International Journal of Geomechanics

In modern geotechnical engineering, the study of the geometry of the porous matrix has been shown to be of fundamental importance. This emerges from the growing usage of numerical methods, which require a computational domain that best represents the simulated medium. Based on those needs, the present paper analyzed and validated the usage of cellular automata as a way to generate a physical-computational model for porous media. First, the possibility of obtaining flow parameters by means of pore-scale simulations in computational domains was discussed. Then, with respect to the three-dimensional (3D) cellular automata (CA), a complete study was performed to obtain rules that are of interest to represent the porous media. This study contemplated the evaluation of porosity and permeability of the artificial medium under the concepts of a representative elementary volume (REV). Finally, a real sand porous medium was modeled by an artificial CA medium, showing that the methodology proposed is applicable to mimicking real porous media.

In this study, first the numerical modeling of the piezocone penetration test (CPTu) is performed. Then the obtained results are used to achieve a reliable solution for determining the undrained shear strength and in situ horizontal effective stress in cohesive soils according to the piezocone measurements. The presented solution results in three main relationships that must be used in a trial-and-error process to obtain the previously mentioned parameters. The proposed equations are then compared with the laboratory piezocone tests and well-known published field measurements. The comparisons indicate an acceptable degree of accuracy for predicting the undrained shear strength and in situ horizontal effective stress from the cone tip resistance and induced pore-water pressure at the cone shoulder, which are measured during a piezocone test.

In the traditional discontinuous deformation analysis (DDA) method, the implicit time integration scheme is used to integrate equations of motion for modeling the mechanical behavior of a highly discrete rock block system. This requires that global equations be constantly solved. Hence, the computational efficiency of the traditional DDA method will decrease, especially when large-scale discontinuous problems are involved. Based on the explicit time integration scheme, an explicit version of the DDA (EDDA) method is proposed to improve computational efficiency of the traditional DDA method. Since a lumped mass matrix is used, there is no need to assemble global mass and stiffness matrices. More importantly, solving large-scale simultaneous algebraic equations can be avoided. The open–close iteration, which can assure the correct arrangement of constraints, is kept in the EDDA method. In addition, the simplex integration method, which is capable of conducting exact integration over an arbitrarily shaped block, is employed. Two numerical examples, including a sliding problem with an analytical solution and an underground cavern, are solved. The numerical results indicate the accuracy and robustness of the proposed EDDA method.

This study aimed to understand the behavior of non-Darcy water fluid flow through a single joint in rock. Water flow tests through three splitting mated granite joints with natural characteristics were conducted beyond the range of previously tested conditions using the designed experimental apparatus. This study expands on previous work as follows: (1) A rough rock joint with natural characteristics was adopted rather than a smooth, parallel plate model; (2) the aperture and surface roughness could be precisely controlled; and (3) the maximum pressure gradient could reach 250. A single fracture was formed by two mated rough joint surfaces with variable apertures ranging from 0.5 to 2 mm (constant opening between upper and lower parallel surfaces). The three-dimensional (3D) surface morphology of the rock joints was obtained from a noncontact, 3D stereotopometric measurement instrument before the rock joints were tested. The roughness parameters of the rock joints were then calculated by self-programmed software. For each specimen, flow tests were conducted for four mechanical apertures and eight pressure gradients (maximum of 250). A nonlinear relationship between hydraulic gradient and water flow velocity was demonstrated and fitted well with Izbash’s law. The effect of joint roughness and aperture on the coefficient λ and power exponent n of Izbash’s law was further explored in this experiment (i.e., to maintain the same joint roughness coefficient or aperture). Finally, a new relationship between aperture ratio (hydraulic aperture to mechanical aperture) and Reynolds number is proposed based on the laboratory observations. These findings may be beneficial for the design of model experiments and computational studies on coupled shear-flow properties through real rock joints or highly jointed rocks.

