Computations of Seismic Passive Resistance and Uplift Capacity of Horizontal Strip Anchors in Sand

In this paper, the limit equilibrium method is used to compute seismic passive earth pressure coefficients and the vertical uplift capacity of horizontal strip anchors in presence of both horizontal and vertical pseudo-static earthquake forces. By considering a simple planar failure surface, distribution of soil reaction is obtained through the use of Kötter’s equation. Presence of pseudo-static seismic forces induces a considerable reduction in the seismic passive earth pressure coefficients. The reduction in seismic passive earth pressure coefficients increases with increase in magnitude of the earthquake accelerations in both horizontal and vertical directions and with increase in wall friction angle. The vertical uplift capacity of horizontal strip anchor is obtained for various values of soil friction angle, embedment ratio and seismic acceleration coefficients in both horizontal and vertical directions by using rigorous computational optimization. Proper justification for selected value of wall friction angle is established. Results are presented in the form of non-dimensional breakout factor for anchor. A significant reduction in breakout factor is observed in presence of both the seismic acceleration coefficients whereas breakout factor increases with increase in soil friction angle and embedment ratio even under the seismic condition. Angles of failure planes keep changing with change in seismic acceleration coefficients and failure zone shifts towards the critical direction of seismic acceleration coefficients. Present results are compared and found in good agreement with some specific available results in literature.     

Seismic uplift capacity of inclined strip anchors in sand using upper bound limit analysis

Pseudo-static approach is adopted in this paper to determine the seismic uplift capacity of an inclined strip anchor using upper bound limit analysis. Two different failure mechanisms are considered to obtain the magnitudes of unit weight component of uplift factor f_γE for different values of soil friction angle, interface friction of anchor plate, anchor inclination, embedment ratio and horizontal seismic acceleration coefficient. The failure mechanism 1 consists of a triangular and quadrilateral rigid blocks; whereas the failure mechanism 2 comprises a logarithmic spiral failure zone with varied focus, sandwiched between a triangular and quadrilateral rigid blocks. It is observed that the magnitude of uplift factor f_γE decreases significantly with the increase in seismic acceleration but increases with the increase in embedment ratio and roughness of the anchor surface. However, a mixed trend in the values of f_γE can be observed for different inclination of the anchor, which is clearly discussed in this paper. The results are compared with the existing values in the literature and the significance of the present methodology for designing the inclined strip anchor is discussed.     

Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N _γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N _γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.     

Seismic interference of two nearby horizontal strip anchors in layered soil

In the present analysis, an attempt is made to explore the seismic response of two nearby horizontal strip anchors embedded in non-homogenous c-? soil deposit at different depths. The analysis is performed by using two-dimensional finite-element software PLAXIS 2D. Each anchor carries equal static safe-working load without violating the ultimate uplift capacity under static condition. The soil is assumed to obey the Mohr?CCoulomb failure criterion. The behavior of single isolated anchor subjected to an earthquake loading is determined first to study the interference effect between two anchors. The horizontal acceleration response obtained from the Loma Prieta Gilroy Earthquake (1989) is considered as the input excitation in the analysis. A parametric study is performed by varying the clear spacing (S) between the anchors at different embedment ratios (??). The magnitude of vertical displacement, shear stress, and shear strain developed at different locations of the failure domain is determined for different clear spacings between the anchors.     

Seismic uplift capacity of strip anchors in soil

Uplift capacity of horizontal strip anchors in soil embedded under an inclined ground surface has been obtained under seismic conditions. Limit equilibrium approach with logspiral failure surface together with pseudo-static seismic forces has been adopted. The results have been presented in the form of seismic uplift capacity factors as functions of ground inclination, embedment ratio, angle of internal friction of the soil and seismic acceleration coefficients. The uplift capacity factors have been worked out separately for cohesion, surcharge and density components. Effect of the vertical seismic acceleration coefficient has been found to always reduce the uplift capacity whereas the effect of horizontal seismic acceleration coefficient has been found to reduce the uplift capacity in most of the cases. The obtained results of seismic uplift capacity factors are found to be the minimum when compared with the results available in literature on the basis of planar failure surface. This revised version was published online in July 2006 with corrections to the Cover Date.     

