Active Earth Pressure Coefficient Research Articles

Numerical Simulation of Polymeric Strap Material Reinforced Walls Under Seismic Excitation

This paper presents a comparison between the two-dimensional finite element and experimental results of shaking table tests on six one-third-scale polymeric strap or polymeric geostrip reinforced walls performed under seismic excitation at given peak ground accelerations [Formula: see text]. The effects of initial tangent stiffness or the stiffness of polymeric strap material [Formula: see text] and the slope angle of the cohesionless backfill material [Formula: see text] on the maximum relative displacement, [Formula: see text], of the reinforced earth wall, the values of the horizontal incremental dynamic earth pressure [Formula: see text] with distributions, acceleration responses, horizontal dynamic active earth pressure coefficient [Formula: see text] and maximum dynamic tensile forces [Formula: see text] were assessed in this study. Moreover, the vertical dynamic active earth pressure coefficients [Formula: see text] and the angles of the resulting dynamic active force with horizontal [Formula: see text] were predicted from the numerical analysis. Closely matched responses between the experimental and numerical studies were attained. Data obtained from experimental and numerical studies illustrated that increasing the slope angle of the cohesionless backfill material resulted in an increase in the values of horizontal displacement in the walls, and in dynamic earth pressure and root mean square acceleration [Formula: see text]. Increasing the stiffness of the reinforcement material caused a decrease in horizontal reinforced earth wall displacement and increases in dynamic earth pressure. In addition, the conventional pseudostatic limit equilibrium methods overestimated [Formula: see text] values, whereas they underestimated [Formula: see text] values, and the recommended [Formula: see text] values by current design codes were not found to be compatible with the numerical and experimental results.

Pseudodynamic Estimation of 3D Active Earth Pressures with a Nonlinear Strength Criterion

This paper presents an analytical framework for predicting three-dimensional (3D) seismic active earth pressures for soils governed by a nonlinear strength criterion. The kinematic limit analysis method that incorporates a pseudodynamic approach is used to carry out the analysis. A generalized tangential technique is adopted to realize transition of the nonlinear criterion into the commonly used linear form. A 3D failure mechanism of rigid rotation is employed. Because the use of the modified pseudodynamic approach leads to a variation of seismic forces along the depth, the work rate due to earthquake effects is calculated by using a horizontal layer–wise summation method. By virtue of the balance equation of work and energy, the thrust of active earth pressures is determined, and the final solutions are expressed as dimensionless active earth pressure coefficients. A comparison between the solutions obtained in this paper and those of the existing studies shows the effectiveness of the developed method. A parametric analysis is carried out to investigate the influences of several parameters. The findings of this work can help understand the service behavior of retaining structures subjected to seismic loadings, which could provide references for designs.

Prediction of Reinforcement Connection Loads in Geosynthetic Reinforced Segmental Retaining Walls Using Response Surface Method

This paper presents an improved earth pressure method that considers the capacity of a wall toe to carry an earth load to predict the connection loads of GRS segmental walls constructed with cohesionless backfills on competent foundations. In this method, a response surface model (RSM) of the lateral earth pressure coefficient replaces the Coulomb active earth pressure coefficient. The parameters of the RSM were determined from numerical studies on the impacts of toe restraint, wall geometry, and backfill properties on the distribution of earth loads between the toe and reinforcement layers. The unknown coefficients of the RSM were obtained through a regression analysis of 705 reinforcement load values from 65 simulated walls. The proposed method was compared to the earth pressure method and the stiffness method using measured connection loads from field and centrifuge GRS segmental walls. The results show that the predictions of the proposed RSM method are in better agreement with the measurements than those of the stiffness method and the earth pressure method, whether under a typical or poor toe restraint condition.

