Seismic Passive Earth Pressure Research Articles

Estimation of seismic passive earth pressure coefficients for caissons in c-φ soils with a 3D log-spiral failure wedge

Passive resistance offered by soil to any embedded structure has been of significant interest to researchers since the inception of the concept. The present study deals with the estimation of passive earth pressure coefficients in seismic conditions that will control the passive resistance offered to a caisson embedded in c (cohesion) – φ (friction) soil in presence of surcharge loading. The three-dimensional (3D) geometry of failure wedge (log-spiral in vertical plane and oval in horizontal plane) has been obtained from the results of numerical analysis and past experimental studies. The critical failure surface has been obtained in the presence of all resisting components [unit weight (γ), cohesion (c) and surcharge (q)] by minimizing the passive resistance. Thereafter, seismic passive earth pressure coefficients for cohesion component (Kspc), surcharge component (Kspq) and unit weight component (Kspγ) have been obtained separately corresponding to the critical failure wedge obtained in the previous analysis. Limit equilibrium method of analysis in conjunction with pseudo-static approach has been used to perform the analyses. Charts for a variety of caisson geometry, soil and site condition and seismic condition have been prepared to facilitate prediction of passive resistance in a more economical and reliable manner since unique failure wedge has been considered for all the components instead of separate failure wedge which would be impractical.

Seismic passive earth pressure resistance for caisson in layered soil using modified pseudo‐dynamic approach

AbstractThe determination of seismic passive earth pressure resistance is of utmost importance during the analysis of geotechnical structures. In the present study, seismic passive earth pressure coefficient for caisson embedded in n‐layered soil is computed using modified pseudo‐dynamic method. Limit equilibrium method of analysis considering poly‐planar failure wedge has been adopted in the study and parametric variation of geometry of failure wedge has also been studied. The current study proposes formulation for variation of horizontal and vertical seismic acceleration profile with depth through various layers and studies the effect of number of layers, relative depths of various layers and relative soil friction angle in those layers, soil‐wall friction angle, horizontal and vertical seismic acceleration coefficients and normalized width of caisson. The study has been extended for submerged soil and the effect of excess pore pressure has been investigated. The results of the present study have been compared with previous theoretical studies and found to be in good agreement. It is observed that the extent of failure wedge formed in front of caisson increases with increasing soil friction angle, soil‐wall friction angle, horizontal seismic acceleration coefficient and width of caisson.

Seismic Stability Analysis of Caissons under Earthquake Forces Considering 3D Log-Spiral Failure Surface

Bridge failure is mostly caused by geotechnical failure. Because caissons are the automatic choice for foundation systems for marine structures, such as bridges and wind turbines, this study addresses the determination of seismic passive earth pressure coefficients for caissons. In the present study, a realistic three-dimensional (3D) failure wedge was assumed to be formed behind caissons of different widths on the basis of the past results of experimental and numerical studies. The limit equilibrium method of analysis was adopted to determine the seismic passive earth pressure coefficients due to the cohesion component, surcharge component, and unit weight component. The current study takes into account the relative width and depth of the geotechnical structure and returns a series of design charts and tables for different soil-soil friction angles, soil-wall friction angles, and horizontal and vertical seismic acceleration coefficients. The results were compared with previous experimental and theoretical studies and found to be in excellent agreement.

A closed-form logarithmic spiral method for seismic passive earth pressure in anisotropic sand

The shear strength of soils is always anisotropic due to the compaction and deposition history. A closed-form logarithmic spiral method combined with an anisotropic failure criterion is proposed to estimate the seismic passive earth pressure coefficient and failure surface of anisotropic sand. The seismic condition is implemented by the pseudo-static approach. The results obtained by the proposed method are validated by methods in the literature and by the finite element method based on a proposed anisotropic Drucker–Prager model. The comparisons show that the method is effective and efficient. In addition, the seismic passive earth pressure coefficients considering various backfill slopes and various soil-wall frictions are presented for reference in engineering design.

An Improved Method of Vertical Slices to Determine Seismic Passive Earth Pressure and Its Point of Application

This paper presents a new approach for calculating seismic passive earth pressure, its point of application, and the approximate stress-state within the rupture wedge. The method of vertical slices combined with the limit-equilibrium (LE) technique was used as the framework for the analysis. While the available LE analyses used the rupture surface of predefined shapes, in this approach, the rupture surface is derived through the analysis. First, the mobilized soil behind the wall was split into thin vertical slices and the rupture plane of every slice was calculated by enforcing the Mohr–Coulomb failure criterion. Thereafter, by adding those rupture planes consecutively, starting from the wall toe, the passive rupture surface was achieved. The inclination of the rupture planes is guided by the soil friction angle, wall friction angle, seismic acceleration, and slice-interface friction angle. The distribution of slice-interface friction angle across the rupture plane was presumed to obey a power function. The exponent of the power function, the seismic passive earth pressure, and its point of application were derived concurrently by satisfying the static equilibrium conditions of the slices and applying a boundary condition. The results show that the outline of the rupture surface is guided by the slice-interface friction angle, and the shape is curvilinear for rough walls. With increasing seismic acceleration, the passive pressure decreases, and the point of application moves predominantly downward for loose sands. The obtained results were compared with those of previous numerical and experimental studies and were found to show good agreement, thus demonstrating the validity of the proposed method.

