Vertical Seismic Acceleration Coefficients Research Articles

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.

Critical Inclination of Failure Surface and Seismic Active Earth Thrust for a Broken Slope Backfill

This paper presents an analytical approach, based on the limit-equilibrium state, to determine the critical inclination of failure surface and active earth thrust for a cohesive-frictional backfill with a broken slope and a surcharge load at a constant distance from a retaining wall under the seismic condition. A combined analysis using Mononobe-Okabe’s and Culmann’s methods within a trial and error procedure is performed in this study. The influences of several parameters such as wall height, surcharge magnitude, cohesion, and internal friction angle of the backfill, adhesion between the wall-backfill interface, tension cracks, horizontal and vertical seismic acceleration coefficients have been investigated on the critical inclination of failure surface and the active earth thrust. Additionally, the performance of the proposed approach is explored by geotechnical software (Geo5) and two available methods in the literature. All of the results and the detailed comparisons are given in tabular and graphical forms.

The Expression of Seismic Surrounding Rock Pressure for a Shallow Tunnel Is Derived Using the Pseudostatic Method

Terzaghi developed a generalized expression of the vertical surrounding rock pressures of shallow tunnels by considering the limit equilibrium of soil masses. In this paper, based on the Terzaghi failure mode, the pseudostatic method is used to derive this expression under seismic loading conditions. The surrounding rock in the fractured zone of the tunnel side wall is analyzed as an isolated body using the limit equilibrium method to obtain the explicit calculation expressions of the horizontal surrounding rock pressures of a shallow tunnel under seismic loading. Case analysis indicates that the proposed method is feasible. In addition, the influence of the seismic acceleration coefficient on surrounding rock pressures is further discussed. The results show that the horizontal surrounding rock pressure decreases with the increase of seismic acceleration coefficients. The vertical surrounding rock pressure increases as the horizontal seismic acceleration coefficient increases, and it decreases with the increase of the vertical seismic acceleration coefficient, and the effect of the seismic acceleration coefficient on surrounding rock pressure is significant. The study results can provide reference for the seismic safety evaluation and structural seismic design of shallow tunnels.

Pseudostatic analysis of soil nailed vertical wall for composite failure

ABSTRACT In the present study, pseudostatic method is used to analyse the stability of soil-nailed vertical wall under seismic conditions. This approach includes an additional inertial force equivalent to the dynamic load caused by earthquake. The soil surface which undergoes failure due to the static and dynamic condition is assumed to be a realistic composite failure surface rather than the conventional planar, circular or log-spiral surfaces. This study investigates the effect of various parameters such as vertical and horizontal seismic acceleration coefficients, friction angle of soil, shear wave velocity, primary wave velocity, amplification factor, nail length, spacing of the nails, and nail inclination on the stability of the vertical soil-nailed wall. A comparison study is made between the results obtained from the present analysis and the values reported in the literature. It is observed the present study with composite failure surface gives higher values of Factor of Safety compared to planar failure surface. Composite failure surface is more realistic and hence more accurate compared to a planar failure surface which gives a conservative value of Factor of Safety.

Seismic stability of obliquely loaded circular plate anchors

The vertical uplift resistance of obliquely loaded circular plate anchors buried in sand subjected to seismic loadings has been obtained in this paper. The pseudo-dynamic approach based on kinematic theorem of limit analysis has been applied for performing the analysis in which the nonlinear acceleration distributions are incorporated considering standing shear (S) and primary (P) wave propagations within the soil medium. Results are obtained in terms of seismic uplift factor (Fγs) due to soil self-weight component for a wide range of parameters. Through a parametric study, the effects of different parameters including normalized frequencies of Shear (S) and Primary (P) waves and damping ratio (ξ) of soil are highlighted. On account of amplified accelerations effects, the value of Fγs has been found to drastically reduce with an increase in load inclination (θ), horizontal and vertical seismic acceleration coefficients (kh and kv). The results show that the influence of damping ratio (ξ) of soil becomes more dominant particularly for frequencies close to the fundamental frequency of P wave.