To obtain the critical collapse pressure of a circular tunnel driven by a pressurized shield for purely cohesive soils, a two-dimensional analysis model is presented based on limit analysis and slip-line theories. When the ratio of the cover depth C to the tunnel diameter D equals 0.5, there are three regions, Zones I, II, and III. When the C/D value is greater than 0.5, the mechanism involves up to four regions, i.e., Zones I, II, III, and possibly IV. Zone II is a transition zone that satisfies the normality condition. Zone IV is a Rankine zone subjected to the influence of the vertical soil arching effect that appears at the top of Zone III. Under Terzaghi’s theory of relative soil pressure, the contribution of Zone IV, including the weight and cohesion of the soils and the uniform surcharge loading, to the critical collapse pressure of the tunnel face is equivalent to an additional load. The proposed failure mechanism improves the existing upper-bound solutions for the face stability of circular tunnels in purely cohesive soils.

Knowledge of underground stresses (e.g., minimum horizontal stress) is vital for many aspects of oil and gas development, such as wellbore stability evaluation, lost-circulation prediction, casing design, hydraulic-fracturing design, sand-production prediction, and reservoir-compaction evaluation. Field injectivity tests performed during drilling a well, such as the extended leak-off test (XLOT) and pump-in and flowback (PIFB) test, are the primary method for obtaining that information. In this study, a fully coupled fluid-flow and geomechanics model was developed for numerical simulation of field injectivity tests. The model takes into account key elements of the tests, including fluid flow into the well, hydraulic fracture propagation, fluid flow in the fracture, pore-fluid flow, and deformation of formation rock. The model is validated against an existing analytical model and a field test reported in the literature. Finally, numerical examples are shown for injectivity tests with pump-in, shut-in, and flowback stages in formations with high permeability and low permeability, respectively. The development of fracture geometry and injection pressure was quantified during the tests. The results show that the essential features of injectivity tests observed from field practices can be captured by the model. It is demonstrated that fluid leak-off on fracture surfaces can significantly influence pressure response and fracture behavior. The results also illustrate that the traditional method for interpretation of the test based on time development of injection pressure has difficulty in properly determining the minimum principal in situ stress in formations with low permeability because of limited leak-off. The model presented in this article provides a useful tool for optimizing the design of injectivity tests, ensuring sufficient and high-quality data, and aiding interpretation of the tests.

Bioreactor landfills using leachate recirculation in municipal solid waste (MSW) undergo complex interrelated hydraulic, mechanical, and biochemical processes. In this study, the authors present a mathematical framework that combines and solves together a hydraulic model, a biodegradation model, and a mechanical model to simulate and predict the coupled hydro-bio-mechanical behavior of MSW in bioreactor landfills. The mathematical framework was implemented in Fast Lagrangian Analysis of Continua (FLAC), a finite difference code. The hydraulic model was a two-phase flow model where the fluid flow was governed by Darcy’s law while the saturated–unsaturated hydraulic behavior was governed by a soil-water retention model. The mechanical behavior of the MSW was evaluated by a plane-strain explicit formulation of the Mohr-Coulomb constitutive model, which accounted for concurrent changes in the MSW properties as a result of the MSW degradation. The MSW decomposition was modeled as a first-order decay kinetics biodegradation model similar to the LandGEM model used by the United States Environmental Protection Agency. The coupled mathematical framework was validated with a published large-scale laboratory experiment and a field-scale experiment. It was applied to simulate the coupled behavior of a typical bioreactor landfill cell undergoing hydro-bio-mechanical interactions. Overall, the study shows that the proposed mathematical framework accounted for both the spatial and temporal changes in the geotechnical properties of the MSW, including the extent of degradation, and predicted the landfill settlement and MSW stabilization time for a typical bioreactor landfill configuration subjected to coupled hydro-bio-mechanical processes. In addition, some of the limitations and key challenges associated with the numerical model are highlighted.