Passive earth pressure of vegetation rooted soils based on limit analysis and quasi-static approach

Although it has been recognized that vegetation roots have a positive effect on the stability of geotechnical structures, few quantitative studies have been performed on the effects of vegetation roots on earth pressures. In this paper, based on the upper bound limit analysis theory and quasi-static method, a new method for calculating the seismic passive earth pressure of vegetation rooted soils is proposed, which considers both the hydrological and mechanical effects of vegetation roots on the passive earth pressure. The proposed method is validated by some existing solutions. The effects of root parameters of shrubs (root transpiration rate, root tensile strength, and root depth), angle of the soil slope surface with the horizontal, and wall interface friction angle on the seismic passive earth pressure coefficient are also investigated. The results show that the passive earth pressure coefficient increases with the increase of root transpiration rate, root tensile strength, root depth, angle of the soil slope surface with the horizontal, and wall interface friction angle. Compared with the mechanical effect, the hydrological effect of vegetation roots on the passive earth pressure coefficient is more obvious. The effects of root parameters on the passive earth pressure ranked in descending order of sensitivity are root transpiration rate, root tensile strength, and root depth. In addition, the effect of vegetation roots on the passive earth pressure becomes more significant with the increase of internal friction angle. The proposed method can provide a reference for the local reinforcement of multi-stage slopes with vegetation.

A Study on the Seismic Passive Earth Pressure on Rigid Retaining Walls Considering Seismic Acceleration Field

ABSTRACT The seismic passive earth pressure is typically calculated by a pseudo static analysis by the PGA on the ground surface which is often assumed to be constant within the soil mass. This may result in an underestimation of the limit load. On the other hand, variations of the acceleration field over time and space render the interpretation of the seismic limit load either very difficult, if a complete elasto-plastic solution is sought at each time step, or argumentative. A rather new procedure is presented in this study which considers the variable seismic acceleration field behind a rigid retaining wall during an earthquake and applied to a series of acceleration time histories. The method of stress characteristics is implemented to estimate the limit load at each time step. This method seems to be more convenient with a clear interpretation of the actual limit load. Results indicated that the conventional pseudo static analyses provide an over-conservative estimate or an underestimation of the passive earth pressure.

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.

Passive Resistance of Retaining Walls Supporting Layered Cohesionless Backfill: A Plasticity Approach

A theoretical model was developed to determine the seismic passive earth pressure on vertical cantilever retaining walls supporting a two-layered cohesionless backfill with a loose sand layer overlying a dense sand stratum. Seismic inertial forces were considered in the analysis by employing the classical pseudostatic approach. The theoretical formulation was developed based on the method of stress characteristics, which does not require any predefined failure mechanism to initiate the analysis. The charts are presented in terms of passive earth pressure coefficient, which includes the contribution of both the layers. In addition to the generation of the actual failure mechanism, rapid mobilization of stresses at the layer interface and at the wall backface is presented in the form of normalized stress contours. The failure surface and the passive earth pressure distribution behind the wall were found to be nonlinear, with different input parameters. The passive resistance of backfill soil decreased in the presence of the loose sand layer resting on the denser soil stratum.

Solutions for Foundation Systems Subjected to Earthquake Conditions

Soil–structure interaction plays an important role in dynamic behaviour of a foundation under combined static and seismic loadings. This paper describes a few case histories with field studies of deeply embedded bridge foundations to showcase the earthquake induced lateral effects using finite element framework. Rigorous dynamic approach with detailed numerical analysis for large diameter pile foundation and pseudo-static approach for rigid caisson foundation presented in this study demonstrated the functionality of foundation systems in seismic conditions. Efficacy of barrettes over piles as a cost-effective foundation solution in high-rise buildings has also been discussed by obtaining higher resistance under static condition. Finally, an analytical methodology considering three-dimensional passive wedge developed in front of the rigid caissons is presented for estimating the ultimate soil resistance under seismic condition. Closed-form expressions to determine seismic passive earth pressure coefficient and its distribution along caisson length for different embedment ratio have been explained here that can be adopted in practice to analyse foundation systems subjected to earthquake condition.