Formulation of seismic active earth pressure coefficient considering adhesive force on back face of retaining wall and cohesion along failure plane in backfill soil

Formulation of seismic active earth pressure coefficient considering adhesive force on back face of retaining wall and cohesion along failure plane in backfill soil

Upper bounds for the three-dimensional seismic active earth pressure coefficients

A numerical implementation of the upper-bound theorem of limit analysis is applied to determine two-dimensional (2D) and three-dimensional (3D) active horizontal earth pressure coefficients considering seismic actions through a horizontal seismic coefficient. Results are obtained for vertical wall, horizontal soil, different friction angles of the soil, soil-to-wall friction ratios, horizontal seismic coefficients and wall width-to-height ratios. The few cases for which 3D active earth pressure coefficients are available in the literature using upper-bound methods were used for comparison with the corresponding earth pressure coefficients obtained in this study. This showed a general improvement of these results, which allows expecting a good accuracy for the set of cases studied. The ratios between the 3D and 2D horizontal active earth pressure coefficients are found to be practically independent of the soil-to-wall friction ratio. An equation is proposed for calculating these ratios. This equation can be easily used in the design of geotechnical structures requiring the determination of 3D active earth pressure coefficients.

Working Face Stability of Box Shield Tunneling under Non-Uniform Support Pressure

This paper proposes a theoretical model for the stability analysis of a box tunnel face in non-cohesive soils considering the uneven distribution of support pressure caused by multiple cutter heads and screw conveyors. The support pressure distribution on the tunnel face is concave. Accordingly, the failure mechanism is composed of a prism and a wedge, both including three blocks. The relatively smaller support pressure acting on the middle blocks lead to the tendency of slide. Assuming that the support pressure acting on the side blocks is obtained using the active earth pressure coefficient, the support pressure acting on block II can be achieved by limit equilibrium analysis considering the interactions between the blocks. The influences of strength parameters and geometric parameters on the tunnel face stability are discussed in the parametric analysis. For comparison, numerical analysis is conducted in the commercial software OptumG3. It is found that the results given by the proposed model agree well with those from the numerical model. Therefore, the rationality of the proposed model in predicting the collapse geometry is verified.

A generalised analytical framework for active earth pressure on retaining walls with narrow soil

Active earth pressure on retaining structures supporting a narrow column of soil cannot be properly analysed using Coulomb's theory. Finite-element limit analysis (FELA) shows that the soil forms multiple failure surfaces if the soil column is sufficiently narrow. This paper proposes a framework for active earth pressure estimation for narrow soils by combining an arched differential element method and a sliding wedge method. The analytical framework considers both soil friction and cohesion, soil arching effects and shear stress between adjacent differential elements. The solution obtained is validated against experimental data and FELA results. Through parametric studies, the effects on the active earth pressure of the aspect ratio, soil friction, soil cohesion and wall–soil interface roughness are examined. To facilitate the use of the proposed framework in design, a modified active earth pressure coefficient and an application height of active thrust are provided.

An exact solution of active earth pressures based on a statically admissible stress field

Static lateral earth pressure problems are a central and long-standing topic in geotechnical engineering, but their exact solutions are lacking. This study is dedicated to providing an exact solution for active earth pressure exerted against rigid retaining walls with various wall geometries, backfill geometries, and wall roughness. A numerical model based on the rigid plastic analysis, namely a fully plastic solution, has been successfully developed to search out statically admissible stress fields in the backfills. In particular, Sokolovski’s theory coupled with the Mohr-Coulomb criterion has been adopted to enable the statically admissible stress fields to be developed. Robust numerical frameworks based on the fifth-order adaptive Runge-Kutta method, and a shooting technique has demonstrated efficacy in coping with the stress singularity that appeared in the analyzed domain, thus the admissible stress fields have been successfully figured out. The accuracy of the proposed solution is satisfactorily verified and validated by comparing the obtained results with exact values and those of experimental results available in the literature. The admissible stress fields explored in the backfills of rigid walls elucidate the load transfer mechanism of cohesionless materials in the backfills; the potential effects of various parameters e.g., wall geometries, backfill geometries, and wall roughness on the active earth pressure coefficients have been disclosed thereof. In essence, this study provided a conservative answer for the static active earth pressure problems whereby the exact values of active earth pressure coefficients are tabulated and provided for engineering practice.