A series of numerical simulations were carried out on two types of superstructures and six types of piled raft foundations to investigate the effects of seismic soil–pile–structure interaction (SSPSI) on the seismic responses of the superstructures. In this research, the effectiveness of a piled raft application was assessed; the pile optimum numbers, locations, and configurations were estimated; and finally, a comparison was made between the nonlinear structural responses of the obtained two-dimensional (2D) and three-dimensional (3D) models. Parametric studies were conducted to achieve strategies for optimized designs of piled raft foundations subjected to the low-to-high intensities of real earthquake records as the input motions. The numerical results represented a reasonable correlation between the shaking intensity rates (SIRs) and maximum interstory drifts of the structures. It was discovered that the performance levels of the structures on a softened ground were a function of the area replacement ratios, lengths, diameters, and spaces between the piles; ground motion features; and height/width ratios of the structures. These important aspects had to be regarded to achieve a reliable design. The aim of this investigation was to ameliorate the characteristics of a system of long–short combined piled raft foundations based on an understanding of the interaction mechanics.

Stress-strain responses, including small-strain behavior, of Hong Kong completely decomposed granite (CDG) were investigated using triaxial specimens prepared from Mazier samples in a manner in which structure in the soil was essentially preserved. The observed behavior was different from what has been reported by previous researchers, which was attributed to the preservation of structure in the specimens. In particular, obvious shearing dilatancy (as measured by ${d\epsilon }_{\mathrm{v}\mathrm{o}\mathrm{l}}/{d\epsilon }_1$) was observed for the tests conducted with confining stress larger than the in situ stress. It was found that the hardening soil small-strain (HSS) model was able to capture most of the observed prefailure behavior, and most of the intrinsic assumptions of the HSS model were satisfied. All input parameters in the HSS model could be determined objectively from the triaxial tests, and the maximum shear modulus at the very-small-strain region could be obtained from the precise small-strain measurements without the need of bender-element testing. The HSS model was then incorporated into a finite-element (FE) study of a basement-raft footing on Hong Kong CDG. This study shows that (1) neglecting the small-strain component in the model could lead to an overestimation of settlement by 55%, and (2) inclusion of cap yield is significant. The FE analysis results clearly demonstrate basement-raft footings can support middle to high-rise buildings in Hong Kong without excessive settlement.

This article presents an optimal design for reinforced pad and strip foundations, based on multiparametric, mixed-integer, and nonlinear programming (MINLP) optimizations. For this purpose, a MINLP optimization model STRIPPAD was developed. The model is based on an accurate objective function of the structure production costs. It was subjected to design, resistance, stiffness, and settlement constraints that satisfy the requirements of the ultimate and serviceability limit states of the Eurocode specifications and recommendations for design and analysis of earth structures using geosynthetic reinforcements. The optimal design of the reinforced pad foundation and strip foundation was investigated for design parameters that have a significant impact on structure costs. A series of MINLP optimizations was done over a wide range of various parameters: different vertical loads on the strip foundation, alternatives of discrete cross sections, and different friction angles of the soil. Based on these results, an optimal design for reinforced pad and strip foundations was developed. Economically suitable foundation types for various soil and load conditions were found.

This paper addresses the problem of the experimental characterization of cement-treated compacted soils in terms of microstructural, hydraulic, and mechanical properties. Tests were conducted on two different types of soil: silty sand and clay as fine soils, and gravelous sand and alterite as granular soils. Samples were mixed with 5% cement and compacted at different levels (i.e., 85, 95, 100, and 105% of the maximum dry density, respectively, as achieved using the standard compaction method). The results of the mercury intrusion porosimetry (MIP) tests performed on these cement-treated soils revealed significant changes regarding macropores. A reduction in both size and volume due to the combined effects of treatment and compaction was observed in fine soils, and an even higher reduction was seen in granular soils. Because the permeability was mainly governed by the macropores, a decrease in the permeability was clearly observed for all tested soils when the degree of compaction increased. This decrease was significantly greater in fine soils, which were more sensitive to compaction effects than granular soils. Unconfined compressive strength (UCS) results showed that the addition of cement improved UCS values due to an increase in cohesion. The cohesion increase was generated by the cement bonding and enhanced by the compaction effect. Based on a recently developed approach, a prediction model for the permeability of cement-treated compacted soils was proposed. Microstructural and compaction characteristics were taken into account. This original predictive model considered the treatment effects on both the pore interconnection and the morphological parameters of the pore structure (i.e., constrictivity and tortuosity).