Seismic Pullout Capacity of Inclined Anchor Plates in Sand

By using the lower bound finite elements limit analysis, the pullout capacity of an inclined strip anchor plate embedded in a cohesionless soil medium has been computed with an inclusion of pseudo-static horizontal earthquake body forces. The variation of the pullout capacity factor (F _γ ) with changes in horizontal earthquake acceleration co-efficient (α _h ) has been computed by varying the inclination angle (β) of the anchor plate between 0° and 90°. The results clearly reveal that the pullout capacity factor (F _γ ) decreases significantly with an increase in the value of α _h . The reduction in the pullout resistance due to seismic forces (1) becomes much more extensive for a vertical anchor plate as compared to the horizontal anchor, (2) decreases generally with increases in the soil friction angle (?) and (3) increases with an increase in friction angle between soil and anchor plate (δ). The developments of the failure zone around the anchor plate were also examined by varying α _h and β. The results obtained from the analysis compare well with the solutions reported in literature.     

A simplified approach for studying the influence of vertical accelerations on seismic response of slopes

ABSTRACT

A simplified approach is presented for estimating permanent displacements in slopes as a result of both vertical and horizontal seismic accelerations. A study of 52 earthquake records showed that the time difference between maximum horizontal and vertical accelerations varied between 0 and 10.3 s. The approach is illustrated for an earth dam embankment by analysing the effects of five of the above earthquake records. The approach combines a pseudo-static slope stability analysis for estimation of the critical (or yield) horizontal-vertical acceleration combinations, and a Newmark type displacement analysis. Guidelines are presented for conservative choice of soil strength parameters of saturated clays for use in the stability analysis. While permanent displacements of up to 40 cm were predicted without considering the vertical acceleration component, no additional displacement above 3.5 cm resulted when this component was included. The predicted additional displacement was consistently less than 10%, and in 50% of the analyses, vertical acceleration led to smaller predicted displacements. The simple approach may be applied in analysis for any slope using real earthquake records. Using existing, empirical expressions for permanent displacement, based only on horizontal accelerations, the effect of the vertical accelerations may be conservatively estimated by increasing the displacement by 10%.     

Influence of overburden pressure and soil rigidity on uplift behavior of square plate anchor in uniform clay

A numerical study incorporating three-dimensional Eulerian large deformation finite element analyses is performed to investigate the pullout process of horizontal square plate anchors in both hypothetical weightless soil and soil with self-weight. The validity of the numerical model is established through verification against published experimental and numerical results. The failure mechanisms during the pullout process under different conditions are then investigated. Three types of failure mechanism are observed; of which only two have been reported in the literature. The third mechanism identified in this study, which is a partially localized flow mechanism, is operative when the soil overburden ratio is not high enough to mobilize the full flow mechanism. The influence of soil self-weight is directly investigated by incorporating the density of the soil in the finite element model and maintaining the gravitational acceleration field throughout the analysis. The critical overburden ratio corresponding to the full transition to a localized plastic flow mechanism is identified in this study. The effect of the soil rigidity index (E/s_u) on the anchor uplift capability has not been systematically investigated in earlier studies. Contrary to the general failure mechanism and the full flow mechanism described in the literature, the capacity factor corresponding to this new mechanism increases with increasing E/s_u. The capacity factors for square plate anchors corresponding to different anchor embedment ratios, overburden ratios and E/s_u are provided in the form of design charts.     