Lateral earth pressure and bending moment on sheet pile walls due to uniform surcharge

Cantilever sheet pile walls are subjected to surcharge loading located on the backfill soil and at different distances from the top of the wall. The response of cantilever sheet pile walls to surcharge loadings at varying distances under seismic conditions is scarce in literature. In the present study, the influence of uniform surcharge load on cantilever sheet pile wall at varying distances from the top of the wall under seismic conditions are analyzed using finite difference based computer program. The results of the numerical analysis are presented in non-dimensional form like variation of bending moment and horizontal earth pressure along the depth of the sheet pile walls. The numerical analysis has been conducted at different magnitudes of horizontal seismic acceleration coefficient and vertical seismic acceleration coefficients by varying the magnitude and position of uniform surcharge from the top of the wall for different embedded depths and types of soil. The parametric study is conducted with different embedded depth of sheet pile walls, magnitude of surcharge on the top of the wall and at a distance from the top of the wall for different angles of internal friction. It is observed that the maximum bending moment increases and more mobilization of earth pressure takes place with increase in horizontal seismic acceleration coefficients, magnitude of uniform surcharge, embedded depth and decrease in the distance of surcharge from the top of the wall in loose sand.

Pseudo-Static Limit Equilibrium Method for Bearing Capacity of Footing on Slope and Seismic Uplift Capacity of Horizontal Strip Anchor

Seismic bearing capacity for a shallow strip footing embedded in a sloping ground is derived along with seismic uplift capacity of horizontal strip anchors. c-ϕ soil medium is used with limit equilibrium method of analysis. A planar failure mechanism has been adopted. The seismic bearing capacity is determined in the form of a single pseudo-static bearing capacity coefficient (N γe ) in association with unit weight, surcharge and cohesion, which becomes more practical to simulate the actual field problem. The seismic forces are considered to act both on the footing and on the soil below the footing. The effects of soil friction angle, soil cohesion, wall friction angle, horizontal and vertical seismic accelerations are taken into account to evaluate the seismic bearing capacity of the foundation. Also seismic uplift capacity factors for horizontal strip anchors is found. The factor is determined as a function of embedment ratio, angle of internal friction of soil, angle of wall friction, cohesion of soil and seismic acceleration coefficients. The uplift capacity factors have been determined for the simultaneous resistance of cohesion and unit weight of soil. Effect of the vertical seismic acceleration coefficient has been found to always reduce the uplift capacity factor whereas the effect of horizontal seismic acceleration coefficient has also been found to reduce the uplift capacity factor in maximum cases. The results obtained from both the cases has been compared with existing literature and the effect of parametric variations discussed.

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.

Seismic Stability Analysis of Waterfront Rock Slopes Using the Modified Pseudo-Dynamic Method

A modified pseudo-dynamic method is introduced in the paper at first, then geometric model of seismic stability on the waterfront rock slope considering the non-linear twin shear criterion is established. Finally the influence factors on the stability of rock slope are analyzed. The conclusions are drawn that the stability of rock slope decreases as the external loading $$q$$ , rock unit weight $$\gamma$$ , horizontal seismic acceleration coefficient $$k_{h}$$ and vertical seismic acceleration coefficient $$k_{v}$$ increases, and it increases as uniaxial compressive strength $$\sigma_{c}$$ , the water depth $$h_{1}$$ and parameters of rock mass properties $$m_{i}$$ and $$GSI$$ of rocks increases. These conclusions can provide great instruction significance for the future engineering design.

Redistribution Principle Approach for Evaluation of Seismic Active Earth Pressure Behind Retaining Wall

The knowledge of seismic active earth pressure behind the rigid retaining wall is very essential in the design of retaining wall in earthquake prone regions. Commonly used Mononobe–Okabe (MO) method considers pseudo-static approach. Recently there are many pseudo-dynamic methods used to evaluate the seismic earth pressure. However, available pseudo-static and pseudo-dynamic methods do not incorporate the effect of wall movement on the earth pressure distribution. Dubrova (Interaction between soils and structures, Rechnoi Transport, Moscow, 1963) was the first, who considered such effect and till date, it is used for cohesionless soil, without considering the effect of seismicity. In this paper, Dubrova’s model based on redistribution principle, considering the seismic effect has been developed. It is further used to compute the distribution of seismic active earth pressure, in a more realistic manner, by considering the effect of wall movement on the earth pressure, as it is displacement based method. The effects of a wide range of parameters like soil friction angle (ϕ), wall friction angle (δ), horizontal and vertical seismic acceleration coefficients (kh and kv); on seismic active earth pressure (Kae) have been studied. Results are presented for comparison of pseudo-static and pseudo-dynamic methods, to highlight the realistic, non-linearity of seismic active earth pressure distribution. The current study results in the variation of Kae with kh in the same manner as that of MO method and Choudhury and Nimbalkar (Geotech Geol Eng 24(5):1103–1113, 2006) study. To increase in ϕ, there is a reduction in static as well as seismic earth pressure. Also, by keeping constant ϕ value, as kh increases from 0 to 0.3, earth pressure increases; whereas as δ increases, active earth pressure decreases. The seismic active earth pressure coefficient (Kae) obtained from the present study is approximately same as that obtained by previous researchers. Though seismic earth pressure obtained by pseudo-dynamic approach and seismic earth pressure obtained by redistribution principle have different background of formulation, the final earth pressure distribution is approximately same.