In slope stability analysis, there are two commonly used methods for calculating the factors of safety (FS). The first is the strength reduction method (SRM), which defines the FS as the ratio of the real material shear strength to the critical shear strength in the limit equilibrium state. The second is the gravity increase method (GIM), which defines the FS as the ratio of the critical increased gravity to the actual gravity. On the basis of a kinematically admissible three-dimensional (3D) failure mechanism, this paper develops a framework to compare these two kinds of FS. Earthquake effects are included in the study by using the quasi-static representation. By means of the kinematic approach of limit analysis, the GIM can give an explicit function about the FS, while the SRM can only provide an implicit equation on the FS. The lowest solutions for both two kinds of FS are obtained by optimizing the variables from the 3D failure mechanism. Numerical results are calculated and presented in the forms of graphs to show the difference between these two kinds of FS. It is shown that the FS calculated by the SRM is equal to that calculated by the GIM when the slope is in the limit state (FS = 1.0), that the FS by the SRM is greater than that by the GIM for an unstable slope (FS < 1.0), and that the FS by the SRM is smaller than that by the GIM for a safe slope (FS > 1.0). Finally, a power function is proposed to approximately express the relationship between these two kinds of FS.

Finite element limit analysis (FELA) was used to investigate the bearing capacity of strip footing on a rock mass with single or multiple continuous voids. The underlying rock mass was assumed to have perfect plasticity and obey the modified Hoek–Brown criterion. A sensitivity study relevant to the material constants, such as intact rock strength, unit weight, and geological strength index, was also conducted; in addition, some other geometric parameters, including the location, size, width, height, and quantity of voids, were addressed. The results include presentations of a series of design charts and descriptions of the failure mechanisms.

Traditionally, factors of safety have been used to design mechanically stabilized earth (MSE) walls; however, the uncertainties associated with input parameters have not been considered. The probabilistic analysis of MSE walls was an appropriate approach to consider all uncertainties. The authors of this paper investigated the performance of MSE walls by using reliability and sensitivity analyses. A finite-element model of an MSE wall was developed and verified on the basis of field measurements of a reference wall to approximate performance functions. The failure probability of the MSE wall was determined using the first-order second-moment (FOSM), first-order reliability method (FORM), and improved Latin hypercube sampling (iLHS) method, considering external and internal stability in addition to the horizontal wall displacement limit state. Uncertainties associated with soil and reinforcement properties, soil–geosynthetic interface friction angle, and the magnitude of surcharge load were considered for the reliability analysis. Probabilistic characteristics of soil unit weight, soil friction angle, soil–geosynthetic friction angle, geosynthetic tensile strength, and modulus of elasticity of the geosynthetic were experimentally determined, and over 500 tests were performed. A sensitivity analysis was then performed through the FOSM and FORM, and the most effective random variables were determined according to each limit state function. The reliability analysis revealed that, although the FOSM and FORM were appropriate methods to determine the initial approximation of the failure probability of a MSE wall, the iLHS method was more practical and accurate for this analysis because of the nonlinearity of the limit states. Furthermore, the sensitivity analysis results indicated that the most effective parameter in sliding and pullout failure was the soil–geosynthetic interface friction angle, and in overturning, it was the soil friction angle. Moreover, the most effective parameter, second only to the tensile strength of the geosynthetic, was the surcharge load in the rupture limit state. In conclusion, the most significant random variables for horizontal wall displacement in the sequence were the modulus of elasticity of the geosynthetic, magnitude of the surcharge load, and soil friction angle.

