Seismic Active Earth Pressure Research Articles

Calculation method for static and seismic active earth pressure on counterweight retaining walls under translation based on two critical slip surfaces

The counterweight retaining wall with polyline wall back is a kind of gravity walls, which can be alternatively used in high embankments. To completely analyze active earth pressure on the polyline back under the wall translation mode, a comprehensive method is proposed based on two planar slip surfaces in the retained soil, an inclined slice method within the frame of limit equilibrium, and the pseudo-static approach. Meanwhile, the two critical slip surfaces include the global and local ones in the soils behind the whole wall and only the upper wall, respectively; and mobilized shear strength coefficients on interslice surfaces are introduced to fully consider the interslice shear forces. Some examples show that the proposed resultant forces on the whole wall are close to the experimental and numerical results generally within 10% error. The dip angle of backfill surface has a significant effect on the two slip surfaces, and the inclination of the lower back mostly influences the global slip surface. The unloading effect of the platform on the lower earth pressure becomes obvious as the upper wall lengthens under a constant height of the whole wall. The magnitude and profile of the seismic earth pressure on the polyline back are greatly influenced by the seismic coefficients.

Numerical Investigation of Seismic Behaviour for a Flexible Cantilever Retaining Wall with Cohesive Backfill

In the seismic design of flexible cantilever walls retaining cohesive backfill soil, the common practice is to neglect the cohesion effect. Dynamic lateral earth pressure is typically evaluated based on approaches primarily intended for cohesionless soils or through analytical pseudo-static methods. Nevertheless, both experimental and theoretical evidence has demonstrated significant effects due to soil cohesion that are not accounted for by these methods. This study involved finite element modeling (FE) of a flexible cantilever wall with a height of 5.4m, supporting homogeneous cohesive backfill under initial static and seismic loadings. The calculated active earth thrust was then compared with values obtained experimentally and through conventional analytical methods. The obtained results indicate that the presence of soil cohesion significantly reduces seismic demands on flexible cantilever retaining walls, resulting in a substantial reduction of seismic active earth pressures and total seismic thrust by up to 50% and 52%, respectively. It enhances also the overall stability of the system by shifting the point of application of seismic thrust toward the base of the wall, thereby increasing the safety margin. In addition, it significantly decreases the wall displacement at the stem top, with reductions of up to 104% compared with the case involving cohesionless backfill. It was observed that the conventional methods recommended by some seismic regulations largely underestimate seismic active pressure.

Seismic active earth pressure for 3D earth retaining structure following a nonlinear failure criterion

Stability analysis for three-dimensional (3D) earth retaining structures (ERSs) is a pivotal problem in geotechnical engineering, particularly for seismically active areas. In this work, the 3D ERSs in soil are assessed for seismic stability following a nonlinear strength criterion. The power-law strength criterion and seismic forces are introduced into the 3D ERS stability analysis via a multi-cone failure mechanism. The coefficient of active soil pressure Ka is derived by exploiting the energy balance equation. The upper bound solutions, that is the maximum results of the Ka are captured with the help of a genetic algorithm. The validity of the current study is verified by a comparative analysis, and the effects of soil strength nonlinearity, the seismic forces, the soil-wall friction angle, the height, the inclined angle and the 3D geometric traits of ERSs on the Ka solutions and the stability of ERSs are investigated. It is indicated that the height and the 3D geometric characteristics of the ERSs will not only determine the Ka solutions directly, but also influence the impact of soil strength nonlinearity on the stability of ERSs. Strength criteria should be chosen combining the geometric characteristics of ERSs to derive more critical estimates on the stability of 3D ERSs. Additionally, a range of seismic and static stability charts used for preliminary design are put forward as well.

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.

Seismic Active Earth Pressure of Infinite Width Backfilled Soil on Cantilever Retaining Wall with Long Relief Shelf under Translational Mode

In the area of high seismic intensity, there were few methods for calculating active earth pressure (Ea). Especially for the cantilever retaining wall with long relief shelf (CRW-LRS), the theoretical method lags behind the practical engineering. The seismic active earth pressure (ES) of the CRW-LRS subject to translational mode was researched. By finite element method (FEM), the failure mode of the active limit state under seismic load was evaluated. The results show that the backfill behind the wall generates the first sliding surface at the wall heel bottom, the second at the wall heel top, and the third at the relief shelf top. The calculation formula of ES under long relief shelf failure mode was proposed using the limit analysis method of a horizontal differential layer. The calculation results were compared with the FEM results to prove the rationality and reliability of the theoretical solution. The effects of relief shelf relative length (l) and position (m), wall heel length (n), internal frictional angle of the backfill (ϕ), seismic horizontal acceleration (ah), and seismic vertical acceleration (aV) on ES were studied.

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

General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

General variational solution for seismic and static active earth pressure on rigid walls considering soil tensile strength cut-off

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.

