Vertical Seismic Coefficients Research Articles

Analysing Slope Stability in Response to Blast-Induced Dynamic Loading by Pseudo-Static Approach

Regular blasting in opencast coal mines generates significant ground vibrations, impacting mine slope stability and posing risks to life and property. This study focuses on monitoring ground vibrations in an opencast coal mine through near-field monitoring and investigating the impact of blast-induced seismic loading on slope stability. The approach involves a pseudostatic method utilising Strength Reduction Factor (SRF), based on Finite Element (FE) numerical modelling software. The study examines a pit slope with a tension crack under seismic loading, varying the intensity of seismic coefficients (Ks) from 0 to 0.5. These coefficients are determined through field vibration monitoring during production blasts. In numerical modelling, seismic loading is considered in both horizontal (outward of slope face) and vertically downward (in-line with gravity). Numerical modelling incorporates dimensionless horizontal seismic coefficient (Kh) and vertical seismic coefficient (Kv), and both directions which is expressed as Seismic Coefficient Ratio (SCR) which is the ratio of Kv and Kh for interpretation of results. Although SCR induces changes in the Factor of Safety (FoS), its impact is minimal compared to seismic loading solely in the horizontal direction. Consequently, increasing SCR leads to a decrease in FoS. The study observes that Peak Ground acceleration (PGA) in the longitudinal direction has greater dominance than in the transverse direction. Additionally, the seismic wave in the horizontal direction destabilises the slope more than the corresponding vertical seismic wave. These findings are elucidated in the context of the Critical Slip Surface (CSS).

Dynamic behavior of gravity segmental retaining walls

AbstractThis work aims to highlight gravity segmental retaining walls with their varied advantages. The paper investigates the dynamic behavior analysis of segmental retaining walls. The stability analysis is conducted on the basis of a pseudo-static Mononobe-Okabe theory that provides safety factors against sliding and overturning failure. The results demonstrate that the crucial safety factor of internal stability is the safety factor against overturning. Moreover, the positive wall inclination angle contributes to an improvement in the stability of the segmental retaining walls and the effect of the vertical seismic coefficient on the stability can be disregarding. Finally, a new equation is proposed for the elementary design of the segmental retaining walls.

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.

Calculation method for reinforcement spacing of bilaterally wrapped reinforced embankments under seismic force

The vertical spacing among reinforcements in geosynthetic-reinforced earth embankment is crucial to its overall stability. Based on the upper bound theorem of plastic limit analysis and pseudo-static approach, an overall stability analysis method for bilaterally wrapped reinforced embankments under strip surcharge and seismic action is put forward in view of the planar and log-spiral failure mechanism of the reinforced embankments, which quantitatively expresses the relationship between the reinforcement spacing and the factor of safety of the embankments. Some examples show that the maximum relative error of the factor of safety between the proposed method and some existing methods is around 10% under a specified reinforcement spacing. The factor of safety is nonlinearly decreasing as the reinforcement spacing increases, and the results by the log-spiral mode are slightly more conservative than those by the planar mode. The proposed method can quantitatively reflect the influence of the filling properties, reinforcement strength, seismic forces, strip surcharge, and embankment geometry on the reinforcement spacing. The nonlinear negative relationship between the factor of safety and the reinforcement spacing is noticeable under different reinforcement strengths. The reinforcement spacing is almost linearly reducing with the increase of the vertical seismic coefficient increases, while it decreases clearly nonlinearly as the horizontal seismic coefficient increases.