Reliability Based Pseudo-Dynamic Analysis of Gravity Retaining Walls

Pseudo-dynamic method of analysis, considering the effect of earthquake loading, shear and primary waves, results in more realistic values of earth pressures than the commonly used pseudo-static method. To account for the uncertainties of geotechnical parameters, conventionally, either a global Factor of Safety (FS) to the entire structure or a constant partial FS to a particular geotechnical variable is applied. The present paper aims at quantifying these uncertainties and proposes partial risk factors based upon the variations of geotechnical random variables. For this purpose, a gravity retaining wall is analyzed by pseudo-dynamic method of analysis against sliding and overturning modes of failure. The backfill and foundation soil properties are treated as random variables and the effect of their variation on stability of the wall for various earthquake conditions is investigated. Probability of Failure (P f ) for the two modes is calculated by Monte Carlo Simulation. Sensitivity analysis of each random variable is carried out by F-Test analysis to analyze the impact of the random variables on the failure modes. Finally, these two are combined mathematically to produce a modification factor called the Probabilistic Risk Factor (R f ) for each random variable. It is observed that apart from the seismic horizontal and vertical pseudo-dynamic coefficients Q h (t) and Q v (t), the variation in friction angle of backfill soil (φ 1 ) and cohesion of foundation soil (c 2 )are the major influential geotechnical parameters in stability of the gravity retaining wall. If the variation of internal angle of friction of backfill and foundation soil exceeds approximately 7–8%, the structure needs to be modified for stability requirements. Similarly, the dimension of the structure needs to be increased if COV of c 2 exceeds 20% to maintain stability. Parametric studies are carried out for different combinations of vertical and horizontal seismic acceleration coefficients, and risk factor based approach is applied in each case.

Probabilistic analysis of the active earth pressure on retaining wall for c-f soil backfill under seismic loading conditions

En este artículo se describe una metodología basada en el método de estimación puntual de Rosenblueth para el análisis del empuje activo desarrollado en un muro de retención con relleno cohesivo-friccionante bajo condiciones de carga sísmica. El principio básico de esta metodología es usar dos estimaciones puntales, i.e., la desviación estándar y el valor medio, para examinar una variable en el análisis de seguridad. Es posible mostrar que aumentando el valor del coeficiente de aceleración sísmica horizontal, el factor de seguridad por volteo decrece y la probabilidad de falla aumenta, especialmente para coeficientes mayores que 0.2. Por otro lado, es observado que el valor medio del factor de seguridad crece cuando aumenta el coeficiente de aceleración sísmica vertical, sin embargo la probabilidad de falla se mantiene prácticamente igual para el valor del factor de seguridad considerado como crítico (1.15).

Non-linear failure surface analysis of seismic active earth pressure on retaining wall considering Rayleigh waves

This paper presents an analytical expression for seismic active earth pressure on the back of a retaining wall supporting c–ϕ backfill using Rayleigh waves. Analysis is done considering non-linear failure surface and using horizontal slice method in which limit equilibrium principle is used. The results as obtained on the basis of analysis are presented in tabular form. Parametric studies has been carried out with the consideration of wall inclination angle (α), soil friction angle (ϕ), wall friction angle (δ), horizontal and vertical seismic acceleration coefficients (kh and kv) and results are shown in both tabular and graphical form.

Investigation of Stability of a Slope Subjected to Water Table and Seismic Load

The stability of the slopes is the major concern in the field of Geotechnical Engineering. Usually three methods of analysis have been proposed for the evaluation of slopes response under seismic loads. These three methods are Pseudo-static method, Newmark’s displacement method and Dynamic finite element analysis method. In Pseudo-static method the earthquake’s inertial forces are simulated by the inclusion of static horizontal seismic acceleration co-efficient (kh) and vertical seismic acceleration co-efficient (kv) in limit equilibrium analysis. It is one of the most dangerous conditions of natural slope when it experiences a seismic vibration the countervailing water pressure has disappeared, it causes a danger to the slope. In this work, by applying the Morgenstern-Price presented by the computer program SLOPE/W was applied to define the potential slip surface and calculate the factor of safety of the defined slope for the maximum horizontal seismic acceleration co-efficient (kh). Calculation of relative lateral displacement of the slope surface and deformed shape of the defined slope due to the effects of horizontal seismic acceleration were done with the help of QUAKE/W software analysis. It was founded that the stability of the defined slope rapidly decreased.