Generalized solution to Coulomb’s seismic active earth pressure acting on rigid retaining wall with cohesive backfill and trial application for evaluation of seismic performance of retaining wall

In this paper, a general solution for evaluating the Coulomb-type seismic active earth pressure that acts on a rigid retaining wall from the cohesive backfill soil is shown together with its derivation process. In the proposed solution, the mobilization of the cohesion on the failure plane in the backfill soil of the retaining wall and the associated increase in shear strength are considered in the pseudo-static limit equilibrium approach under the assumption that the cohesion is uniformly distributed in the backfill soil. The angle of the failure plane and the seismic active earth pressure calculated by the proposed equation completely agree with the calculation results by the trial wedge method, which shows the validity of the proposed solution. In addition, by combining the concept of the Modified Mononobe-Okabe method and the proposed equation, a calculation method for the seismic active earth pressure is proposed. It can consider the effect of backfill cohesion and can be applied even under a large seismic load. Furthermore, a series of trial analyses on the effect of backfill cohesion on the seismic performance of the retaining wall is also conducted using the proposed equation. A series of analyses using the case of a retaining wall damaged during the 1995 Hyogo-ken Nanbu earthquake shows that the effect of backfill cohesion is significant in the seismic performance evaluation and the design of aseismic reinforcements.

Estimation of seismic active earth pressure on reinforced retaining wall using lower bound limit analysis and modified pseudo-dynamic method

Present study estimates seismic active earth pressure on the reinforced retaining wall by combining the lower bound finite element limit analysis and the modified Pseudo-dynamic method. A series of parametric analyses are performed by varying seismic acceleration coefficient, time period of seismic loading, soil friction and dilation angles, reinforcement spacing, length of reinforcement, soil-reinforcement interface, damping ratio of soil, soil-wall interface, wall inclination, and ground inclination. Maximum active earth pressure is exerted when natural time period of reinforced soil matches with the time period of an earthquake. Reinforcement is found to be effective in terms of reducing active earth pressure significantly on the wall subjected to seismic loading. Effectiveness of reinforcement depends upon two factors, namely vertical spacing and soil-reinforcement interface friction angle. For relatively smaller reinforcement spacing, soil-reinforcement behaves like a composite block, which helps to constraint stresses within a small area behind the wall. Maximum tensile resistance is developed when fully rough interface condition is assumed between soil and reinforcement layer. Failure patterns are provided to understand the behaviour of reinforced retaining wall under different time of seismic loading.

Seismic pseudo-static active earth pressure of narrow c-φ soils on gravity walls under translational mode

This study utilises adaptive finite element analysis to investigate the failure mechanisms of narrow cohesive backfill under seismic conditions, and five classical failure modes are summarized. The pseudo-static solution is developed for the case when a narrow cohesive backfill is behind a gravity retaining wall and experiences seismic conditions. Our analytical solution uses the limit equilibrium method, Rankine's theory and the horizontal differential layer method. It considers the effect of soil cohesion, the interface friction angles, backfill geometries, seismic acceleration, the soil arching effect and the effect of shearing forces between adjacent elements on seismic active earth pressure. We propose a new approach that utilises the finite difference method to determine the tension crack depth of the narrow cohesive backfill, and an iterative calculation to determine the critical failure angle of the backfill wedge.

Inertial behavior of gravity-type quay wall: A case study using dynamic centrifuge test

Quay walls have been extensively investigated since the 1995 Kobe earthquake, with most studies focusing on the revision of design codes and evaluation of seismic active earth pressure. To ensure the quay wall's safety during a strong earthquake, many studies evaluated the interaction between the wall and the backfill soil. Although several studies have reported that the inertial behavior of the quay wall can cause the failure due to its inertia force, the test case describing the dynamic inertial behavior of the quay wall and its failure development has not been introduced enough. In this study, a centrifuge test was introduced to describe failure mechanism of a gravity-type quay wall manifested by its large inertia. The frequency characteristics of the quay wall was discussed using analytical calculations and the transfer functions from the test results. It showed that the analytical calculations well predicted the natural frequencies of the wall under a weak dynamic loading. Under a strong shaking, the natural frequencies of the wall were significantly different from that of the backfill and it implied that the phase difference occurrence between the wall and the backfill due to the wall's inertial behavior. The test results showed that soil liquefaction was induced during the strong dynamic loading only at the backfill soil, followed by vertical settlement of ground due to void redistribution. Consequently, horizontal sliding failure due to the inertial motion of the quay wall was also noted.

Study on Seismic Amplification Effect and Active Earth Pressure of Retaining Wall Based on Pseudo-Dynamic Method and Numerical Simulation

Abstract In this paper, the finite element numerical analysis verified that the critical failure surface of the backfill under active conditions was curved, and it was consistent with the composite form of a logarithmic spiral and a straight line assumed by the study based on the pseudo-dynamic method. On the basis of the failure surface of the backfill as a curved surface, the seismic active earth pressure on the retaining wall was calculated by the pseudo-dynamic method and the finite element method respectively. Results showed that in the finite element analysis, the acceleration amplitude of the backfill had an obvious amplification effect along the depth of the retaining wall, and this amplification effect was related to many factors. Under the action of low-frequency seismic load, linear amplification effect occurred, while nonlinear amplification effect occurred under the action of high-frequency seismic load. The amplification factors increased with the increase of retaining wall height. According to the characteristics of the amplification effect, after modifying the input seismic acceleration in the pseudo-dynamic method, the distribution of seismic active earth pressure on the retaining wall was close to that obtained by finite element analysis.

