envelope of lime-treated soils based on unconfined compressive strength (σc) and splitting tensile strength (σt) of such materials, without the necessity of carrying out triaxial testing. Based on a previously established concept that the σt/σc relationship is unique for each specific fine-grained soil and lime blend, it is shown that the effective angle of shearing resistance of a given lime-treated soil is independent of the porosity and the amount of lime of the specimen and that effective cohesion intercept is a direct function of σc (or σt) of the improved soil; this in turn depends on the porosity and volumetric amount of lime in the soil–lime blends. Finally, the concepts are successfully tested for clayey sand treated with lime at two distinct curing time periods, considering weak to moderate cementation levels.

A method proposed for the assessment of failure envelopes of cemented sandy soils

This study aims at quantifying the influence of the amount of cement (C), the porosity (η) and the porosity/cement ratio (η/Civ) in the assessment of the Mohr–Coulomb failure envelope of artificially cemented sands centered on splitting tensile strength (σt) and unconfined compressive strength (σc). Based on the concept previously established by Consoli et al. that the σt/σu relationship is unique for each specific sandy soil and cement agent, it is shown that the effective angle of shearing resistance of a given cemented sandy soil (Ø′) is independent of the porosity and the amount of cement of the specimen and that effective cohesion intercept (c′) is a direct function of the unconfined compressive strength (σc) [or splitting tensile strength (σt)] of the improved granular material, which depends on the porosity/cement ratio (η/Civ) of the soil–cement blends. These concepts are tested with success for a uniform fine sand treated with early strength Portland cement and a silty sand treated with ordinary Portland cement, considering weak, moderate and strong cementation levels, as well as for a volcaniclastic formation deposit composed of moderately cemented fine sand and silt-size particles (naturally cemented soil). The methodology developed herein allows estimating c′ and Ø′ for any specific condition comprised inside the range of porosity and amount of cement employed during basic testing, without the necessity of carrying out triaxial testing or any other complex and time consuming tests.

Foundation Stability of a Levee

Stability of a levee and its foundation soil during flood is governed by seepage forces. In this study, the seepage forces in the flow domain have been determined using conformal mapping technique. Stability of foundation soil has been studied for a levee with and without cut-off wall on permeable soil of infinite depth. In situ effective normal and shear stresses due to self-weight, additional induced stresses due to levee structure and ponded water on upstream sloping face have been determined by assuming soil to be elastic. Besides, components of seepage stress acting at a point on two orthogonal planes, i.e., on vertical and horizontal planes, are considered and the Mohr’s circle is drawn. Mohr–Coulomb failure envelope is drawn for the foundation soil with known effective cohesion (\(c^{\prime}_{1}\)) and angle of internal friction (\(\varphi^{\prime}_{1}\)), and then the stability of the foundation soil has been assessed. Probable zone of general shear failure considering seepage flow has been identified. Zones vulnerable to foundation failure for different width of levee and depth of cut-off wall have been computed. The hydraulic unstable zone in downstream side of the levee resembles a log spiral. The provision of cut-off wall restricts the progress of failure zone only in the downstream side; otherwise, the zone of failure will enter the foundation of the levee. The stability of the foundation soil of an existing ring levee along the rivers Ganga, Sone and Punpun, near Patna (India), has been evaluated.

A practical methodology for the determination of failure envelopes of fiber-reinforced cemented sands

This study aims to estimate the Mohr–Coulomb failure envelope of fiber-reinforced and non-reinforced artificially cemented sands based on splitting tensile strength (σt) and unconfined compressive strength (σc) of such materials, without the necessity of carrying out triaxial testing. Based on the concept previously established by Consoli et al. that the σt/σc relationship is unique for each specific soil, fiber and cement agent, it is shown that the effective angle of shearing resistance of a given fiber-reinforced or non-reinforced cemented sandy soil (ϕ′) is dependent of the σt/σc ratio of such geomaterials and that effective cohesion intercept (c′) is a direct function of the unconfined compressive strength (σc) [or splitting tensile strength (σt)] and σt/σc ratio of the fiber-reinforced/non-reinforced improved soil. Finally, the concepts presented herein are successfully checked for glass fiber-reinforced/non-reinforced silty sand treated with ordinary Portland cement, considering weak, moderate and strong cementation levels.