Horizontal Seismic Coefficient Research Articles

Pseudo-dynamic active force and pressure behind battered retaining wall supporting inclined backfill

Knowledge of seismic active earth pressure behind rigid retaining wall is very important. Commonly used Mononobe–Okabe method considers pseudo-static approach, which gives the linear distribution of seismic earth force. In this paper, the pseudo-dynamic approach, which considers the effect of primary and shear wave propagations, is adopted to calculate the seismic active force. Considering the planar rupture surface, the effect of wide range of parameters like inclination of retaining wall, inclination of backfill surface, wall friction and soil friction angle, shear wave and primary wave velocity, horizontal and vertical seismic coefficients are taken into account to evaluate the seismic active force. Results are presented in terms of seismic coefficients in tabular form and variation of pressure along the depth.

Seismic analysis for translational failure of landfills with retaining walls

In the seismic impact zone, seismic force can be a major triggering mechanism for translational failures of landfills. The scope of this paper is to develop a three-part wedge method for seismic analysis of translational failures of landfills with retaining walls. The approximate solution of the factor of safety can be calculated. Unlike previous conventional limit equilibrium methods, the new method is capable of revealing the effects of both the solid waste shear strength and the retaining wall on the translational failures of landfills during earthquake. Parameter studies of the developed method show that the factor of safety decreases with the increase of the seismic coefficient, while it increases quickly with the increase of the minimum friction angle beneath waste mass for various horizontal seismic coefficients. Increasing the minimum friction angle beneath the waste mass appears to be more effective than any other parameters for increasing the factor of safety under the considered condition. Thus, selecting liner materials with higher friction angle will considerably reduce the potential for translational failures of landfills during earthquake. The factor of safety gradually increases with the increase of the height of retaining wall for various horizontal seismic coefficients. A higher retaining wall is beneficial to the seismic stability of the landfill. Simply ignoring the retaining wall will lead to serious underestimation of the factor of safety. Besides, the approximate solution of the yield acceleration coefficient of the landfill is also presented based on the calculated method.

Pseudo-Dynamic Active Response of Non-Vertical Retaining Wall Supporting c-Φ Backfill

Knowledge of seismic active earth pressure behind rigid retaining wall is very important. In this paper, the pseudo-dynamic approach, which considers the effect of both compression and shear wave propagation, is adopted to calculate the seismic active force supporting c-Φ backfill. Considering a planar rupture surface, the effect of wide range of parameters like inclination of retaining wall, wall friction and soil friction angle, shear wave and compression wave velocity, horizontal and vertical seismic coefficients are taken into account to evaluate the seismic active force. Results are presented in terms of seismic coefficients in tabular form and variation of pressure with depth.

Seismic bearing capacity of shallow foundations near slopes using the upper-bound method

The seismic bearing capacity factors of spread and embedded foundations near slopes have been analytically investigated. The pseudo-static approach was used and the seismic forces consisted of a horizontal load applied to the foundation and the inertia of the soil mass. The upper-bound method of limit analysis was employed and a non-symmetrical failure mechanism was proposed. This mechanism comprises a triangular active wedge, a logarithmic spiral shear zone and a passive wedge. The shear transfer coefficient was introduced to calculate the seismic bearing capacity of spread foundations with variable shear transfer at the base of foundations. The validity of the results from the present analysis was confirmed by comparing with the results proposed by other investigators. Finally, the lowest upper-bound solutions of the seismic bearing capacity factors of shallow foundations near slopes were presented in the form of design charts for practical use in geotechnical engineering. It has been shown that the seismic bearing capacity factors reduce considerably with the increase of horizontal seismic coefficient. In addition, the magnitude of bearing capacity factors decreases further with increase in slope inclination and increase with the embedment and the distance of slope crest from the beginning of loading.

