Mohr-Coulomb Failure Envelope Research Articles

Improving Strength by Increased Compaction of Gypsum—Enriched Soil under Long-Term Soaking Conditions

This study investigated the effect of compaction effort and soaking time on the shear strength properties of fine-grained gypsum-containing soils. The objective was to demonstrate that increasing compaction effort increases soil strength, specifically cohesion and the angle of shear strength, when subjected to soaking in freshwater. Unconsolidated undrained triaxial tests were carried out on CBR soil samples with different soaking times. The results showed a transition from brittle to ductile failure behaviour as the soaking time increased. Mohr–Coulomb failure envelopes showed reduced cohesion and angle of shear strength with increasing soak time. Regression models were developed to establish correlations between soaked and unsoaked strength parameters. Strong relationships were found between soil strength properties, compaction effort and soaking time. Empirical equations were proposed to estimate the cohesion and angle of shear strength from compaction effort and soaking time. This study highlighted the importance of considering gypsum-rich soils in civil engineering design. Gypsum dissolution during wetting significantly affected soil strength parameters. The regression models and empirical equations provide engineers with tools to assess the influence of compaction effort and soaking time on soil strength, thus aiding decision making when designing structures on gypsum-rich soils.

Feasibility of Strengthening Sandy Soils Using Industry Waste as Geo-Fiber

Abstract Re-using waste generated from daily domestic usage to improve weak soils such as dune sand gives a profitable solution to both environment and the construction sector. In this paper, weak sandy soil was modified with two types of fibers derived from daily domestic use. Plastic bottle waste fiber and tainted polypropylene sediment filter fiber were embedded in the sandy soil with a rate of (0.5%,1%,1.5%, and 2%) by weight of dry soil. Toward this, the direct shear test was conducted to confirm the optimum fiber content and evaluate other parameters such as shear strength, normalized ultimate shear strength, angle of internal friction, and adhesion. The results showed that the 1.5% fiber content showed higher values of angle of internal friction and the normalized ultimate shear strength for both types of fibers. The reinforcement with plastic bottle waste fiber and tainted polypropylene sediment filter fiber enhanced the shear strength parameters and normalized ultimate shear strength. Significant improvement was noticed in the adhesion value with the addition of 2% of tainted polypropylene sediment filter fiber. finally, the effect of fiber addition on the Mohr-coulomb failure envelope was discussed.

Inclined Plane Shear Behaviour of a Recycled Construction and Demolition Material–Geocomposite Interface

Over the years, recycled construction and demolition (RC&D) materials have become useful and valuable construction materials. The applications of these materials have been increasing, and there are cases where they may be in contact with geosynthetics. This work, which is part of a broader investigation into the feasibility of replacing soils used in landfill final cover systems by RC&D materials, analysed the inclined plane shear behaviour of the interface between a fine-grained RC&D material and a drainage geocomposite. Inclined plane shear tests were performed with different vertical stresses and different compaction conditions (degree of compaction and water content) of the RC&D material. The friction angle at the RC&D material-geocomposite interface was estimated by two approaches: the standard and the one based on the Mohr–Coulomb failure envelope. The sliding mechanism of the RC&D material over the geocomposite was examined. For comparison with the RC&D material-geocomposite interface, the behaviour of the RC&D material under inclined plane shear movement was also characterised. The main findings of the work included: the friction angle (standard approach) at the RC&D material-geocomposite interface decreased by increasing the applied vertical stress and the RC&D material water content (with meaningful changes in the slinging mechanism in the latter case), and tended to increase by increasing the degree of compaction of the RC&D material; the behaviour of the RC&D material under inclined plane shear movement did not differ significantly from that of the RC&D material-geocomposite interface; the failure envelope approach was more conservative (smaller friction angles) than the standard approach.

A Constitutive Model for Circular and Square Cross-Section Concrete Confined with Aramid FRP Laminates

