At-rest lateral earth pressure coefficient under narrow backfill widths: A numerical investigation

Fathipour H., Bahmani Tajani S., Payan M., Jamshidi Chenari R., Senetakis K.

In this study, the influence of transient flow on the active and passive lateral earth pressures of variably saturated backfills is thoroughly evaluated employing the lower bound theorems of the finite element limit analysis with second-order cone programming. In order to account for the tempo-spatial variations of suction stress within the soil stratum during infiltration, a closed-form solution derived for one-dimensional transient flow through variably saturated porous media is adopted. The unsaturated ground condition is simulated by incorporating the well-established unified effective stress approach into the soil yield function. The soil medium is considered to be both isotropic and anisotropic, due primarily to the various distributions of suction stress along different directions within the partially saturated porous medium. In order to model the soil suction stress anisotropy, an iterative procedure is employed by differentiating between the mobilized suction stress within the horizontal and vertical planes. In general, the influence of the transient flow condition is magnified for cohesive soils compared with granular backfills. In either case, such an effect is more noticeable for the active lateral earth pressure as compared to the passive counterpart. In the anisotropic condition, while the suction stress anisotropy within the soil medium has fairly negligible influence on the contribution of transient flow to the lateral earth pressure coefficient in the active state, the influence of elapsed infiltration time on the passive earth pressure coefficient turns out to be more at play at lower anisotropy ratios. • Soil-environment-structure interaction is examined with emphasis on lateral earth pressures. • FELA analyses are performed incorporating transient flow of the unsaturated backfill. • The influence of anisotropic matric suction is accounted for based on grain-scale considerations. • The results highlight the important influence of transient-flow and suction-stress anisotropy. • The effect of elapsed infiltration time is magnified in the presence of higher suction anisotropy.

Mirmoazen S.M., Lajevardi S.H., Mirhosseini S.M., Payan M., Chenari R.J.

In this paper, a detailed numerical study is conducted to evaluate the lateral earth pressure acting on geosynthetic-reinforced retaining walls with an anisotropic granular backfill subjected to strip footing loadings. To this end, the well-established lower bound theory of limit analysis coupled with the robust second order cone programming (SOCP) and the finite element discretization method is exploited and implemented in the stability analysis of reinforced retaining structures. For the finite element limit analysis, a number of constraints associated with the lower-bound axioms are satisfied, including element equilibrium, discontinuity equilibrium, boundary conditions and the yield criterion enforcement. By adopting second-order cone programming (SOCP) optimization, the nonlinear Mohr-coulomb failure criterion is simulated using three nodal auxiliary variables defined as functions of nodal stresses generated at each point. In addition, the primal-dual interior-point algorithm is adopted to gain the optimal solution for the unknown stress variables in the SOCP optimization problem. Accordingly, the contribution of soil inherent anisotropy to the influence of a number of parameters on the lateral earth pressure is thoroughly examined. It was observed that as the anisotropy ratio increases (the horizontal friction angle decreases) and the number of reinforcement layers decreases, the coefficient of active earth pressure increases in all cases of geosynthetic-reinforced retaining structure. Decreasing the number of reinforcement layers in the retained backfill will be translated into an equivalent softened material; hence, increasing the active earth pressure coefficient. In addition, the increase in the anisotropy ratio leads to the overall decrease in the shear strength of the backfill soil, causing the retaining structure to reach the limit state earlier at smaller displacements, thus giving rise to the increase in the coefficient of active lateral earth pressure. The rate of increase in the coefficient of active earth pressure with anisotropy ratio grows with the increase in the foundation width and load intensity and the decrease in the foundation-wall distance.

Fathipour H., Payan M., Jamshidi Chenari R., Senetakis K.

Realistic constitutive ground models are critical in the evaluation of soil-structure interaction problems and the assessment of key design parameters in the seismic analysis of infrastructure systems. In the present study, the modified pseudo-dynamic lateral earth pressures acting on retaining structure with granular backfill of depth-varying damping ratio are evaluated adopting the lower bound limit analysis in conjunction with the finite element (FE) discretization method using second-order cone programming (SOCP). The earthquake loading is simulated by the propagation of shear and primary waves through non-constant inertia forces in the horizontal and vertical directions, respectively. The influence of varying damping ratio alongside the retaining wall height on the seismic active and passive lateral earth pressures is effectively taken into account by adopting well-established formulas published in the literature. It is shown that failing to consider the damping variation with depth while performing the modified pseudo-dynamic analysis could lead to precarious, unrealistic estimates of design parameters.

Fathipour H., Payan M., Jamshidi Chenari R.