Reliability Analysis of Earth Dams

In the present study, results of reliability analyses of four selected rehabilitated earth dam sections, i.e., Chang, Tapar, Rudramata, and Kaswati, under pseudostatic loading conditions, are presented. Using the response surface methodology, in combination with first order reliability method and numerical analysis, the reliability index (beta) values are obtained and results are interpreted in conjunction with conventional factor of safety values. The influence of considering variability in the input soil shear strength parameters, horizontal seismic coefficient (alpha(h)), and location of reservoir full level on the stability assessment of the earth dam sections is discussed in the probabilistic framework. A comparison of results with those obtained from other method of reliability analysis, viz., Monte Carlo simulations combined with limit equilibrium approach, provided a basis for discussing the stability of earth dams in probabilistic terms, and the results of the analysis suggest that the considered earth dam sections are reliable and are expected to perform satisfactorily.

Pseudo-Static Analysis of Soil Nailed Excavations

In this paper, a pseudo-static analysis has been presented to investigate the stability of soil nailed vertical/nearly vertical excavations. The failure surface is assumed as the arc of log-spiral passing through the toe of the excavation and intersecting the ground at right angle. The horizontal and vertical seismic forces are taken in terms of horizontal and vertical seismic coefficients. The internal failure mode of the nailed cut is considered either by pull-out or rupture or excessive bending whichever is critical. Expression for the factor of safety is derived using moment equilibrium method. Results have been arranged in tabular form considering ranges of the design parameters usually occur in practice. A typical table for the design of nailed excavation with driven nails is presented in the paper. Analytical results have been compared with the findings of model tests and reasonably good agreement has been observed.

Effects of Horizontal and Vertical Seismic Loads on the Bearing Capacity of a Surface Footing Adjacent to a Slope

The correction factor (η ie ) for the ultimate bearing capacity of a footing placed adjacent to a slope, taking into account the combined effect of horizontal and vertical seismic loads, represented by horizontal and vertical seismic coefficients, k h and k v , respectively, was derived using a modified Janbu's slice method. The influence of slope angles ‘α’ on the values of ‘η ie ’ are studied here. It was found that the values of η ie can be expressed as an exponential function of ‘ k h /(1- k v )’ and ‘α’, with a measurable interdependency between ‘α’ and ‘η ie ’. The influence of ‘α’ on the value of ‘η ie ’ increases as the input value of ‘ k h /(1- k v )’ increases. Equations derived based on the analytical results are proposed to account for this effect. Based on the analyses of 11 near-fault seismographers obtained in the 1999 Chi-Chi earthquake in Taiwan, a ratio between the vertical and the horizontal seismic coefficients, λ, of between ±0.25 is suggested for including the combined effect of vertical and horizontal seismic forces in evaluating the seismic bearing capacity of footings located in near-fault areas.

Active Earth Pressure on Retaining Wall for c-ϕ Soil Backfill under Seismic Loading Condition

This technical note describes the derivation of an analytical expression for the total active force on the retaining wall for c-ϕ soil backfill considering both the horizontal and vertical seismic coefficients. The results based on this expression are compared with those obtained from earlier analytical expressions for the active force for c-ϕ soil backfill under seismic conditions, and found to have a similar trend of variation. The parametric study shows that the inclination of the critical failure plane with the horizontal plane decreases with the increase in values of seismic coefficients; the decrease being more for their higher values. The total active force increases with the increase in value of horizontal seismic coefficient; while it decreases with the increase in value of vertical seismic coefficient except for a very high value of horizontal seismic coefficient. Design charts are presented for various combinations of horizontal and vertical seismic coefficients (kh and kv), and values of cohesion and angle of shearing resistance for estimating the total active force on the retaining wall for c-ϕ soil backfill for practical applications.