On the External Failure Surface in PSEs: Numerical and Theoretical Methods

The evolution of soil arching, involving internal and external failure surfaces, is of significance to the load transfer mechanism of pile-supported embankments (PSEs), and external failure surfaces are generally observed in cases of greater embankment height. In this study, the evolution of external failure surfaces was investigated by both numerical and theoretical methods. To begin with, numerical simulations of trapdoor tests were carried out by a two-dimensional discrete element method. The influences of two key parameters (i.e., embankment height and net spacing between piles) on the development of external failure surfaces were emphasized. The measured coefficient of lateral earth pressure around the external failure surface was close to the predicted coefficient of active earth pressure. Then, a theoretical solution considering inclined external failure surfaces, more realistic compared to those adopted in Terzaghi’s method, was proposed. Compared with Terzaghi’s method, the proposed solution exhibited better consistency with laboratory observations, especially when external failure surfaces were significantly observed.

Limit Analyses of the Active Earth Pressure on Rigid Retaining Walls under Strip Loading on Backfills

Recent studies of retaining walls include experimental studies, numerical analysis and analytical models. Although active earth pressure against retaining structures has received much attention, the evaluation of active earth pressure of backfill when loaded by a strip foundation, has been slightly studied. This paper studies the effect of a strip load on the active pressure force and the distribution of the horizontal stresses on a rigid wall, using a finite element limit analysis. The strip loading is located at different distances from the vertical face of the wall. The OptumG2 code is used to analyze the effect of width of strip surcharge (soil-wall), interface friction angle and soil internal friction angle. New interesting results are demonstrated and presented here: the dependency of the active earth pressure coefficient on both position and width of the strip load, in one hand, and the effect of the internal friction angle of the soil, the soil-wall interface, and the position of the strip loading on the failure mechanism, in the other hand.

Extending Mononobe-Okabe theory to account for arbitrary backfill topography and variable density of surcharge

Coulomb proposed a formula for the static earth pressure acting on a rigid gravity retaining wall supporting a soil. Many researchers have generalized this theory and several analytical studies were achieved regarding the evaluation of seismic action. Following the work of Mononobe and Okabe, investigations have considered cohesive backfill, and with some restrictions the topography of the backfill and the pattern of surcharge acting on its surface. In this work an extension of the Mononobe-Okabe theory was proposed to deal with the most general case of backfill having an arbitrary shape and also vertical surcharge acting with variable density at the ground level. Equilibrium of Coulomb wedge was applied to express the active earth pressure coefficient related to a given orientation of the failure plane. Then, numerical optimization was performed to fix the critical angle providing its maximum value. Parametric studies were conducted after that. It was found that both the upward and downward vertical seismic acceleration should be considered. The obtained results indicate that the backfill surface shape and surcharge density have a significant effect on seismic action. The maximum relative variation of the pressure coefficient with regards to the reference case is however limited to 20%.

Influence of soil amplification and backfill angle on seismic earth pressure coefficients by pseudo dynamic method

ABSTRACT The knowledge of earth pressure concepts plays a major role to design a retaining wall. The most traditional pseudo-static methodology as proposed by Mononobe–Okabe gives the direct approximation of earth pressure in seismic condition. This paper utilised the pseudo-dynamic methodology to figure out the seismic earth pressure on rigid wall with cohesion less backfill along with considering the effects of time, phase difference, soil amplification factor along with the variation in seismic velocities. The main contribution is the soil amplification and backfill inclination which is not given much attention before. By considering the above factors coefficients the seismic earth pressure against retaining wall is determined. The coefficient of seismic passive earth pressure decreases with the increase of soil amplification keeping other properties as standard values. The value of coefficient of seismic active earth pressure increases with increase of soil amplification. The comparison is also done without taking backfill angle for both coefficients of seismic earth pressures. The influence of all the soil properties like backfill angle, wall friction angle, soil friction angle, non-dimensional parameters are shown in tabular format as well as in the graphical with respect to the soil amplification which is more realistic towards the design.