Seismic soil resistance for caisson design in sand

The exact solution of the passive resistance acting on a caisson foundation due to earthquake-induced loading is important for the seismic design of caissons. In this study, the three-dimensional soil–caisson interaction was taken into account in the determination of the ultimate soil resistance by considering the idealised passive wedge developed in front of a rectangular caisson in sand. A simplified analytical formulation of the seismic passive earth pressure coefficient and its distribution along the wedge height was developed by using the limit equilibrium method and a pseudo-static approach. For the same dataset of input parameters, the seismic passive earth pressure coefficient with a horizontal seismic acceleration coefficient value of 0·2 was approximately 62·7% lower than that for a static condition. The present study emphasises the requirement of correct estimation of the mobilised soil–soil interface friction angle and the height of the passive wedge in order to determine soil resistance. Parametric studies were also carried out to understand the effects of horizontal and vertical seismic acceleration coefficients and the soil–soil interface friction angles. The results of the study compare well with the available experimental data. The solutions proposed should be useful for the seismic design of caissons.

A finite element performance-based approach to correlate movement of a rigid retaining wall with seismic earth pressure

The paper presents a unique finite element model-based investigation and development of a relationship between the seismic active and passive earth pressure and the movement of a rigid retaining wall. A hardening soil with small strain model with consideration of the Rayleigh damping has been adopted for modelling soil. Validation of the finite element model has been carried out by using centrifuge test results already available in the literature. Unique design charts have been proposed highlighting the relationship between the seismic earth pressure and the wall movement. It is observed that the seismic active earth pressure is independent of the seismic input motion and hence does not depend upon the wall movement during an earthquake, while on the contrary the seismic passive earth pressure is significantly affected by it. Comparison of the results of the present study with the Mononobe-Okabe and pseudo-dynamic methods clearly highlights that the latter overestimates the seismic earth pressure. The proposed design charts and other results provide an important cue to the design engineers.

Derivation of Shukla's generalized expression of seismic passive earth pressure on retaining walls with cohesive-frictional backfill by the inclined slice element method

Shukla developed a generalized expression for the dynamic passive earth pressure from cohesive -frictional soil backfill by considering the equilibrium of a passive failure wedge (International Journal of Geotechnical Engineering 2013; 7(4): 443–446). In this paper, the inclined slice element approach is used to derive this expression under seismic loading conditions. Using this method, the nonlinear distribution of passive earth pressure and its application position are obtained with a few assumptions. By taking the failure surface as a plane, the analytical expression for the critical angle of failure surface is also derived. The generalized expressions can be applied to the calculation for cohesive or cohesionless backfill for specialized cases static and dynamic conditions. The total passive forces from the derived expressions are consistent with Rankine's expression, Coulomb's expression, and Mononobe-Okabe's expressions.

Kinematical analysis of 3D passive earth pressure with nonlinear yield criterion

SummaryConventional methods for calculation of passive earth pressure were mainly based on the assumptions of the linear Mohr‐Coulomb yield condition and plane strain failure mechanism. However, both theoretical and experimental studies have shown that such assumptions are not satisfied in some geotechnical projects. Herein, a novel method incorporating a kinematically admissible 3‐dimensional (3D) rotational failure mechanism and the nonlinear power‐law yield criterion is proposed to compute the passive earth pressure acting on the inclined retaining walls. Instead of using the nonlinear yield criterion directly, a straight line tangential to the nonlinear yield curve is employed to represent the strength of soils, and therefore, the nonlinear problem is transformed into the traditional linear problem. The 3D failure mechanism is generated through rotating a circle defined by 2 log‐spirals, and a plane strain block is inserted into the mechanism to consider the retaining walls with different widths. Earthquake effects are taken into account by using quasi‐static representation, and the horizontal seismic coefficient concept is adopted for the estimation of passive earth pressure under seismic conditions. An analytical expression about the 3D passive earth pressure is educed by means of the upper bound theorem of limit analysis. Numerical results for different practical parameters are obtained from an optimization scheme where the minimum of passive earth pressure is sought. Compared with available 2‐dimensional and 3D solutions, the proposed method is validated. A parametric study is conducted to investigate the effects of different parameters on the 3D static and seismic passive earth pressure.

