Seismic vertical uplift capacity of horizontal strip anchors using pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis to determine the seismic vertical uplift capacity of a horizontal strip anchor using upper bound limit analysis. However, in the literature, the pseudo-static approach was used by few researchers to compute the seismic vertical pullout resistance, where the real dynamic nature of earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of uplift factor f_γE are determined for different magnitudes of soil friction angle, soil amplification, embedment ratio and seismic acceleration coefficients both in the horizontal and vertical directions. It is observed that the uplift factor f_γE decreases significantly with the increase in seismic accelerations and amplification but increases with the increase in embedment ratio. The results are compared with the existing values in the literature and the significance of the present methodology for designing the horizontal strip anchor is discussed. In presence of vertical earthquake acceleration and amplification of vibration, the present values of f_γE compare reasonably well with the existing pseudo-static values obtained by modifying the horizontal acceleration coefficient.     

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.     

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.     

Uplift Capacity of Horizontal Strip Anchors in Cohesionless Soil

This paper presents the details of the theoretical analysis of net uplift capacity of horizontal strip anchor in cohesionless soil using Kötter’s equation. A plane failure surface inclined at a characteristic angle with the ground surface is assumed. Results obtained using the proposed method are compared with the available experimental results of 30 cases for dense to loose cohesionless soil, with the maximum embedment ratio of 8. It is observed that the proposed method leads to the predictions of net uplift capacity of horizontal strip anchor that are very close to the experimental results in 93% cases. The comparison of results with available theoretical solutions shows that, proposed method makes better predictions for anchor embedment ratio less than 8 in dense cohesionless soils.     

Seismic Bearing Capacity of Shallow Strip Footing with Coulomb Failure Mechanism using Limit Equilibrium Method

In this paper, an effort is made to evaluate the seismic bearing capacity of shallow strip footing resting on c–ф soil. The formulation is developed to get a single coefficient of bearing capacity for simultaneous resistance of weight, surcharge and cohesion. Limit equilibrium method in Pseudo-static approach with Coulomb mechanism is applied here to evaluate the seismic bearing capacity. The seismic bearing capacity of footing (q_uE) is expressed in terms of single coefficient N_γE. The effect of various parameters viz. angle of internal friction of soil (ф), angle of wall friction (δ), cohesion (c), ratio of depth to width of footing (d_f/B₀), seismic acceleration (k_h, k_v) are studied on the variation of seismic bearing capacity co-efficients.     

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.     

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.     

基于上限法的条形锚板抗拔承载力分析

以极限分析上限理论为基础,利用旋转块体集的组合来构造条形锚板的运动许可速度场。分析了不排水黏土中深埋和浅埋条形锚板的抗拔承载力上限解,研究了锚板在不同埋置倾角和深度条件下的抗拔承载力和破坏面的特性,并将计算结果与已有计算方法进行了对比。分析结果表明：在不排水黏土中深埋条形锚板抗拔承载力与锚板的埋置方位和锚板的粗糙度无关,但完全光滑条件下破坏面扇圆部分的半径只有完全粗糙条件下的一半;在考虑无重土情况下浅埋条形锚板的抗拔承载力系数随锚板埋深比的增大而增大,破坏面也随埋深比的增加而逐渐扩大。所得上限解与已有文献解答较为吻合,而且求解所得破坏面更为直观,能为工程设计提供参考依据。     

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.     

Numerical Investigation of the Inclined Pullout Behavior of Anchors Embedded in Clay

Two-dimensional plane strain finite element analysis has been used to simulate the inclined pullout behavior of strip anchors embedded in cohesive soil. Previous studies by other researchers were mainly concerned with plate anchors subjected to loads perpendicular to their longest axis and applied through the centre of mass. This paper investigates the behavior of vertical anchors subjected to pullout forces applied at various inclinations with respect to the longest anchor axis, and applied at the anchor top and through the centre of mass. The effects on the pullout behavior of embedment depth, overburden pressure, soil–anchor interface strength, anchor thickness, rate of clay strength increase, anchor inclination, load inclination and soil disturbance due to anchor installation were all studied. Anchor capacity is shown to increase with load inclination angle for anchors loaded through the centre of mass; greater effects are found for higher embedments. The results also show that anchor capacity improves at a decreasing rate with higher rates of increase of soil shear strength with depth. In addition, the capacity of vertically loaded anchors is shown to approximately double when the soil–anchor interface condition changes from fully separated to fully bonded. Similarly, disturbed clay strengths adjacent to the anchor following installation cause a significant reduction in anchor capacity. The results showed a significant effect of the point of load application for anchors inclined and normally loaded. The effects of other parameters, such as anchor thickness, were found to be less significant.     

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.     