Active earth pressure of 3D earth retaining structure subjected to rainfall infiltration

Rainfall infiltration is a key factor that determines the active earth pressure on an earth-retaining structure. Previous investigations on the stability of earth retaining structures were mainly conducted under the assumption that the backfills was dry, saturated, or subjected to a steady unsaturated flow, ignoring the time-varying characteristics of the rainfall infiltration process. Based on the upper bound theorem of limit analysis, this study conducted a stability analysis of a three-dimensional (3D) earth retaining structure (ERS) subjected to various rainfall infiltration patterns. An analytical model that was, capable of calculating the pore water pressure distribution due to rainfall infiltration, was employed to calculate the time-dependent pore water pressure change of unsaturated soil. A horizontal slice method was employed to take into account the change of effective unit weight of soil. Afterward, an analytical expression of the active earth pressure coefficient is derived from the energy balance equation. The effects of the 3D characteristics of ERSs and rainfall patterns on the active earth pressure coefficient and the failure pattern of ERSs were investigated. It was found that compared with plain strain conditions, the 3D characteristics of ERSs lead to a lower value for the active earth pressure and better stability. The rainfall patterns not only directly determined the stability and active earth pressure of an ERS, but also played a dominant role in critical failure pattern of the ERS.

Active lateral earth pressure of geosynthetic-reinforced retaining walls with inherently anisotropic frictional backfills subjected to strip footing loading

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 ofa 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.

Calculation of active earth pressure on retaining walls with line surcharge effect and presentation of design diagrams in cohesive – frictional soils

In this study, a formulation and models have been proposed to calculate the active earth pressure on the wall and to determine the angle of failure wedge with line surcharge effect and taking into account the soil cohesion. The proposed method has the advantage of taking into account soil parameters such as cohesion, the angle of friction between the soil and the wall, the surcharge effect in the elasto-plastic environment, and the range that determines the critical surcharge. This paper presents dimensionless diagrams for different soil specifications and surcharges. According to these diagrams, it is easy to determine the distribution of excess pressure caused by surcharge, the distribution of the total active earth pressure on the wall, the angle of the failure wedge as well as the minimum and maximum active coefficient of the pressure with respect to surcharge distance. Furthermore, all soil parameters, surcharge and the results have been addressed. In general, the results indicated that increasing the angle of internal friction of the soil and cohesion would result to a nonlinear reduction in the active earth pressure coefficient, contrary to the line surcharge, which increases the active earth pressure of the soil and ultimately increases the active earth pressure coefficient. In this research, a diagram has been presented that expresses the surface that the active earth pressure coefficient changes with respect to the surcharge distance. The lower limit of each graph expresses the minimum active earth pressure coefficient (kas (min)) at the minimum surcharge distance, whereas the upper limit indicates the maximum active earth pressure coefficient (kas (max)) at the maximum surcharge distance from the wall. Comparison of the results of the proposed method with previous methods, codes and numerical software shows that in general, the proposed method is able to simplify the analysis of walls with surcharge effect in cohesive-frictional soils. In addition to the formulation and diagrams, a computer program in MATLAB software has been written. Using the results of these codes, the pressure on the wall with the linear surcharge effect, angle of failure wedge and pressure distribution on the wall in the cohesive-frictional soils can be calculated for all scenarios.

Limit analysis of lateral earth pressure on geosynthetic-reinforced retaining structures using finite element and second-order cone programming

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.