Fiber-reinforced polymer (FRP) has been used for seismic retrofitting and structural reinforcement over recent decades. Numerous researchers have created stress–strain models based on experimental data to predict the mechanical properties of FRP-confined concrete. In this study, circular and square cross-section specimens with different design concrete strength were prepared, and the compressive strength of the specimens confined with different layers of aramid FRP (AFRP) were measured in compressive tests. A constitutive model was proposed to simulate the uniaxial compressive stress–strain relationship of the AFRP-confined concrete, which was derived from the Mohr–Coulomb failure envelope theory, and the corresponding axial strain was determined from the regression analysis. The internal friction angle of the proposed constitutive model was determined for the cylindrical concrete specimens confined with one and two layers of AFRP. The compressive strength of one and two layers of AFRP-confined concrete specimens were used to obtain the parameters of the constitutive model; the absolute average error between experimental and predicted compressive strength was 7.01%. Then, the constitutive model was used to predict the strength of a three-layer AFRP-confined concrete specimen, and the absolute average error was 4.95%. The cross-sectional shape coefficient of the square concrete specimen was obtained analytically. Substituting the cross-sectional shape coefficient into the proposed constitutive model, the average absolute error of the square cross-section concrete specimen was about 3.84%. The results indicated that the proposed constitutive model can predict the compressive strength of circular and square cross-section concrete specimens confined with AFRP.

Mechanical and hydraulic properties of carbonate rock: The critical role of porosity

Carbonate rocks are extensively used in civil infrastructure and play a critical role in geoenergy geoengineering, either as hydrocarbon reservoirs or potential repositories for CO 2 geological storage. Carbonate genesis and diagenetic overprint determine the properties of carbonate rocks. This study combines recent data gathered from Madison Limestone and an extensive dataset compiled from published sources to analyze the hydraulic and mechanical properties of limestone carbonate rocks. Physical models and data analyses recognize the inherently granular genesis of carbonate rocks and explain the strong dependency of physical properties on porosity. The asymptotically-correct power model in terms of (1- ϕ / ϕ ∗) α is a good approximation to global trends of unconfined stiffness E and unconfined compressive strength UCS , cohesive intercept in Mohr-Coulomb failure envelopes, and the brittle-to-ductile transition stress. This power model is the analytical solution for the mechanical properties of percolating granular structures. We adopted a limiting granular porosity ϕ ∗ = 0.5 for all models, which was consistent with the loosest packing of monosize spheres. The fitted power model has exponent ( α = 2) in agreement with percolation theory and highlights the sensitivity of mechanical properties to porosity. Data and models confirm a porosity-independent ratio between unconfined stiffness and strength, and the ratio follows a log-normal distribution with mean ( E/UCS ) ≈ 300. The high angle of internal shear strength measured for carbonate rocks reflects delayed contact failure with increased confinement, and it is not sensitive to porosity. Permeability spans more than six orders of magnitude. Grain size controls pore size and determines the reference permeability k ∗ at the limiting porosity ϕ ∗ = 0.5. For a given grain size from fine to coarse-grained dominant carbonates, permeability is very sensitive to changes in porosity, suggesting preferential changes in the internal pore network during compaction.

Mechanical Characterization of Cemented Paste Backfill

Mechanical characterization is important to the design and analysis of cemented paste backfill (CPB) structures. Unconfined compressive strength (UCS) tests have been widely used owing to their relative simplicity to characterize a material’s response to unconfined compressive loading. However, the UCS represents a single strength parameter and does not fully describe the material’s strength (or failure) envelope. In this study, we analyzed UCS tests with direct shear and uniaxial tensile strength tests conducted on the same CPB materials to provide mechanical characterization of CPB under a more complete range of loading conditions. The results demonstrate the Mohr–Coulomb failure envelope provides a consistent description of strengths arising from the three different test methods. Furthermore, a better estimate of the tensile strength is UCS/4, which is considerably higher than the conventional assumption that the tensile strength is equal to USC/10 or UCS/12. This has a significant impact on the assessed required strengths particularly for undercut designs using Mitchell’s sill mat analysis method and suggests that in future the conventional UCS tests should be complemented with direct tension and direct shear tests to improve underground designs using CPB.

Effect of the Addition of Aggregates Derived from Used Tires on the Mechanical Behavior of Clay

The study of the shear strength parameters of mixtures comprising tire-derived aggregates (TDA) and clay was the main objective of this experimental work. The tests were performed using the direct shear box. First, the test was performed on specimens comprising only clay in its natural state and then on mixtures consisting of clay and TDA in increasing contents. A total of four samples (natural clay and natural clay with 2, 4, and 6% tire-derived aggregates)) were made and tested at three normal stress levels (100, 200, and 300 kPa). Then, Mohr-Coulomb failure envelopes were drawn to determine the internal friction angle and cohesion for all mixes. The results were compared to find the optimum TDA content and to study the stress-strain behavior of the mixtures. It was observed that mixing TDA up to 6% by weight with clay significantly changes the shear strength, and the internal friction angle increases from 27.47 to 59.39º (an increase of 46.25%). However, the cohesion significantly decreases from 45 to 26 kPa (a decrease of 57.77%). On the other hand, it was observed that increasing the TDA content reduces the density and increases the shear strength of the mixtures. Also, the addition of TDA increases the mixture consolidation and deformation level at failure.