In this paper, a thorough numerical study is conducted to rigorously evaluate the lateral earth pressures exerted on the retaining walls backfilled with geosynthetic-reinforced soil strata. With this aim, the lower bound theorem of limit analysis is exploited in conjunction with the finite element discretization method. The computational programming adopting second-order cone optimization is employed to model the Mohr-Coulomb yield criterion in its respective nonlinear form. The reinforcement layers are assumed to bear solely axial tension; but not bending moment, which is the common characteristic of all geosynthetic materials. Results show that the horizontal stress field behind retaining structures is heavily disturbed by placing geosynthetic layers, especially in close proximity to the retaining structure. Accordingly, the failure zone shrinks in size and the lateral earth pressure decreases by either adding more reinforcement layers or increasing their relative lengths. Through a comprehensive parametric survey, the influence of several parameters, including internal friction angle, soil-wall and soil-reinforcement interface friction angles, length and number of reinforcements, soil inherent anisotropy and surface loading on the lateral earth pressure is meticulously examined. The employed formulations are rigorously compared with results published in the literature. A design table is also provided so as to effectively estimate the active earth pressure coefficient of geosynthetic-reinforced walls accounting for all contributing parameters.

Safardoost Siahmazgi A., Fathipour H., Jamshidi Chenari R., Veiskarami M., Payan M.

Design of shallow foundations subjected to dynamic loading is an important topic in the geotechnical engineering practice. In this study, an attempt has been made to evaluate the seismic bearing ca...

Lade P.V., Duncan J.M.

Based on the results of cubical triaxial tests on Monterey No.0 Sand, an elastoplastic stress-strain theory was developed for cohesionless soil. The theory incorporates a new failure criterion, a new yield criterion, a new flow rule, and an empirical work-hardening law. The theory is applicable to general three-dimensional stress conditions and it models several essential aspects of the soil behavior observed in experimental investigations: nonlinearity, the influence of σ 3 , the influence of σ 2 , stress-path dependency, shear dilatancy effects, and coincidence of stress increment and strain increment axes at low stress levels with transition to coincidence of stress and strain increment axes at high stress levels. Results of cubical triaxial tests, torsion shear tests, and tests performed using various stress-paths were analyzed using the theory, and it was found that the stress-strain and strength characteristics observed in these tests were predicted with reasonable accuracy.

Fathipour H., Siahmazgi A.S., Payan M., Veiskarami M., Jamshidi Chenari R.

Abstract This paper aims at analyzing the active and passive lateral earth pressures exerted on retaining walls due to the anisotropic medium of dry and noncohesive backfill subjected to the modifi...

Kodicherla S.P., Gong G., Fan L., Wilkinson S., Moy C.K.

This article studies the influences of particle morphology on the behaviors of granular materials at both macroscopic and microscopic levels based on the discrete element method (DEM). A set of numerical tests under drained triaxial compression was performed by controlling two morphological descriptors, i.e. ratio of the smallest to the largest pebble diameter, ξ , and the maximum pebble–pebble intersection angle, β . These descriptors are vital in generating particle geometry and surface textures. It was found that the stress responses of all assemblies exhibited similar behavior and showed post-peak strain-softening. The normalized stress ratio and volumetric strains flatten off and tended to reach a steady value after an axial strain of 40%. While the friction angles at peak state varied with different morphological descriptors, the friction angles at critical state showed no significant variation. Moreover, evolution of the average coordination numbers showed a dramatic exponential decay until an axial strain of about 15% after which it stabilized and was unaffected by further increase of axial strain. In addition, stress ratio q / p and strong fabric parameter ϕ d s / ϕ m s were found to follow an approximately linear relationship for each assembly. These findings emphasized the significance of the influences of particle morphology on the macroscopic and microscopic responses of granular materials.

Fathipour H., Safardoost Siahmazgi A., Payan M., Jamshidi Chenari R.

This paper aims at studying the active and passive earth pressures on the retaining structures having an unsaturated backfill. To this end, the well-established lower bound limit analysis coupled with the finite element method and the second-order cone programming (SOCP) has been employed to generate the admissible stress field within the soil medium behind the retaining wall. In order to simulate the unsaturated soil condition, the unified effective stress approach is adopted and implemented in the universal Mohr-Coulomb yield criterion. Using the results of several numerical simulations, the influence of various controlling parameters, including flow rate condition, soil–water retention curve (SWRC) and groundwater table level on the response of the retaining wall with an unsaturated backfill is thoroughly examined. Furthermore, the active and passive earth pressures are rigorously evaluated accounting for the variations of the wall height, soil type, effective internal friction angle, soil-wall roughness and soil inherent anisotropy. It is shown that as the existence of suction stress in unsaturated soils results in the greater values of the effective stress, and consequently the soil shear strength, it would lead to the lower active and higher passive lateral pressures exerted on the retaining structure.

Garcia‐Suarez J., Asimaki D.