Seismic Active Earth Pressure of Limited Backfill with Curved Slip Surface Considering Intermediate Principal Stress

The traditional method for seismic earth pressure calculation has certain limitations for retaining structures under complex conditions. For example, when the soil width is small, the results obtained by the traditional method will be much larger. Therefore, this paper assumes that the soil slip surface is a logarithmic spiral. Based on the plane strain unified strength theory formula, while also considering the soil arching effects and tension cracks, the analytical solutions of the lateral earth pressure coefficient and the active earth pressure under the earthquake action were deduced. The mechanism and distribution of seismic active earth pressure with limited width were discussed in terms of some relevant parameters. The results indicated that the seismic active earth pressure presented a “convex” nonlinear distribution along the retaining structure. As the contribution of the intermediate principal stress increased, the strength limit of the material was effectively utilized, and the earth pressure was reduced by 22.96%. The resultant force increased as the horizontal seismic coefficient increased. However, this effect was no longer evident when the wall–soil friction angle was close to the internal friction angle. The resultant force action point increased with the wall–soil friction angle, and it should be noted that ha>H/3 was true when δ/φ0>0.55. Finally, by drawing a comparison with previous studies, we verified that the method proposed in this paper is reasonable and can provide a new idea for subsequent 3D seismic earth pressure research.

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.

Upper bound solution to seismic active earth pressure of submerged backfill subjected to partial drainage

Upper bound solution to seismic active earth pressure of submerged backfill subjected to partial drainage

Seismic pseudo-static active earth pressure of narrow granular backfill against an inverted T-type retaining wall under translational mode

Rankine and Coulomb earth pressure theories are not applicable when the backfill behind the retaining wall is narrow. This paper analytically investigates the seismic active earth pressure of an inverted T-type retaining wall with narrow granular backfill under translational mode using a pseudo-static method for four typical seismic active failure mechanisms simulated with adaptive finite element software. Considering the failure surface reflections on soil–wall and soil–rock interfaces, four corresponding theoretical solutions using the limit equilibrium method, Rankine theory and the horizontal differential layer method are established to obtain the seismic active earth pressure of the backfill and the inclination angles of the failure surfaces. The derived formulae can be degenerated into either the static or the semi-infinite backfill situations. The proposed theoretical solutions are verified by comparisons with the finite element results and several existing theoretical solutions.

1 g Shaking table model tests on seismic active earth pressure acting on retaining wall with cohesive backfill soil

The effects of backfill cohesion on the seismic behavior of a retaining wall are discussed on the basis of a series of 1 g shaking table model tests. The model test results show that a retaining wall having cohesive backfill soil is more stable than a wall without it. The following aspects are observed in the cases of cohesive backfill soil from a detailed analysis using the measured seismic active earth pressure acting on the retaining wall: 1) the existence of a stable region at the top part of the backfill soil, 2) the increase in shear force acting on the boundary between the back face of the wall and the backfill soil, and 3) the mobilization of cohesion along the failure plane in the backfill soil.The existence of a stable region results in reductions in both the driving force and the overturning moment, while it tends to disappear under a high seismic load. The increase in shear force acting on the back face of the wall contributes to an increase in the resistant moment against the overturning of the wall with respect to the base of the footing, and it mobilizes even under a high seismic load. Mobilized cohesion along the failure plane contributes to the support of the soil wedge, resulting in a decrease in the seismic active earth pressure. It also continuously mobilizes even under a high seismic load.These observations indicate that giving consideration to the backfill cohesion when calculating the seismic active earth pressure leads to the rationalization of the evaluation of the seismic performance of the retaining wall even though further study is required, namely, carrying out the validation in the prototype scale and setting the applicable conditions for the seismic design.

Lower bound analysis of modified pseudo‐dynamic lateral earth pressures for retaining wall‐backfill system with depth‐varying damping using FEM‐Second order cone programming

AbstractRealistic 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.

Pseudo-dynamic analysis of three-dimensional active earth pressures in cohesive backfills with cracks

Most of the existing studies on seismic active earth pressure evaluation use a pseudo-static method to consider seismic actions and are carried out under two-dimensional conditions. However, the pseudo-static approach characterizes the earthquake acceleration as a constant, which is a simplified mode and neglects some crucial seismic inputs. Additionally, the collapse of retained soil masses has a three-dimensional (3D) feature in practice. In this study, a framework that combines the kinematic approach of limit analysis and a pseudo-dynamic approach was established to predict 3D seismic active earth pressures in cohesive backfills with cracks. The resultant active earth pressure was obtained from the work-energy balance equation and was expressed by a dimensionless coefficient. The proposed approach was validated by comparison with an extant study. The results indicate that considering 3D effects and soil cohesion can trigger a distinct decrease in the active earth pressure, whereas the consideration of cracks and seismic effects has the opposite effect.