El impacto de incluir el coeficiente sísmico vertical kv en el análisis de estabilidad pseudoestático de tranques de relaves construidos con arenas mediante el método constructivo aguas abajo

In Chile, the limit equilibrium analysis under pseudostatic conditions is compulsory according to the Supreme Decree 248 (DS248, 2007), which establishes a minimum factor of safety (FoS) of 1.2 for stability analysis. In Chilean geotechnical practice, it is usually considered just the horizontal seismic coefficient (kh) for the analyses. However, there is a constant discussion about the necessity of applying both horizontal and vertical seismic coefficient (kv) into the analyses. In addition, there is uncertainty about what kv/kh should be considered and the effect that the sense of application (upward or downward) could have on the FoS. This paper presents an analysis of the effect of considering different |kv|/kh from 0 to 1 on both analysis directions for generic downstream tailings sand dam. Based on this, different dam heights, beach lengths and seepage conditions are also analysed. The obtained results show that when both kh and kv are applied, the FoS increase if kv acts downward and decrease when it acts upward. In addition, the effect for |kv|/kh ≤ 0.5 is almost neglectable, especially for kh ≤ 0.15. Furthermore, although a short beach length significantly impacts the FoS, the influence of applying both kh and kv seems to be independent of the beach length

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.

Vertical seismic analysis of roof truss in Indonesia

Based on a 1×680MW thermal power plant in Indonesia, the large-scale general finite element software ABAQUS was used to analyze the vertical seismic time history of the steel roof truss of the main plant of the thermal power plant, and study the vertical seismic effects of different seismic areas and site types on the steel roof truss Impact. Through analysis, a table of vertical seismic action coefficients of steel roof trusses with different parameters (the ratio of the standard value of vertical seismic action to the representative value of gravity load in frequent cases) is given for future engineering design reference.

Psuedo static stability analysis of rock slope using patton\u2019s shear criterion

A deterministic model for the factor of safety of an idealized rock mass for planar mode of failure is developed adopting Limit Equilibrium Method (LEM) using Patton’s shear strength criterion and considering practically occurring conditions such as the effect of tension crack, water filled up in tension crack, horizontal and vertical seismic acceleration, rock bolt stabilizing force and surcharge. In the Pseudo-static analysis horizontal seismic acceleration is taken outward from the slope and vertical seismic acceleration is considered in both the direction i.e. towards the direction of gravity (downward) and opposite to the direction of gravity (upward). An expression of normal stresses as limiting criterion has been derived in order to compare the field normal stresses along the failure surface. A detailed parametric study has been presented to investigate the influence of vertical seismic coefficient for both the direction on the stability of rock slope using developed expression. For high normal stress along the failure plane, it is observed that the factor of safety decreases with increase in the value of vertical seismic coefficient towards the direction of gravity and increases linearly with increase in the value of vertical seismic coefficient against the direction of gravity and the opposite trend has been found for lower normal stress. The vertical seismic coefficient against the direction of gravity has predominant effect on factor of safety of rock slope as the rate of increase/decrease of factor of safety with vertical seismic coefficient is more against the direction of gravity. Hence in determining the critical factor of safety, effect of vertical seismic coefficient against the direction of gravity should be considered.

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.

Taylor's slope stability chart for combined effects of horizontal and vertical seismic coefficients

Taylor's slope stability chart for combined effects of horizontal and vertical seismic coefficients

Rock slope reliability analysis using Barton-Bandis failure criterion with modified pseudo-dynamic approach

A modified pseudo-dynamic approach was used for a reliability-based stability analysis of plane failure rock slopes. The Barton-Bandis nonlinear failure criterion and the limit equilibrium principle were adopted to account for the nonlinear characteristics of rock joint shear strength and safety factor of slope, respectively. The Monte Carlo simulation method was used to analyze the rock slopes. Comparisons of the present method to a numerical simulation and to a pseudo-static case, were implemented. The influence of different parameters and tension cracks on slope stability was analyzed. Results showed that the stability of the rock slope decreases with increasing rock unit weight, horizontal seismic coefficients and vertical seismic coefficients, and increases with increasing residual friction angle, joint roughness coefficient and joint compressive strength. The location of the tension crack has significant influence on the stability of rock slopes, while the influence of inclination of the tension crack is negligible.