An interesting operation has been developed to estimate the critical normalized surface settlement for shallow tunnels in undrained clay (idealized as a homogeneously Tresca material). The upper-bound finite-element method in combination with a plastic-dissipation-based mesh adaptive strategy is used to obtain upper-bound solutions and velocity fields. Based on the vertical velocity field, the corresponding critical surface settlement field is obtained by introducing an assumed constraint related to soil deformation. The results show that the critical normalized surface settlement pattern is similar to a plug with concentrated strain at the bottom, and the calculated settlement data are fitted well by superimposing two Gaussian curves. The widths of the main settlement trough and the plug increase with increasing dimensionless unit weight γD/c, and the plug-type settlement pattern is easily recognized with an increase of dimensionless depth H/D. For different combinations of H/D and γD/c, a new normalized equation is developed to evaluate the critical normalized surface settlement. The results agree reasonably well with the solutions reported in the literature.

The development of shear rupture in granular media due to boundary deformation was captured using the distinct element method (DEM). Assemblages of nonspherical, three-dimensional particles undergoing direct shear test simulations exhibited a range of soil responses, from highly contractive to highly dilative depending on their initial void ratio as well as the applied normal stress. Arched structures of strong contact forces that are consistent with the stress-arching phenomenon developed during anchor pull-out and trapdoor simulations. Earthquake fault rupture propagation through soil varied systematically for reverse and normal faults dipping at various angles. The final shapes of the shear rupture surfaces were consistent with those expected based on a model developed through sandbox experiments. Key details of the shear rupture mechanisms during surface fault rupture were elucidated through examination of particle rotations, frictional dissipation, shear strains, volumetric strains, and contact forces. The mechanism of graben formation was shown through the reduction of the magnitude of the contact forces at the top of the soil arch that formed above the bedrock fault. DEM simulations provided useful insights into boundary deformation problems.

Weak infilled discontinuities commonly exist in rock masses, in which the infill degree of saturation largely influences the overall joint shear behavior and ground stability. However, so far, research on the shear of infilled joints at unsaturated conditions is rare, especially those performed in numerical simulation. To the authors’ knowledge, no attempts have been made to investigate the shear-induced variations in unsaturated soil parameters, which are vital for proposing the infilled-joint constitutive models. For the first time, a series of constant water content direct shear tests on the unsaturated infilled-joint soil were conducted using the numerical software Fast Lagrangian Analysis of Continua (FLAC)/Two-Phase Flow. Intrinsic soil-water retention and permeability models were updated in the FISH subroutine to consider porosity. Results highlight the disadvantage of the built-in models in FLAC. Initial infill saturation and other factors, including physical shear rate, joint roughness, infill thickness, and normal stress, all showed effects on the joint shear strength consistent with literature reports. Shear-induced variations in the mean values of Bishop effective stress and permeability of the infill layer were emphasized.

The quasi-static collapse of granular material where the effect of particle inertia is negligible is an important topic of interest in various natural phenomena and industrial processes. However, less focus has been placed on experimental and numerical studies of this type of collapse. To provide a better understanding of the quasi-static and dynamic collapses of granular materials and the transitional behavior between these two collapses, a three-dimensional (3D) smoothed particle hydrodynamics (SPH) model was developed and used to investigate the collapse of rectangular sand columns with aspect ratios ranging from 0.26 to 11. To model the sand under flow-type failure, the Drucker–Prager constitutive model with nonassociated flow rule was implemented in the SPH formulations. The quasi-static collapse was initiated by slowly moving one of the side walls, and dynamic collapse was modeled by suddenly removing the wall. The SPH results reveal that both quasi-static and dynamic collapses show qualitative similarities and primarily depend on the initial aspect ratio of the column, resulting in two deposit morphologies, including a truncated wedge-like final deposit with a flat surface at the top for small aspect ratios and a wedge-like deposit with a tip for large aspect ratios, which is consistent with experimental observations in the literature. For quasi-static collapse, the final deposit profile (e.g., final height, runout distance) and energy dissipation were theoretically derived and were found to be in close agreement with SPH simulations and experiments. The sensitivity of the deposit profile to the wall velocity was also investigated to provide useful insight into the transitional behavior between quasi-static and dynamic collapses. This sensitivity analysis revealed that the transition between quasi-static and dynamic collapses occurs within a small range of Midi numbers.