Comparison of the pseudo-static and dynamic behaviour of gravity retaining walls

Summary Pseudo-static and dynamic non-linear finite element analyses have been performed to assess the dynamic behaviour of gravity retaining walls subjected to horizontal earthquake loading. In the pseudo-static analysis, the peak ground acceleration is converted into a pseudo-static inertia force and applied as a horizontal incremental gravity load. In the dynamic analysis, an actual measured earthquake acceleration time history has been scaled to provide peak ground acceleration values of 0.1 g and 0.3 g. Good agreement is obtained between the pseudo-static analysis and analytical methods for the calculation of the active coefficient of earth pressure. However, the results from the dynamic analysis require careful interpretation. In the pseudo-static analysis, the increase in the point of application of the resultant active force with the horizontal earthquake coefficient k _h from the one-third point to the mid-height of the wall is clearly observed. In the dynamic analysis, the variation in the point of application is shown to be a function of the type of wall deformation. Both finite element analyses indicate the importance of determining the magnitude of the predicted displacements when assessing the behaviour of the wall to seismic loading.     

Pseudo-static Analysis of Reinforced Earth Retaining Wall considering Non-linear Failure Surface

The seismic stability of reinforced earth has been investigated in this paper using pseudo-static method of analysis considering horizontal and vertical seismic acceleration with non-linear failure surface. The sliding wedge is divided into a number of horizontal slices to determine the strength and length of the geo-synthetic reinforcement for seismic internal stability of battered face rigid retaining wall supporting c-Φ backfill. Results are presented in graphical form representing the required length of geo-sythetic reinforcement under seismic condition to maintain the internal stability of reinforced soil. The influences of horizontal and vertical seismic acceleration, soil friction angle, cohesion, adhesion and wall inclination angle on the required length of the geo-sythetic reinforcement have been studied. From the present study it is seen that the required length of geo-synthetic reinforcement increases due to increase in the value of seismic accelerations.     

Equivalent-linear seismic analyses of MSW landfills using DEEPSOIL

Responses of municipal solid waste (MSW) landfills during earthquakes are gaining worldwide importance due to the devastating nature of earthquake on landfills. Apart from the post-earthquake safety and serviceability issues which pose environmental and public health problems, other important concerns are related to the behavior of closed landfills during and after earthquake. In present study, one dimensional (1-D) equivalent-linear analysis was carried out to model the behaviour of MSW landfills subjected to seismic base accelerations using the DEEPSOIL software. Influence of foundation types, height and stiffness of MSW landfills and seismic base accelerations on the seismic responses in terms of surface accelerations, normalized stresses (i.e., shear stress/effective vertical stress) and spectral amplification are evaluated. The results showed that height and stiffness of landfills, type of foundation and amount of seismic base acceleration and period play important role in evaluating the seismic responses of MSW landfills. Assumption of constant unit weight and shear wave velocity for landfills underestimates maximum horizontal acceleration (MHA), normalized shear stresses and spectral amplification at the top of landfills. Landfill models with smaller heights (up to 40 m high) showed higher amplification ratio for low seismic base accelerations with mean period near to that of soil and landfill resonance for all sites. A complex behavior was observed at higher seismic base accelerations due to non-linear behavior of landfill materials.     

顺层岩质边坡地震动力响应研究

地震作用下边坡的动力响应研究是边坡动力稳定分析的基础,利用FLAC3D有限差分软件建立一个顺层岩质边坡动力数值模拟模型,对其在竖向和水平向地震耦合作用下的动力响应全过程进行研究。研究表明,地震竖向和水平向耦合作用模拟比简单的模拟水平向振动更加接近实际情况,对岩土体的破坏更大;顺层岩质边坡在耦合地震作用下存在垂直放大和临空面放大作用;坡面水平向和竖向加速度均随高程增加呈增大趋势,在结构面处增大特别明显;竖向地震波产生的水平与竖向拉裂是触发斜坡体产生初期崩滑破坏的主控因素;边坡动力响应特征值的放大效应表明,其放大系数值从大到小依次是：竖向加速度＞水平加速度＞竖向速度＞水平速度;耦合地震波作用下,随着av /aH的增大,坡面监测各点横向位移基本呈增大趋势,说明竖向地震作用起了重要的破坏作用。     