Matric suction and its effect on the shape stability of 3D printed concrete

The mix design of 3D printed concrete has adopted various types of binders and additives to enhance its casting performance and shape stability. Matric suction, as an attractive force among partially unsaturated particles of the binders and additives, influences the shape stability of firm cement paste composing 3D printed concrete. Higher matric suction induces higher compressive strength (or green strength) and higher elastic modulus. The extended Mohr–Coulomb failure envelope describes the stress state of the 3D printed concrete considering its matric suction. Variation of the matric suction takes parallel shifting and rotation of the shape failure envelope. The test results on the matric suction finally confirm the effect of binders and additives. Change in the water-to-binder ratio contributes to higher matric suction related to the paralel shift of the Mohr-Coulomb failure envelope, while incorporating nanoclay or polycarboxylate ether affects the internal friction angle of the binder.

Determination of Mohr–Coulomb failure envelope, mechanical properties and UPV of commercial cement-lime mortar

Mortar in masonry structures can be subjected to both uniaxial and triaxial loading. Determining the mechanical properties and/or failure criteria of the commonly used mortar is necessary for the structural performance assessment of new and existing masonry buildings using non-destructive testing and/or finite element modelling methods. In this paper, the stress–strain behaviour of a commercially available cement-lime mortar is investigated under uniaxial and triaxial loading. The axial compressive strength, modulus of elasticity, Mohr–Coulomb failure envelopes of the mortar are determined over a range of conditions. Mortar specimens were prepared with a water to cementitious material ratio (w/cm) of 0.6–0.7 and were tested at curing ages of 3, 7, 14, and 28 days, under confining pressures of 0, 100, 250, 500 and 750 kPa. Ultrasonic pulse velocity (UPV) of the specimens were measured before the destructive testing. The results indicate that the influence of curing age and confining pressure on the axial compressive strength of the mortar can be predicted using proposed linear correlations between (i) The confining pressure and the axial compressive strength and (ii) The UPV and the axial compressive strength. From the test results, the strength parameters of the Mohr–Coulomb failure criterion were also determined. It is observed that cohesion is more sensitive to changes in curing age and w/cm than the friction angle, which varied between 32 and 33 degrees.

Flexural Models for Vacuum-Packed Particles as a Variable-Stiffness Mechanism in Smart Structures

Vacuum-packed particle (VPP) systems have been recently used in the development of smart structures due to their ability to actively change material stiffness through the mechanism of granular jamming. By altering the strength of the vacuum pressure applied to the particles, the material can be proportionally and reversibly transitioned from a liquidlike low-stiffness state to a stiff state. The ability to control material stiffness in this way opens up different possibilities for the design of morphing and smart structures by allowing them to soften during deformation to reduce actuation energy requirements and to then stiffen once the desired shape has been achieved to provide a zero-energy holding mechanism. The following research describes two useful models that predict the mechanical response of VPP beams under flexural loading. Firstly, four-point bending tests with digital image correlation strain mapping are performed in order to measure the axial and transverse strains in a bending beam made from vacuum-packed particles. The test results show a nonlinear mechanical response, including a change in beam thickness with deformation, that motivated an analytical model of the structure incorporating a nonlinear material stress model based on the Mohr-Coulomb failure envelope. In addition, finite-element simulations are implemented using a Johnson-Cook model extension to predict the response under loading of three-dimensional beam elements at different vacuum pressure levels. Lastly, the models are compared to the experimental results, indicating good agreement. Both methods are shown to be useful for predicting the variation of stiffness of vacuum-packed particle beams.

RELATIVE DENSITY EFFECTS ON DRAINED SAND BEHAVIOR AT HIGH PRESSURES

A high-pressure triaxial compression and extension apparatus was employed to investigate the effects of initial relative density on the drained behavior of sand. Experiments were performed on cylindrical specimens of Cambria sand with initial relative densities of 30% and 60%, and compared with previously published results for 90%. Confining pressures in the range of 0.25 to 60 MPa were employed to obtain the characteristic behavior of the sand over a large range of pressures. As the confining pressure increased particle crushing increasingly influenced the stress-strain and volume change relations, producing increasing strains to failure and increasingly contractive volume changes. Beyond certain high values of mean normal stress at failure, increasing with initial relative density, the volumetric contraction and strains to failure began to decrease. The Mohr-Coulomb failure envelopes show the greatest curvature for the highest density, but the failure envelopes merge at high pressures where, due to particle crushing, the relations between void ratio and isotropic pressure are described by a single curve. The experiments show clearly that the rates of dilation at failure and the friction angles are directly related to each other, as has been proposed by many investigators. The friction angles are higher in extension than in compression for lower confining pressures, but a crossover occurs and the friction angles are higher in compression than in extension for higher confining pressures.