Reliability-Based Analysis and Design of Strip Footings against Bearing Capacity Failure

This paper presents a reliability-based approach for the analysis and design of a shallow strip footing subjected to a vertical load with or without pseudostatic seismic loading. Only the punching failure mode of the ultimate limit state is studied. The deterministic models are based on the upper-bound method of the limit analysis theory. The random variables used are the soil shear strength parameters and the horizontal seismic coefficient. The Hasofer-Lind reliability index and the failure probability are determined. A sensitivity analysis is also performed. The influence of the applied footing load on the reliability index and the corresponding design point is presented and discussed. It was shown that the negative correlation between the soil shear strength parameters highly increases the reliability of the foundation and that the failure probability is highly influenced by the coefficient of variation of the angle of internal friction of the soil and the horizontal seismic coefficient. For design, an iterative procedure is performed to determine the breadth of the footing for a target failure probability.

Seismic ultimate bearing capacity of strip footings on slope

The influence of earthquake forces on ultimate bearing capacity of foundations on sloping ground was studied. A solution to seismic ultimate bearing capacity of strip footings on slope was obtained by utilizing pseudo-static analysis method and taking the effect of intermediate principal stress into consideration. Based on limit equilibrium theory, the formulae for computing static bearing capacity factors, N q, N c, N γ, and dynamic bearing capacity factors, N qd, N cd, N γd, which are associated with surcharge, cohesion and self-weight of soils respectively, were presented. A great number of analysis calculations were carried out to obtain the relationship curves of the static and dynamic bearing capacity factors versus various calculation parameters. The curves can serve as the practical engineering design. The calculation results also show that when the values of horizontal and vertical seismic coefficients are 0.2, the dynamic bearing capacity factors N qd, N cd and N γd, in which the effects of intermediate principal stress are taken into consideration, increase by 4%–42%, 3%–27% and 34%–57%, respectively.

Seismic bearing capacity of foundations on reinforced soil slopes

Different methods have been proposed for the analysis of the stability of reinforced soil. One of them is the method of characteristics, which treats the reinforced soil as a homogeneous but an-isotropic material. Soil masses are weak under the application of reversible/dynamic forces and reinforcing would be much helpful in these cases. In this paper, the idea of homogenization and the method of characteristics have been used to analyze the seismic bearing capacity of reinforced soil slopes. A new method has been used for deriving the equilibrium-yield equations along the characteristics, which is different from the conventional procedure used in the method of characteristics. A computer code has been written for the analysis, which calculates the geometry of plastic zone and the ultimate applicable load for the assumed material and geometrical characteristics of reinforced soil slopes. Non-uniform reinforcement and non-uniform distribution of horizontal or vertical seismic coefficients can also be considered in the analysis. Results of analysis of simple cases have been presented in the form of non-dimensional graphs to facilitate preliminary design.

Seismic Stability of Cement Treated Ground by Tilting and Dynamic Shaking Table Tests

A series of tilting tests and shaking table tests was conducted with a geotechnical centrifuge apparatus to determine the dynamic active earth pressure of cement treated clay ground by investigating the seismic stability of cement treated clay ground having an unsupported vertical slope. In the tilting tests, the horizontal seismic inertia force was simulated statically by tilting the whole model ground in accordance with the horizontal seismic coefficient kh. The tilted model ground was subjected to monotonically increasing centrifugal acceleration until it failed due to the enhanced selfweight. In the shaking table tests, on the other hand, the model ground was subjected to dynamic excitations under a high centrifugal acceleration field. The magnitude of the dynamic excitation was increased stepwise until the model ground failed. It was found from both test results that the model ground failed with a combination of a vertical tensile crack and a straight shear failure plane, which was much different from the failure phenomenon of sandy or clayey ground. It was also found that the conventional pseudo-static limit equilibrium method such as Mononobe-Okabe’s earth pressure theory was not able to evaluate the critical height and the failure zone of the model ground accurately. Based on the model test results, a modified pseudo-static limit equilibrium method incorporating the tensile force along the crack plane was proposed in this study. In the method, the critical height and the failure zone of the cement treated ground were influenced by the strength ratio of the tensile strength to the compressive strength of the treated soil. It was found that the proposed method with a suitable strength ratio was able to predict the tilting test results with fairly high accuracy. Also, the proposed method seemed to be able to reasonably explain the shaking test results if the dynamic response acceleration of the model ground was carefully taken into account. Dynamic active earth pressure of cement treated clay ground was also discussed in which the importance of incorporating the failure pattern was emphasized.