Seismic bearing capacity of shallow strip footings

Seismic bearing capacity of shallow strip footings in soil has been obtained in the form of pseudo-static seismic bearing capacity factors N_cd, N_qd and N_d, denoting the cohesion, surcharge and unit weight components, respectively, by an extensive numerical iteration technique. Limit equilibrium method of analysis with composite failure surface is assumed. The validity of the principle of superposition is examined. Effects of both the horizontal and vertical seismic acceleration coefficients have been found to always reduce the ultimate bearing capacity significantly. Results obtained by the present method of analysis are compared with the available results and are found to be the least in the seismic case.     

Soil height randomness influence on seismic response: Case of an Algiers site

The paper deals with the effect of the depth to bedrock randomness on the seismic response of an Algiers site in time and frequency domains. Stochastic soil profile seismic analysis is carried out via Monte Carlo simulations coupled to the stiffness matrix method. The soil height is assumed to be a random variable with a log-normal distribution. The stochastic behavior of extreme ground acceleration and its response spectrum, transfer function, fundamental frequency, maximum amplitude, short- and mid-period amplification factors are derived from 1000 samples, as a parametric study is performed accounting for the influence of the coefficient of variation of the depth to bedrock. As the study herein considers a SH wave propagation pattern (SH stands for shear horizontal), the accelerations under study correspond to the E–W and N–S horizontal directions. The seismic acceleration corresponds to the Boumerdes earthquake (Algeria, May 21, 2003, M_w = 6.5). The probability density functions of the output parameters are derived using the maximum entropy principle, and compared to the log-normal distribution.The soil height heterogeneity causes an increase in the fundamental frequency of the soil profile, as well as a wider frequency content, in such a way that a larger number of structures are concerned by the resonance phenomenon.     

地震效应和坡顶超载对均质土坡稳定性影响的拟静力分析

基于强度折减技术和极限分析上限定理,假定机动容许的速度场破坏面,考虑坡顶超载、水平和竖向地震效应影响推导了边坡稳定性安全系数的计算表达式。采用序列二次规划迭代方法（和内点迭代方法）对边坡安全系数目标函数进行能量耗散最小化意义上的优化计算,与多个算例的对比验证了其方法和程序计算的正确性;对影响土质边坡动态稳定性的一些因素进行了参数分析,分析表明：随着边坡倾角?、坡顶超载q、水平和竖向地震效应影响系数的增大,边坡稳定性安全系数显著下降;随着坡顶超载q、水平地震效应影响系数kh的增大、竖向地震效应影响系数kv的减小,边坡的潜在滑动面越来越深,潜在破坏范围越来越大。竖向地震效应对边坡稳定性也有一定影响,强震条件下的设计计算必须考虑竖向地震效应的影响。     

Estimation of Pullout Capacity of Vertical Plate Anchors in Cohesionless Soil Using MARS

Vertical plate anchors provide an economical solution to safely resist the large horizontal forces experienced by the foundation of different structures such as bulkheads, sheet piles, retaining walls and so forth. This paper develops a multivariate adaptive regression spline (MARS) model-based approach for the determination of horizontal pullout capacity (P _u ) of vertical plate anchors buried in cohesionless soil by utilizing experimental results reported by different researchers. Based on the collection of forty different pullout experimental test results reported in the literature for anchors buried in loose to dense cohesionless soil with an embedment ratio ranges from 1 to 5, a predictive approach for P _u of vertical plate anchors has been developed in terms of non-dimensional pullout coefficient (M _γq ). The capability of the proposed MARS model for estimating the values of M _γq is examined by comparing the results obtained in the present study with those methods available in the literature. Using different statistical error measure criteria, this study indicates that the present approach is efficient in estimating the horizontal pullout capacity of vertical plate anchors as compared to other methods. The sensitivity analysis indicates that the embedment ratio (H/h, where H = embedment depth of anchor, and h = height of anchor) and internal friction angle (?) of soil mass are the two most important parameters for the evaluation of non-dimensional pullout coefficient (M _γq ) using the proposed MARS model.     