The assessment of forces exerted on walls by the backfill is a recurrent problem in geotechnical engineering, owing to its relevance for both retaining systems and underground structures. In particular, the work by Arias and colleagues, and later also the one by Veletsos and Younan, among others, becomes pertinent when considering pressure increments on underground structures triggered by seismic events. As a first step, they studied the response of a rigid retaining wall resting on rigid bedrock subjected to SV waves, introducing some simplifying assumptions. This paper presents the exact solution to this reference problem. The solution is given in horizontal wavenumber domain; hence, it comes in terms of inverse Fourier transforms, which can be approximated numerically in Mathematica , which in turn are verified against finite‐element simulations. Specific features of this exact solution that were not captured by prior engineering approximations are highlighted and discussed.

Kodicherla S.P., Gong G., Yang Z.X., Krabbenhoft K., Fan L., Moy C.K., Wilkinson S.

This study examines the influence of particle elongation on the direct shear behaviour of granular materials using the discrete element method. A series of numerical direct shear test simulations were performed, and both the macroscopic and microscopic behaviour of elongated assemblies at the critical state were examined. The macroscopic response of elongated particles exhibits an initial hardening followed by post-peak strain softening, prior to reaching the critical state. The peak state friction angles initially increase and stay stable as the dimensionless elongation parameter ($$\eta$$) increases, whereas the critical state friction angles increase with the increase of $$\eta$$. Independent of the applied normal stresses, all samples reach a critical state at a unique normalized stress ratio (i.e., $$\tau /\sigma = 0.51$$) after ~ 25% shear strain. The stress-fabric relationship is mainly governed by the strong force subnetwork which is more affected by the change of η than the weak force subnetwork. Particle elongation generates a downward shifting of critical state lines (CSLs) in $$e - p^{{\prime }}$$ space. Furthermore, the correlations between CSL parameters and $$\eta$$ are well-fitted by a second-order polynomial function. These findings highlight the significance of particle elongation on direct shear behaviour of granular materials.

Behravan Rad A.

Solids that exhibit negative Poisson's ratio are called auxetic materials. Static behavior of the auxetic-porous structures has not been investigated so far, especially for structures composed of multi directional heterogeneous materials. The two parameter elastic foundation (Pasternak type) is developed by taking into account the torsional interaction and horizontal friction force. The material properties of the plate except the Poisson's ratio are assumed to be graded in the thickness and radial directions according to exponential functions. The governing state equations are derived in terms of displacements based on 3D poroelasticity theory. These equations are semi-analytically solved using state-space based differential quadrature method. A detailed parametric study is carried out to highlight the influences of key parameters on the static response of non-uniform bi-directional functionally graded auxetic-porous material (FGAPM) circular plates to compound mechanical tractions. Finally, the static response of circular plates composed of various functionally graded materials to compound mechanical loads is compared. Results reveal that the auxeticity of the material, torsional couples on the plate and rotary interaction of the elastic foundation play important roles on the static behavior of the plate.

Zheng Y., Fox P.J., McCartney J.S.

AbstractThis paper presents a numerical investigation of the deformation and failure behavior of geosynthetic reinforced soil (GRS) bridge abutments. The backfill soil was characterized using a non...

Kodicherla S.P., Gong G., Fan L., Moy C.K., He J.

This paper investigates the effects of different preparation methods (dry tamping, moist tamping, dry pluviation and wet pluviation) on inherent fabric anisotropy of reconstituted sand samples in t...

Leshchinsky D., Leshchinsky B., Leshchinsky O.

Conventional design of geosynthetic-reinforced soil structures is divided into two categories, walls and slopes, based on the batter of its facing system. Internal stability, characterized as sufficient reinforcement anchoring and strength, is performed using earth pressure-based design criteria for reinforced walls while reinforced slopes are founded on limit equilibrium (LE) slope stability analyses. LE analyses are also used to assess the global or compound stability of both types of structures, accounting for the geometry of the reinforced, retained and foundation soils. The application of LE-based methods typically results in determination of a slip surface corresponding to the lowest attained Safety Factor (SF), known as the Factor of Safety (Fs); however, it yields little information about reinforcement loading or connection load. In this study, use of the analyzed spatial distribution of SF known as a Safety Map, is modified to attain a prescribed constant Fs at any location in the reinforced soil mass. This modified framework, implemented through an iterative, top-down procedure of LE slope stability analyses originating from the crest of a reinforced structure and exiting at progressively lower elevations on the facing, enables the determination of a Tension Map that illustrates the required distribution of reinforcement tension to attain a prescribed limit state of equilibrium. This tension map is directly constrained by a pullout capacity envelope at both the rear and front of each reinforcement layer, providing a unified, LE-based approach towards assessing an optimal selection of mutually dependent strength and layout of the reinforcement. To illustrate the utility of the Limit State framework, a series of instructive examples are presented. The results demonstrate the effects of facing elements, closely-spaced reinforcements, secondary reinforcement layers, and is compared to conventional design approaches.