Seismic stability analysis of fractured rock slopes by yield design theory

This paper deals with the problem of stability of fractured rock slope located in seismic area. The rock mass is crossed by two sets of fractures which are considered to be planar, parallel and persistent. The effects of both horizontal seismic coefficient and strength characteristics of fractures are addressed. The analysis is based upon the kinematic approach of the yield design theory and the pseudo-static method as well. The fundamental inequality of the kinematic approach is invoked and the failure of the fractured rock slope is considered through simple translational mechanism involving a one-partsliding block. Rigorous upper bounds of the so-called stability factor for the structure under study of given slope angle, strength properties of constituent materials and seismic loads are obtained. The results are presented in the form of stability charts relating the estimated upper bound solutions to the friction angle of fractures. The used procedure highlights the destabilizing effects of the seismic loadings and is capable of conducting parametric studies. Furthermore, the results obtained far from various sets of data show good performance and further research work is planed to extend the analysis to include a large number of sub-problems.

Investigation on Seismic Slope Stability Based on Pseudo-static Analysis.

This study presents a numerical procedure by means of shakedown analysis to assess the seismic stability of slope based on the pseudo-static concept. The factor of safety was defined with the strength reduction coefficient as commonly employed in slope stability. The applicability of the numerical procedure was examined firstly to the static slope stability assessment through the comparison in factor of safety with the Taylor's friction circle method. It was clearly shown that the factors of safety of two methods were in good agreement and the proposed method assessed the static slope stability properly. Secondly, the seismic stability of slope was investigated in the frame of pseudo-static concept. The effect of earthquake load direction on the seismic stability was widely investigated for cohesive and frictional soils. The factor of safety obtained for the horizontal seismic coefficient was found to be close to the critical factor of safety in direction. Thirdly, the effect of repeated change in both direction and magnitude of earthquake load on the factor of safety was especially examined. It was found that the repeated change in earthquake load affected the seismic slope stability significantly, especially in the case of frictional soil. However, it was found that the factor of safety for the horizontal alternating load was close to that for the alternating load in every direction in the same way with the monotonic earthquake load.

EVALUATION OF HORIZONTAL SEISMIC COEFFICIENT FOR CAST IN PLACE PILE UNDER THE CONSIDERATION OF UNCERTAINTIES IN REINFORCED CONCRETE BRIDGE SYSTEMS

耐震設計では, 様々な不確定要因を考慮した上で, 設計上想定しない限界状態が生起することを防ぐ必要がある. 本研究では, RC橋脚および場所打ち杭基礎からなる橋梁システムを対象として, 従来確定的に用いられてきた杭基礎-地盤間ばねの不確定性が, 橋脚や杭の地震時応答に与える影響を統計論的立場から検討した. そして, 定量的に評価された各応答値のばらつきをもとに, 場所打ち杭基礎を耐震設計する際に, その設計水平震度をRC橋脚の保有水平耐力に相当する震度に対して, どの程度割増すれば地震時の場所打ち杭基礎の降伏を防ぐことができるのかを, 動的解析と信頼性理論の両面から検討した.

A Modified Procedure to Evaluate Active Earth Pressure at High Seismic Loads

ABSTRACT A modified and pseudo-static limit-equilibrium approach to evaluate active earth pressure at high seismic load levels is proposed. Although it is similar to the Mononobe-Okabe method, the proposed method considers the effects of strain localization in the backfill soil and associated post-peak reduction in the shear resistance from peak to residual values along a previously formed failure plane. The proposed method can reflect differences in the peak shear resistance of the backfill soil with different degrees of compaction; yields a realistic active earth pressure coefficient which is smaller than that predicted by the Mononobe-Okabe method using a residual shear resistance; can be adapted to analyses with a large horizontal seismic coefficient where the Mononobe-Okabe method using the residual shear resistance is not applicable; and renders a reduced and more realistic size of active failure zone in the backfill soil at high seismic load levels compared to that predicted by the Mononobe-Okabe method.