This paper proposes an innovative concept of adaptive constitutive soil modeling to optimize the complexity of the numerical simulation of shield tunneling. This concept involves the use of an adequate constitutive model for soil, in accordance with mechanical incidents in the domain, to reduce the number of complex soil parameters and computational costs, focusing on the accuracy of numerical predictions. In such an approach, adequate soil investigation can be scheduled by designing a limited number of sophisticated laboratory tests at certain locations, while the rest of the domain can be explored with basic conventional laboratory tests to identify ordinary soil parameters. This concept leads to obtaining adequate and dominant soil parameters at each depth to accurately simulate the phenomenological aspects of soil behavior and soil–tunnel boring machine (TBM)–tunnel interactions without inducing inadmissible uncertainty in terms of advanced soil parameters for unaffected zones. The numerical model accounts for such constructional components face support, grouting in the annular gap, and lining installation. The numerical model responses are studied through the investigation of the evolution of the ground subsidence, as well as soil stresses and lining forces. The behavior of the soil is assumed to be described by a family of hierarchical elastic–plastic constitutive models based on Mohr-Coulomb failure theory. In addition, the size of the target zone where the model adaption should be conducted is studied while its influences on model responses are addressed. Finally, the contribution of the proposed solution to reduce the uncertainty of the numerical predictions is evaluated.

A series of one-way and long-term (10,000 cycles) cyclic triaxial tests was carried out to investigate the cyclic behavior of peaty soil from Kunming, China. The organic components of the peaty soil were generally highly decomposed and amorphous. The cyclic behavior of the peaty soil under long-term cyclic loading was found to be highly dependent on the ratio between cyclic stress amplitude and shear strength [cyclic stress ratio (CSR)], loading frequency, drainage conditions, and consolidation stress conditions. The cyclically induced accumulations of permanent strain and excess pore pressure at a given number of cycles were found to increase with an increase of CSR and decrease with an increase in loading frequency. The permanent strain accumulation rate was greater for the peaty soil than that for the inorganic soils reported in the literature. In addition, the permanent strain during cyclic loading was always larger for anisotropically consolidated specimens than for isotropically consolidated specimens. A correction factor of 1.44 is proposed for the isotropically consolidated specimens to reflect the anisotropic consolidation condition. The permanent strain was greater in undrained specimens than that in partially drained specimens for a high CSR. The strain difference was greatly reduced with a decrease of CSR, and more permanent axial strain presumably would be accumulated in a partially drained specimen if CSR further decreased. Finally, an advanced model for the peaty soil subjected to long-term cyclic loading under the undrained condition is proposed by combining classical elastoplastic theory and empirical equations. This model is implemented in finite-element formulations and validated through simulations of element tests and a shallow foundation subjected to long-term repetitive loading.

Rainfall-induced landslides are common natural hazards in tropical regions. The present study investigates a rainfall-induced landslide that occurred in 2009 in the Marappalam area of Nilgiris district, Tamil Nadu, India. It was triggered by a high-intensity short period of rainfall that occurred after a prolonged low-intensity rainfall at Marappalam. The effect of rainfall infiltration on the unsaturated residual soil slope was investigated by transient seepage analysis using the finite difference method. The fluid–mechanical interaction of unsaturated soil has been obtained using coupled fluid flow analysis. The analysis was carried out in two stages. The first stage saw prolonged low-intensity rainfall of 710 mm over 8 months. The second stage showed a short-duration, high-intensity rainfall of 719 mm in just 10 days, which caused a landslide in Marappalam. It was observed that the first rainfall event saturated the Marappalam slope to a degree of saturation of 0.6. The saturation level increased during the second rainfall, which advanced the wetting front to the lower layer of the Marappalam slope and saturated the slope to the degree of saturation of 0.8. The wetting front reached the soil–rock interface at the end of the second rainfall event, increasing soil saturation and seepage force, accompanied by reduction in matric suction and the subsequent development of positive pore water pressure. The development of positive pore water pressure decreased the effective stress, thus reducing the shear strength of the soil along the soil–rock interface, causing landslide in Marappalam. The study also described the relationship between rainfall and landslide occurrence based on daily and antecedent rainfall in conjunction with past landslide events occurring in the Marappalam region. The rainfall-threshold relationship provided the optimum level of daily and 5-day antecedent rainfall required to trigger landslides in the Marappalam region, which can be used for early warnings at the regional level.