SEISMIC ANALYSIS OF A SOIL SLOPE TO DEVELOP CORRELATIONS FOR FACTOR OF SAFETY CONSIDERING HORIZONTAL AND VERTICAL SEISMIC COEFFICIENTS

Seismic analysis of soil slopes is required to get safe value for slope design. Especially in earthquake zones. Normally a variation in factor of safety values is observed in normal analysis of a slope where seismic coefficients are kept zero as compare to seismic analysis where seismic coefficients are considered in the analysis. In this research, seismic horizontal coefficients are used to find the factors of safety. Correlations are developed between factor of safety values and seismic coefficients. The correlation can be used to find the factor of safety in any slope stability project for a homogenous slope. The outcome of this work are the correlations. These correlations can be used to find the factor of safety values considering horizontal seismic coefficient, vertical seismic coefficient and both.

Comparative study of seismic and non-seismic analysis of a soil slope to develop correlations for factor of safety considering horizontal and vertical seismic coefficients

Seismic and non-seismic analysis of any engineering project always gives different results. A soil slope is analysed in this research and both seismic and non-seismic analysis is performed to know about the difference in the factor of safety values. Correlations are developed between both these cases. These correlations are applicable for homogenous slopes only.

Seismic Analysis of a Soil Slope to Develop Correlations for Factor of Safety Considering Horizontal and Vertical Seismic Coefficients

Seismic analysis of soil slopes is required to get safe factor of safety value for slope design. Especially in earthquake zones. Factor of safety value is always effected by seismic coefficients, such as horizontal and vertical coefficients. Normally a variation in factor of safety values is observed in normal analysis of a slope where seismic coefficients are kept zero as compare to seismic analysis where seismic coefficients are considered in the analysis. In this research, seismic horizontal coefficients as well as vertical seismic coefficients are used to find the factors of safety. Correlations are developed between factor of safety values and seismic coefficients. The correlation can be used to find the factor of safety in any slope stability project for a homogenous slopes. The outcome of this work are the correlations. These correlations can be used to find the factor of safety values considering horizontal seismic coefficient, vertical seismic coefficient and both.

Upper bound analysis of collapse failure of deep tunnel under karst cave considering seismic force

When tunnels are excavated in karst areas, the existence of karst caves in the surrounding rock usually results in the collapse failure of tunnels. Tunnel collapse has always been a challenging issue because it seriously threatens the safety of tunnel builders. To investigate the collapse of a deep tunnel under a karst cave, we constructed the collapse mechanisms of the rectangular and circular tunnels under a karst cave, and obtained the expressions of the collapse failure in tunnel considering seismic force and seepage force by means of the variational principle and limit analysis theory. Compared with previous results and numerical solutions, it is found that the results in this paper are consistent with those results and numerical solutions, which indicates that the proposed method in this work is rational. According to the analytical solutions, the shape of the collapsing blocks of the deep rectangular and circular tunnels under a karst cave are drawn, and the effects of different parameters, especially the vertical seismic coefficient kv, on the collapsing blocks are analyzed. The findings in this paper indicate that the range of collapsing blocks decreases with increased kv. The two formulas for calculating the critical height between the tunnel and the karst cave are given by derivation.

Effect of vertical seismic coefficient on cohesive-frictional soil slope under generalised seismic conditions

ABSTRACT In the present work, seismic performance parameters have been reviewed by considering the possible combined action of vertical and horizontal seismic loadings of the ground motion during the earthquakes. Analytical expressions of factor of safety, yield seismic coefficient and permanent seismic displacement of a cohesive-frictional soil slope have been developed by following deterministic sliding block approach in a two-dimensional pseudo-static framework. The slope with a planar failure surface is assumed to follow the Mohr-Coulomb criterion by considering a slice of unit thickness through the slope. For a given range of slope geometrical and soil parameters, the role of vertical seismic coefficient has been analysed in the presence of cohesion to investigate its effect on factor of safety, yield seismic coefficient, and consequently on the permanent seismic displacement of the slope through a set of graphical presentations. The results show that avoidance of vertical seismic component of the ground motion in the stability analysis may lead to severe slope failures. The general expressions proposed herein can be used to carry out a quantitative stability assessment of cohesive- frictional soil slopes during earthquakes in real-life projects.

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.