Geotechnical Properties Determination of Thickened Fluid Fine Tailings

AbstractFluid fine tailings (FFT) comprising clayey-silt solids pose environmental and financial challenges. Currently, mining operators are depositing thickened FFT in deep-pits counting on self-weight consolidation to form stable ground. The motivation of this study is to model the long-term prospects of such deposits utilizing consolidation and direct shear strength measurements. The tests were conducted using scroll decanter centrifuge separated FFT sediment referred to as cake. Drained direct shear tests of the cake gave a linear Mohr–Coulomb failure envelope of 1.2 kPa cohesion intercept and 9° internal friction angle for normal stresses up to 1 MPa. Hydraulic conductivity of the cake was non-linear with normal stress decreasing to 1.7 × 10–11 m/s at 300 kPa. Consolidation results confirmed that the cake exhibits properties similar to those of active clay minerals. The cake compression index is governed by the same relationship as for active clays. The coefficient of consolidation for the cake was nearly constant and had a mean value of 2.25 × 10–3 m2/y, also similar to that of active clays. The void ratio—effective stress—hydraulic conductivity power law empirical relations were used to simulate settlement with a finite-strain model. Numerical results show that the top portion of an FFT deep-pit deposit remains in the liquid state while the lower portion whose maximum solids content converges to 74% is in plastic state. These mean that options that improve hydraulic conductivity and increase the shear strength of the thickened FFT should be integrated prior to final placement in order to create stable ground.

Cemented Paste Backfill (CPB) Material Properties for Undercut Analysis

A longstanding mine backfill design challenge is determining the strength required if the (partially) cured backfill is subsequently undercut. Mitchell (1991) called the undercut backfill a sill mat and proposed an analytical solution that is still often used, at least for preliminary design, and has motivated subsequent empirical design methods. However, fully employing the Mitchell sill mat solution requires knowledge of the backfill material’s Unconfined Compressive Strength (UCS), tangent Young’s modulus (Et), tensile strength (σt), as well as estimates of stope wall closure. Conducting a high-quality UCS test poses challenges but relating the test result to the remaining material parameters is more difficult. Some new material testing data is presented and compared to available published results. Using the parameter mi=UCS/σt the range of available testing data is found to be mi= 3 to 22, however, the most compelling data is obtained when the Mohr’s failure circle in tension is tangential to the corresponding Mohr–Coulomb failure envelope determined from other strength tests. In these cases, the value mi= 4 is found for the materials tested, which is much lower than the value mi= 10 commonly assumed and implies a limiting UCS 60% lower compared to the conventional assumption. It is also found that the relationship between Et and UCS is described by a power function that is close to linear, but the values for the constant and exponent in the power function depend on the material tested. However, for given tailings the power function is found to be independent of void ratio, binder type or concentration, curing time, and water salinity, within the ranges these parameters were investigated. Therefore, when Et is used in the Mitchell sill mat solution it should be correlated with the UCS using the appropriate power function. These correlations are then used with the Mitchell sill mat solution and published measurements of backfill closure strains to estimate the Mitchell solution’s range of applicability based on its underlying assumptions, and a similar analysis is extended to an “empirical design method” motivated by the Mitchell sill mat solution. It is demonstrated that these existing approaches have limited applicability, and more generally a full analysis in support of rational design will require numerical modeling that incorporates the effect of confining stress on the material’s stiffness and mobilized strength.