This paper presents the results of monitoring the diaphragm wall and ground surface settlement and three-dimensional finite element analyses of the Xizhi excavation case history. The Xizhi excavation was 9.2 m deep, covering an area of about 195.7 m $\times$ 88.6 m. The soil layers above the final excavation level are dominated by a soft-to-medium clay layer (N_SPT = 2–7) and a loose silty sand layer (N_SPT = 2–6). Because of its large excavation geometry, this project utilized diaphragm walls, buttress walls (BWs), and partial floor slabs as a BW strut-free retaining system to reduce the construction cost and period. This project was successfully constructed with a ratio of the maximum wall deflection to excavation depth equal to 0.55% and a maximum ground surface settlement of 27 mm. The mechanism of the BW strut-free retaining system in controlling wall deflections was governed by two factors: the combined stiffness between the buttress and diaphragm walls and the frictional resistance between BWs and adjacent soils, where they contributed 72% and 10.5% reduction of the wall deflection, respectively. In addition, the effectiveness of the first partial floor slabs in reducing the top wall deflection depended on the length of the diaphragm wall. The shape, location, and length of BWs had only moderate effects, while the groundwater level had a major effect on the performance of the BW strut-free retaining system.

Vegetation induces heterogeneity in the soil porous structure and, hence, relative permeability ($k_r)$ as well. The main objective of this study is to address the uncertainties associated with relative permeability using probabilistic analysis for vegetated covers (i.e., grass and tree species). Bare cover is used as control. For this purpose, the dependence structure of suction, $\psi$, and volumetric water content,${\theta }_w$, is established via copula theory, and the $k_r$ curves are predicted with respect to varying levels of suction–volumetric water content correlation. It is found that the $k_r$ of vegetated covers is substantially lower than that in bare covers. The reduction in $k_r$ (with drying) is more in treed cover than grassed cover, since tree roots induce higher levels of suction. Moreover, the air entry value (AEV) of the soil depends on the magnitude of suction–volumetric water content correlation, which, in turn, is influenced by the type of vegetation in the soil. The $k_r$ is highly uncertain in the desaturation zone of the relative permeability curve, which is likely due to inaccuracy of suction measurements beyond 100 kPa. The stochastic behavior of $k_r$ is found to be most significant in treed covers. Finally, a simplified case study is also presented in order to demonstrate the impact of the uncertainty in relative permeability on the stability of vegetates slopes. The factor of safety (FS) is found to vary around 4 to 5% for both bare and vegetated slopes.

This note presents an analytical method for predicting the uplift capacity of a single pile embedded in sand, considering the arching effect. Taking into account the passive stress state of dense sand and the active stress state of loose sand adjacent to uplift pile, a theoretical solution for the lateral earth pressure coefficient for sand with different soil densities is proposed. The failure surface was assumed to be an inverted frustum of a cone with a characteristic angle of inclination. Using the limit equilibrium method, a closed-form solution for the uplift capacity of a single pile embedded in sand was established without requirement of any charts or tables. To assess the roles of the arching effect on the accurate prediction of uplift capacity and the reliability of the proposed analysis approach, comparisons between theoretical and available laboratory experiments and field test results, on sand ranging from loose to dense, were made.