Vertical Uplift Capacity of Equally Spaced Multiple Strip Anchors in Sand

The ultimate uplift resistance of a group of multiple strip anchors placed in sand and subjected to equal magnitudes of vertical upward pullout loads has been determined by means of model experiments. Instead of using a number of anchor plates in the experiments, a single anchor plate was used by simulating the boundary conditions along the planes of symmetry on both the sides of the anchor plate. The effect of clear spacing (s) between the anchors, for different combinations of embedment ratio (λ) of anchors and friction angle (ϕ) of soil mass, was examined in detail. The results were presented in terms of a non-dimensional efficiency factor (ξ_γ), which was defined as the ratio of the failure load for an intervening strip anchor of a given width (B) to that of a single strip anchor plate having the same width. It was clearly noted that the magnitude of ξ_γ reduces quite extensively with a decrease in the spacing between the anchors. The magnitude of ξ_γ for a given s/B was found to vary only marginally with respect to changes in λ and ϕ. The experimental results presented in this study compare reasonably well with the theoretical and experimental data available in literature.     

Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis

The vertical uplift resistance of two interfering rigid rough strip anchors embedded horizontally in sand at shallow depths has been examined. The analysis is performed by using an upper bound theorem of limit analysis in combination with finite elements and linear programming. It is specified that both the anchors are loaded to failure simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the anchors, the magnitude of the efficiency factor (ξ_γ) is determined. On account of interference, the magnitude of ξ_γ is found to reduce continuously with a decrease in the spacing between the anchors. The results from the numerical analysis were found to compare reasonably well with the available theoretical data from the literature.     

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.     

Horizontal Pullout Resistance for a Group of Two Vertical Plate Anchors in Clays

The horizontal pullout capacity of a group of two rigid strip plate anchors embedded along the same vertical plane in clays, under undrained condition, has been determined. An increase of cohesion with depth has also been incorporated. The analysis has been performed by using an upper bound finite element limit analysis in combination with linear optimization. For different clear spacing (S) between the anchors, the efficiency factor (η_cγ) has been determined to evaluate the group failure load for different values of (1) embedment ratio (H/B), (2) the normalized rate (m) which accounts for a linear increase of cohesion with depth, and (3) normalized unit weight (γH/c_o). The magnitude of the group failure load (1) becomes maximum corresponding to a certain spacing (S_cr) between the anchors, and (2) increases with an increase in the γH/c_o up to a certain value before attaining a certain maximum magnitude. The value of S_cr/B has been found to vary generally between 0.7 and 1.2. The maximum magnitude of η_cγ, associated with the critical spacing, (1) increases generally with increases in H/B, and (2) decreases with an increase in m. For a greater spacing between the anchors, the analysis reveals the development of a local shear zone around the lower anchor plate. The numerical results developed are expected to be useful for purpose of design.     

Seismic active earth pressure on walls with bilinear backface using pseudo-dynamic approach

This paper presents a study on the seismic active earth pressure behind a rigid cantilever retaining wall with bilinear backface using pseudo-dynamic approach. The wall has sudden change in inclination along its depth and a planar failure surface has been considered behind the retaining wall. The effects of a wide range of parameters like soil friction angle, wall inclination, wall friction angle, amplification of vibration, variation of shear modulus, and horizontal and vertical seismic accelerations on the active earth pressure have been explored in the present study. Unlike the Mononobe-Okabe method, which incorporates pseudo-static analysis, the present analysis predicts a nonlinear variation of active earth pressure along the wall. The results have been compared with the existing values in the literature.     

锚板在正常固结黏土中的承载力

在岩土工程中,锚板通常被用来提供竖直或水平抗拔力,比如发射塔的基础、板桩墙结构和悬浮式海洋平台的基础。采用弹-塑性有限元方法对正常固结不排水黏土中的条形锚板进行数值分析,以图表形式给出了不同埋深率、不同上拔倾角、不同锚-土黏结形式下条形锚板的承载力系数和周围土体的流动机构,分析了土体自重对锚板承载力的影响,并给出了不同情况下锚板的极限承载力系数。采用基于重新划分网格并插值状态变量的大变形分析方法（RITSS）,分析了正常固结黏土中锚板在连续拔出过程中的承载力变化以及土重对锚-土分离模式的影响。     

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-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.     

Pseudo-dynamic methods for seismic passive earth pressure behind a cantilever retaining wall with inclined backfill

The designing of retaining walls requires the complete knowledge of earth pressure distribution. Under earthquake conditions the design needs special attention to reduce the devastating effect, but under seismic conditions, the available literature mostly uses the pseudo-static analytical solution as an approximate to the real dynamic nature of the complex problem. This paper shows a detailed study on the seismic passive earth thrust behind a cantilever retaining wall with inclined backfill surface by pseudo-dynamic analysis. A planar failure surface has been considered. The effect of variation of parameters such as soil friction angle, wall friction angle and back fill inclination have been explored. A complete analysis shows that the time dependent non-linear behaviour of the pressure distribution obtained in the present method results in more realistic design values of earth pressures under earthquake conditions. Results are provided in tabular and graphical non-dimensional form and compared thoroughly with the existing values in the literature.