3D Field-Scale Geomechanical Modeling of Potential CO2 Storage Site Smeaheia, Offshore Norway

Injection-induced rock mechanical failure risks are critical in CO2 sequestration, and thus there is a need to evaluate these occurrences to ensure safe and reliable subsurface storage. A stress–strain-based numerical simulation can reveal the potential mechanical risks of any CO2 sites. This study investigated the hydromechanical effect on geomechanical failure due to injection-induced stress and pore pressure changes in the prospective CO2 storage site Smeaheia, offshore Norway. An inverted-seismic-property-driven 3D field-scale geomechanical model was carried out in the Smeaheia area to evaluate the rock failure and deformation risks in various pressure-build-up scenarios. A one-way coupling between the before- and after-injection pressure scenarios of nine different models has been iterated using the finite element method. The effect of the sensitivity of total pore volume and pore compressibility on rock mechanical deformation is also evaluated. Although various models illustrated comparative variability on failure potential, no model predicted caprock failure or fracture based on the Mohr–Coulomb failure envelope. Moreover, the lateral mechanical failure variation among different locations indicated the possibility to identify a safer injection point with less chances of leakage. In addition, the pore volume and pore compressibility significantly influence the mechanical behavior of the reservoir and caprock rocks. Although this analysis could predict better injection locations based on geomechanical behavior, a fluid simulation model needs to be simulated for assessing lateral and vertical plume migration before making an injection decision.

Effect of overburden spatial variability on field-scale geomechanical modeling of potential CO2 storage site Smeaheia, offshore Norway

Although geological CO2 sequestration is an essential solution for reducing anthropogenic carbon dioxide from the atmosphere, the method needs critical evaluation of injection-induced mechanical risks for safe and reliable CO2 storage. 3D field-scale geomechanical modeling is a preeminent solution for assessing mechanical risks of subsurface geological CO2 storage. However, data scarcity of seals and overburden rocks might limit building the 3D field-scale geomechanical model. This study focuses on seismic data-derived 3D field-scale geomechanical modeling of potential CO2 storage site Smeaheia, offshore Norway. The geomechanical properties inverted from seismic data are resampled in the 3D grid to consider spatial variabilities of seal and overburden rock properties. This method allows us to investigate the effect of overburden rock spatial variability imposed in seismic data on the 3D geomechanical model of Smeaheia. The model was built in Petrel-2019, while the one-way geomechanical simulation is iterated using the finite element method. Simplified constant overburden property models are also constructed to analyze the sensitivity of the overburden rock properties. The results reveal that the seismic data-driven spatially distributed overburden properties model workflow used in this study is a convenient and robust solution for 3D field-scale geomechanical modeling. The maximum vertical estimation of rock deformation is doubled in the simplified (isotropic) overburden rock property model compared to the new spatially variable (anisotropic) overburden rock property model. The Mohr-Coulomb failure envelope reveals that the new modeling approach is less prone to failure than the simplified (isotropic) model, which might influence the project decision. Moreover, our study demonstrates the importance of considering the spatial variability of overburden rock properties in building the 3D field-scale geomechanical model.

Development of swelling induced shear and slickensides in Vertisols

Vertisols shrink and crack as they dry, and swell as they wet. Shear surfaces, sometimes called slickensides, are often observed within the profile of such clay soils. A hypothesis for the appearance of these surfaces is in reaction to lateral swelling forces that induce shear within the soil mass. No direct proof supporting this hypothesis is found in the literature.Test data presented verify the development of lateral soil swelling pressure in response to wetting of a compacted clay soil. The data illustrate that the swell induced pressure can cause the soil to reach failure conditions and in essence, shear itself.During wetting, laboratory compacted specimens of clay were subjected to constant vertical pressure and allowed to swell in the vertical direction. Strain in the lateral direction was restrained and the horizontal soil pressures monitored as they approached a residual magnitude. From the series of tests it was found that the ratio between the residual horizontal swell pressure to the applied vertical pressure decreased monotonously with increase of applied vertical pressure.Mohr's circles representing the state of stress within the specimen at the residual state align along the Mohr-Coulomb failure envelope for tests performed at vertical pressures of 4 kPa through 27 kPa.These results provide credence to the hypothesis that slickensides are formed due to internal shear of the clay, and as such are expected to form at limited depths.

Loading rate-dependent frictional resistance of a sawcut fracture in granite for prediction of thermoshearing

The coupled TM behavior of fractured rock masses should be evaluated for the long-term safety of the deep geological repository. Thermally induced fracture shear slip, i.e., fracture thermoshearing, might cause increase in fracture permeability. In this study, the thermally induced shear slip of a sawcut granite fracture was investigated in laboratory. Multistage biaxial shear test, consisting of mechanical shear test and thermoshearing test, was conducted on the true triaxial apparatus, and acoustic emission (AE) signals were recorded throughout the experiment. Effect of loading rate on frictional resistance of the fracture was investigated by conducting mechanical shear tests, and we found that friction coefficient of the fracture decreases in proportion to the increase in the logarithm of loading rate. Under mechanical loading rates of 1×10−3 MPa/s and 5×10−3 MPa/s, the failure envelopes with friction coefficients of 0.78 and 0.74 were obtained, respectively. Thermoshearing test was conducted via heating in the direction of the constant minimum principal stress while expansion was restricted in the other direction of the maximum principal stress. A maximum loading rate caused by thermal stress was observed at around 0.9×10−3 MPa/s. Shear slip of the fracture occurred during the heating, and this can be well predicted by the Mohr-Coulomb failure envelope, which was obtained from the mechanical shear test at a similar loading rate.