Discretization-based kinematical analysis of three-dimensional seismic active earth pressures under nonlinear failure criterion

The available theoretical models for evaluating seismic active earth pressures are limited to plane strain analyses and linear failure criterion. To fill this research gap, with a combination of the kinematical approach of limit analysis, the spatial discretization technique as well as the pseudo-static approach, this work develops a discretized three-dimensional failure mechanism of sloping backfills that is composed of an end cap and a central plane-strain insert to estimate the seismic active earth pressure coefficient under nonlinear failure criterion. Compared with the existing three-dimensional kinematically admissible failure mechanisms, the developed one has three significant merits: (1) the normality condition is strictly satisfied in the generation of the end cap; (2) the work rates can be computed by a summation of elementary work rates conveniently instead of tedious integral schemes; (3) the considerations of the nonlinear failure criterion and the sloping backfill. Comparisons with the existing upper bound solutions and experimental results in terms of active earth forces or active earth pressure coefficients are conducted to verify the proposed model. Parametric studies are performed to study the influences of model parameters, including the seismic coefficient, the sloping angle of backfills as well as the nonlinear parameters, on the active earth pressure coefficients.

Active Earth Pressure of Limited C-φ Soil Based on Improved Soil Arching Effect

For c-φ soil formation (cohesive soil) of limited width with ground surface overload behind a deep retaining structure, a modified active earth pressure calculation model is established in this study. And three key issues are addressed through improved soil arching effect. First, the soil-wall interaction mechanism is determined by considering the soil arching effect. The slip surface of a limited soil is proved to be a double-fold line passing through the retaining wall toe and intersecting the side wall of the existing underground structure until it reaches the ground surface along the existing side wall. Second, the limited width boundary is explicated. And third, the variation in the active earth pressure from parameters of limited c-φ soil is determined. The lateral active earth pressure coefficient is nonlinear distributed based on the improved soil arching effect of the symmetric catenary curve. Furthermore, the active earth pressure distribution, the tension crack at the top of the retaining wall and the resultant force and its action point were obtained. By comparing with the existing analytical methods, such as the Rankine method, it demonstrates that the model proposed in this study is much closer to the measured and numerical results. Ignoring the influence of soil cohesion and the limited width will exponentially reduce the overall stability of the retaining structure and increase the risk of accidents.

Three-dimensional active earth pressure under transient unsaturated flow conditions

The active earth pressure evaluation was typically conducted assuming dry backfills and/or two-dimensional collapse mechanisms. In practice, retained slope collapse usually shows a three-dimensional (3D) feature and soils are usually unsaturated. The present work develops a framework for evaluating the 3D active earth pressure under transient unsaturated flow conditions. The framework is implemented by using the kinematic approach of limit analysis, in conjunction with a closed-form solution for the transient unsaturated flow. Based on a 3D horn-like failure mechanism, the active earth pressure coefficient is determined. Results for three hypothetical soils of fine sand, silt, and clay are calculated. It emerges that the inclusion of 3D effects and unsaturated transient flow leads to a smaller active earth pressure coefficient. The 3D effects are mainly influenced by the width-to-height ratio of walls; several certain cases analyzed in this paper show that the difference in the active earth pressure coefficient with and without considering 3D effects can be as much as about 27% when the width-to-height ratio equates to 2, whereas this difference decreases to about 10% and 5% when the ratio reaches to 5 and 10. The contribution of transient flow is mainly affected by the soil types; considering the unsaturated flow effect in clay can approximately reduce the active earth pressure of 67%, whereas this difference corresponds to 34% and 22% in silt and fine sand. The obtained results can help to quantitatively understand changes in the active earth pressure due to 3D effects and the presence of transient infiltration.

Calculation of Active Earth Pressure in the Non-Limit State Based on Wedge Unit Method

Based on the wedge unit method, the active earth pressure against a retaining wall in the non-limit state is studied. According to the relationship between the displacement of the retaining wall and the mobilized internal frictional angle of filling in the non-limit state obtained by earlier researchers, the influences of the internal frictional angle and the displacement ratio of the wall on the unit active earth pressure coefficient, the distribution of the active earth pressure, and the application point of the active earth pressure in the non-limit state are discussed. Finally, through comparison with experimental data, the distribution of the active earth pressure calculated by the method proposed is shown to agree well with experimental results. Therefore, the method proposed in this paper has theoretical significance and engineering value.