Soil slopes under combined horizontal and vertical seismic accelerations

Conventional methods of designing earth structures are based on pseudo-static stability analysis employing a horizontal seismic coefficient. This paper discusses the stability and permanent displacement of a slope subject to combined horizontal and vertical accelerations. A log-spiral failure mechanism is used. It is shown that seismic force has a significant effect on stability and permanent displacement of slopes. The parametric study reveals that vertical acceleration may play an important role on stability and permanent displacement if the corresponding horizontal acceleration is large. © 1997 John Wiley & Sons Ltd.

Earth Pressure On Reinforced Earth Walls Under General Loading

The limit equilibrium analysis applied to a plane failure surface is utilized for the evaluation of the active earth pressure on reinforced-earth walls under different loading conditions, such as seismic loading, pore water pressures into the fill, vertical and horizontal loads acting on the top at some distance. Due to the complexity of boundary and loading conditions considered, a limit equilibrium method with a plane failure surface has been used because this allows to deduce closed form solutions that could be quite helpful in design reinforced-earth vertical walls. The analysis presents two different loading conditions on a reinforced earthfill and two solutions in terms of earth pressure coefficient are given. Earth pressure coefficients are a function of non-dimensional parameters such the ratio λ between the distance d of the applied surcharge and the height of the wall H, or the ratio m between the horizontal and the vertical surcharge qh and qv respectively. Pore water pressure effects on earth pressure have been taken into account by means of the pore pressure ratio ru = u/yH. Seismic loading have been taken into account in a pseudo-static way, in terms of horizontal and vertical seismic coefficients. In a conventional design procedure, the analysis allows to define spacing or number of reinforcement as well as their length according to the failure wedge predicted.

Pseudo-Static Seismic Analysis Of Geosynthetic-Reinforced Segmental Retaining Walls

The paper examines seismic stability analyses of geosynthetic-reinforced segmental retaining walls (modular block walls). Stability analyses are developed within the framework of a pseudo-static approach that gives factors of safety against collapse mechanisms or rupture of component materials. The Mononobe-Okabe method is used to estimate dynamic earth pressures. Parametric analyses of forces and factors of safety related to external, internal and facing failure modes for walls constructed on competent foundations are presented. Shear interfaces between facing units are considered as possible planes of failure in facing stability analyses. The potential for local toppling of the facing column is also investigated. The results of analyses demonstrate that there is a limiting value of the horizontal seismic coefficient above which the margin of safety against base sliding and overturning may be unacceptably low during a seismic event for segmental retaining walls designed to just satisfy minimum factors of safety under static loading conditions. Pseudo-static seismic analyses of the performance of two geosynthetic-reinforced segmental walls during the Northridge Earthquake in Los Angeles in 1994 are demonstrated to be consistent with visual observation of tension cracks in the soil backfill. Limitations of pseudo-static methods are discussed and recommendations for further research are made.

COEFFICIENT OF EARTH PRESSURE OF SAND DURING CYCLIC SHEAR

The coefficients of earth pressure of dry sand C0 and C′0 was obtained by means of cyclic shear tests using Kjellman's type simple shear test apparatus fixed on a shaking table. C0 was defined by the ratio of horizontal stresses to vertical stresses, developed in sand during cyclic shear, and C′0 the ratio of minor or intermediate principal stress to major principal stresses. It was found that C0 and C′0 increased with increasing the horizontal seismic coefficient kh, and C0 in shear direction was 1.2-1.5 times as large as C0 in the direction perpendicular to that up to kh=0.4. It was also found that the internal friction angle of sand φ′ decreased by 2.5° with increasing kh by 0.1.For the case of liquefaction tests on saturated sand, the variations of C0 and C′0 with number of cycles were presented.