Study of the shear strength evolution over time of two-component backfilling grout in shield tunnelling

The two-component backfilling system is the most commonly used method to fill the annular void created during the advancement of shield machines. This unavoidable void, strictly linked to the technology of shield machines, must be filled continuously in order to avoid mostly surface displacements and lining movements. Today, this technology is the most frequently used due to operative and technical advantages, which lead to economic savings. However, despite intensive use of this backfilling technology, very little information is currently available concerning the evolution of the material in function of the curing time. Historically, the uniaxial compressive strength has been used as the main parameter for testing the compliance of a certain grout with the site-specific technical requirements, but nowadays shear strength is also starting to be considered by designers even if this topic has never been investigated.In this work, a laboratory test campaign focused on shear strength and its evolution in function of curing was performed. These tests put alight the fast mechanical growing of the two-component grout from the shear strength point of view and it should be remarked that at the current state of research there are no investigations concerning the shear strength in the context of a drainage approach.Both short and long curing times were investigated according to the direct shear test, performed under drained conditions. The Mohr-Coulomb failure envelope model was selected for the study and its widening in time highlights the peculiarity of this technology. Starting from a liquid phase at t0, values of cohesion (c’) and friction angle (φ’) grow in function of curing, reaching 126 kPa and 22° at 3 h and exceeding 270 kPa and 40° at 28 days.

Incorporating shear stress ratio and load cycle number in a simple permanent deformation model for unbound material

A power model (ε = A. NB) to estimate permanent strain (ε) from single-stage repeated load triaxial (RLT) tests can simulate both shakedown and incremental collapse. When the exponent B < 1, the ε versus load cycle number (N) plot concaves downwards, resembling that of a material that shakes down. When B > 1, the same plot concaves upwards, mimicking that of a material that incrementally collapses. A power model that relates A and B to the shear stress ratio (SR = 1/factor of safety), a measure of how far the RLT specimen is away from static failure, is proposed. Use of SR as an independent variable in a PD model is advantageous because it embodies the geomaterial’s gradation, physical state, suction, stress level, shear strength and margin of safety against static failure. No other parameters bar N and SR are needed, enabling the number of independent variables and hence model complexity to be kept low. This model was applied to a virgin and a recycled concrete aggregate utilizing 2 independent variables (N and SR) with A and B both functions of SR. A rational procedure to estimate the mobilized shear stress is presented and a methodology to quantify SR that considers non-linearity of the Mohr-Coulomb failure envelope and cohesion due to suction in the unsaturated RLT specimens is proposed; such considerations have been absent in previous models. For the materials tested, A was found to decrease non-linearly with increasing SR while the relationship between B and SR is quite linear. The resulting model was able to simulate the RLT test data quite well with four fitting parameters. The fitting parameters can be easily derived using linear regression on a spreadsheet and were all statistically significant with a confidence level exceeding 95%. Once B is known, the shakedown limit can be estimated by setting B < 1. An appropriate margin of safety can be incorporated on the shakedown load to limit the permanent strain.

Displacement Analyses for a Natural Slope Considering Post-Peak Strength of Soils

A natural slope undergoing recurrent movements caused by rainfall-induced groundwater table rises is studied using a novel method. The strength and displacement parameters are back-calculated using a force-equilibrium-based finite displacement method (FFDM) based on the first event of slope movement recorded in the monitoring period. Slope displacements in response to subsequent rainfall-induced groundwater table rises are predicted using FFDM based on the back-calculated material parameters. Important factors that may influence the accuracy of slope displacement predictions, namely, the curvature of the Mohr-Coulomb (M-C) failure envelope and post-peak strength softening, are investigated. It is found that the accuracy of slope displacement predictions can be improved by taking into account post-peak stress-displacement relationship in the analysis. The accuracy of slope displacement predictions is not influenced by the curvature of the M-C failure envelope in the displacement analysis.