Seismic bearing capacity of shallow foundations resting on rock masses subjected to seismic loads

This paper analyzes the bearing capacity of shallow foundations resting on rock masses subjected to seismic loads based on limit analysis theory. The non-linear twin shear strength criterion is used to consider the effects of intermediate principal stress on the bearing capacity of shallow foundations. The pseudo-dynamic approach is applied to account for the effects of seismic loads on the bearing capacity of shallow foundations. Both the horizontal and vertical seismic acceleration coefficients and the effects of an amplification factor on the upper bound evaluations of the foundation's bearing capacity are investigated. The ?-functions are then applied to derive the upper bound solution of the load-bearing capacity. A numerical computation is performed and indicates that the seismic acceleration coefficients, amplification factor and the intermediate principal stress parameter significantly affect the bearing capacity of shallow foundations.

Seismic Stability of Gravity Retaining Structures by Pseudo-Dynamic Method

An analytical expression of a gravity retaining wall's seismic stability against sliding and overturning is proposed in this article. The derivation, aiming at the cohesionless soil with inclined backfill surface and nonvertical wall back, is based on limit equilibrium analysis and the pseudo-dynamic method. The variations of the sliding and overturning stability safe factors with the horizontal seismic acceleration are investigated for different seismic amplification factors, soil friction angles, wall friction angles, vertical seismic acceleration coefficients, wall back inclination angles, and backfill surface inclination angles. The results indicate that the soil friction and horizontal seismic action significantly impact the seismic stability. The increase of vertical earthquake action changes the curvature of stability factor curves. The wall friction and back inclination strengthen the gravity retaining wall's resistance to sliding and overturning failure while the backfill surface inclination plays a negative role in the seismic stability. We also found that the seismic stability safe factors calculated by the proposed method are larger but more reasonable than those by the Mononobe-Okabe method.

Seismic Design and Parametric Study of Rigid Retaining Walls

The main objective of the paper is to develop a simplified procedure for the seismic design of a rigid retaining wall. For the design of a rigid retaining wall various parameters that are taken in to consideration include height of the wall, angle of inclination of backfill, backface angle of the wall, surcharge on backfill, safe bearing pressure of base medium and horizontal as well as vertical seismic acceleration coefficients. Safe design of a wall should satisfy four criteria, namely, factor of safety against sliding shall not exceed given limits, factor of safety against overturning shall be less than its permissible value, maximum pressure at the base of wall shall not exceed safe bearing pressure of the base soil and minimum pressure at the base of wall shall be greater than zero. In this paper an attempt has been made to give a simplified procedure for the seismic design of a rigid retaining wall. A parametric study to check the effect of various parameters affecting the seismic design of wall is carried out.

Seismic stability of reinforced soil walls under bearing capacity failure by pseudo-dynamic method

In order to evaluate the seismic stability of reinforced soil walls against bearing capacity failure, the seismic safety factor of reinforced soil walls was determined by using pseudo-dynamic method, and calculated by considering different parameters, such as horizontal and vertical seismic acceleration coefficients, ratio of reinforcement length to wall height, back fill friction angle, foundation soil friction angle, soil-reinforcement interface friction angle and surcharge. The parametric study shows that the seismic safety factor increases by 24-fold when the foundation soil friction angle varies from 25° to 45°, and increases by 2-fold when the soil-reinforcement interface friction angle varies from 0 to 30°. That is to say, the bigger values the foundation soil and/or soil-reinforcement interface friction angles have, the safer the reinforced soil walls become in the seismic design. The results were also compared with those obtained from pseudo-static method. It is found that there is a higher value of the safety factor by the present work.

Seismic Passive Earth Pressure with Seepage for Cohesionless Soil

The authors deal with the computing seismic passive earth pressure acting on a vertical rigid wall. The wall is provided with a drainage system along soil-structure interface and retains the cohesionless backfill subjected to water seepage. A general solution for the seismic passive earth pressure is presented. The solution is based on Coulomb's theory wherein seismic forces are assumed to be pseudostatic. The solution considers the pore water pressures induced by water seepage and earthquake shaking. Some important parameters are included in the solution. The parameters are the soil effective internal friction angle, wall friction, soil unit weight, and horizontal and vertical seismic acceleration coefficients. The comparison of the total seismic passive earth pressure in horizontal direction from the present method with published works indicates that the present method may be reasonable. The variations of the passive earth pressure coefficient with the soil effective internal friction angle are investigated for different wall friction angles and seismic forces. The effect of the water seepage on the seismic passive earth pressure is also investigated.