Three-dimensional numerical analysis of the keying of vertically installed plate anchors in clay

Plate anchors, such as suction embedded plate anchors and vertically driven plate anchors, offer economically attractive anchoring solutions for deep/ultra-deep water offshore developments. The rotation/keying processes of plate anchors will cause embedment losses, which lead to decreases of the uplift resistances of the anchors in normally consolidated soil. In the present paper, the keying processes of vertically installed strip and square plate anchors are simulated using the 3-D large deformation finite element method. The effects of loading eccentricity and pullout angle on the embedment loss during keying are investigated. Both the development of the uplift resistance and the soil flow mechanisms are presented. The numerical results show that the loading eccentricity e/B has a much larger effect on the embedment loss than the pullout angle does. The anchor shape has a minimal effect on the loss in anchor embedment. The shape factors (square/strip) are 1.05–1.09 for loss of embedment and 1.10–1.19 for capacity.     

Seismic Passive Earth Pressure Behind Non-vertical Retaining Wall Using Pseudo-dynamic Analysis

This paper shows a detailed study on the seismic passive earth pressure behind a non-vertical cantilever retaining wall using pseudo-dynamic analysis. A planar failure surface has been considered behind the retaining wall. The effects of soil friction angle, wall inclination, wall friction angle, horizontal and vertical earthquake acceleration on the passive earth pressure have been explored. Unlike the Mononobe–Okabe method, which incorporates pseudo-static analysis, the present analysis predicts a nonlinear variation of passive earth pressure along the wall. The results have been thoroughly compared with the existing values in the literature.     

Pseudo-dynamic approach of seismic active earth pressure behind retaining wall

Knowledge of seismic active earth pressure behind rigid retaining wall is very important in the design of retaining wall in earthquake prone region. Commonly used Mononobe-Okabe method considers pseudo-static approach, which gives the linear distribution of seismic earth pressure in an approximate way. In this paper, the pseudo-dynamic method is used to compute the distribution of seismic active earth pressure on a rigid retaining wall supporting cohesionless backfill in more realistic manner by considering time and phase difference within the backfill. Planar rupture surface is considered in the analysis. Effects of a wide range of parameters like wall friction angle, soil friction angle, shear wave velocity, primary wave velocity and horizontal and vertical seismic accelerations on seismic active earth pressure have been studied. Results are provided in tabular and graphical non-dimensional form with a comparison to pseudo-static method to highlight the realistic non-linearity of seismic active earth pressures distribution.     

桩板式抗滑挡墙地震响应的振动台试验研究

汶川地震路基震害调查表明,在顺层或堆积体边坡中的桩板式抗滑挡墙具有良好的抗震性能。为了更好地了解该结构的抗震性能和优化抗震设计方法,以大型振动台模型试验为手段对其进行研究。为明确地震作用下桩板式抗滑挡墙的地震响应特性,试验采用缩尺的卧龙台站实测地震波对模型激励。试验结果揭示了土压力沿桩身分布规律、桩体位移和边坡岩土体加速度的地震响应特征。研究表明,地震土压力沿桩身呈非线性分布,竖向地震荷载对水平加速度有放大效果。所以,双向加载时的地震土压力比水平单向加载时大,但二者差距在地震基本烈度VII、VIII度区域不显著。滑坡推力、滑床对桩的土体抗力和桩身位移均与输入地震动峰值加速度成正比,即随着地震动峰值加速度的增加,加速度放大比增大;滑动面材料剪切强度折减,滑坡推力、土体抗力和抗身位移均增大,且增大速率加快。此外,结合试验成果,建议了桩板式抗滑挡墙设计时地震综合影响系数Cz的合理取值,对应地震基本烈度VII、VIII、IX度区分别为0.2、0.35、0.4。试验结果有助于揭示该结构抗震机制,也为其抗震设计提供了可靠依据。