Seismic passive earth pressure on an inclined cantilever retaining wall using method of stress characteristics – A new approach

This paper depicts the computation of passive earth pressure on an inclined retaining wall supporting a cohesionless backfill subjected to earthquake loading condition. The method of characteristics in association with the pseudo-dynamic approach has been adopted for the intended purpose. Unlike the previous studies considering the limit equilibrium or limit analysis method, a priori failure mechanism is not assumed in this analysis. The effect of various parameters such as angle of internal friction of the backfill soil, inclination and roughness of the wall, and phase difference of the seismic waves is discussed in detail. While comparing with the available literature, the present values of seismic passive earth pressure coefficient are mostly found to be lesser than the values reported by earlier pseudo-dynamic analyses assuming the linear failure surface.

Evaluation of seismic passive earth pressure of inclined rigid retaining wall considering soil arching effect

Evaluation of seismic passive earth pressure is an important topic of research in geotechnical engineering. In this study seismic passive pressure on an inclined rigid retaining wall supporting horizontal cohesionless backfill is estimated considering arching effect. A planar failure surface is considered in the present analysis. Seismic forces are considered to be pseudo-static in nature. The effect of different parameters on the seismic passive earth pressure is studied in details. The normal stress distribution along the depth of the backfill is found to be nonlinear in nature. Friction angle between wall and the backfill soil has the most significant effect on the distribution of normal stress along the depth of the backfill. The point of application of seismic passive pressure shifts gradually downward for higher seismic forces. Present method is validated with the experimental results available in the literature for static conditions. Comparison of present method with other theories is also presented showing the merit of the present study. Arching effect in the backfill should be considered for high values of wall inclination angle as the present seismic passive resistance is found to be the lowest as compared to other theoretical solutions.

Semi-Analytical Approach to Evaluate Seismic Passive Earth Pressures Considering the Effects of Soil Cohesion and a Curvilinear Failure Surface

AbstractThe widely acknowledged Mononobe-Okabe (MO) model is not recommended for seismic passive earth pressures analysis because it yields nonconservative results when the ratio of the wall’s to t...

Seismic passive earth resistance using modified pseudo-dynamic method

In earthquake prone areas, understanding of the seismic passive earth resistance is very important for the design of different geotechnical earth retaining structures. In this study, the limit equilibrium method is used for estimation of critical seismic passive earth resistance for an inclined wall supporting horizontal cohesionless backfill. A composite failure surface is considered in the present analysis. Seismic forces are computed assuming the backfill soil as a viscoelastic material overlying a rigid stratum and the rigid stratum is subjected to a harmonic shaking. The present method satisfies the boundary conditions. The amplification of acceleration depends on the properties of the backfill soil and on the characteristics of the input motion. The acceleration distribution along the depth of the backfill is found to be nonlinear in nature. The present study shows that the horizontal and vertical acceleration distribution in the backfill soil is not always in-phase for the critical value of the seismic passive earth pressure coefficient. The effect of different parameters on the seismic passive earth pressure is studied in detail. A comparison of the present method with other theories is also presented, which shows the merits of the present study.

Seismic passive earth resistance in submerged soils using modified pseudo-dynamic method with curved rupture surface

ABSTRACTThe sparsity of examination of seismic passive earth pressure acting on retaining wall holding soil backfill with full submergence, which is more common in waterfront areas, can be noticed from the literature. In the current study, a closed-form solution to compute the seismic passive earth pressure on nonvertical rigid retaining wall retaining a backfill with full submergence is proposed using the modified pseudo-dynamic approach. A nonlinear rupture surface (logarithmic spiral + straight line) in a submerged backfill of viscoelastic nature has been assumed. The presented modified pseudo-dynamic method overcomes the limitations of the existing pseudo-dynamic method for submerged soils. The proposed methodology has been thoroughly validated with the available literature. The influences of seismic acceleration coefficients, excess pore water pressure ratio, wall inclination, and soil and wall friction angles have been studied. It has been noticed that the consideration of excess pore pressure ratio leads to significant decrease in seismic passive resistance of the soil which in turn lead to extra hydraulic pressure acting on the wall in submerged backfill. There is a 57% decrease in seismic passive earth pressure coefficient as the wall inclination changes from −15° to 15°.

A closed-form solution for seismic passive earth pressure behind a retaining wall supporting cohesive–frictional backfill

The evaluation of seismic passive earth pressure is an important aspect in designing safe retaining walls. In this paper, a slice analysis method is adopted to study the nonlinear distribution of seismic passive earth pressure while considering most of the possible parameters. The closed-form expressions for the resultant force of seismic passive earth pressure, earth pressure distribution, and its application position are obtained. The explicit solution for the critical failure angle of seismic passive earth pressure is proposed by simplifying the relation between the resultant force and the failure angle based on a graphical analysis method. Under certain conditions, the present method correlates with classical passive earth pressure theories. By comparing the present method with test results and previously published solutions, the results are found to be consistent. The influence of the seismic coefficients on seismic passive earth pressure is also studied.