Response of circular footings and anchor plates in non-homogeneous elastic soils

The axisymmetric elastic response of circular footings and anchor plates in a linearly non-homogeneous elastic soil is analysed. It is assumed that footings/anchors are flexible and subjected to axisymmetric vertical loads. The response of the footing/anchor is modelled by using the classical Poisson–Kirchhoff thin plate theory. A variational technique is used to analyse the interaction problem. A representation for the contact stress is established by using a fundamental solution corresponding to a unit vertical pressure acting over an annular region in the interior of the non-homogeneous soil. The fundamental solution can be derived by using rigorous analytical procedures. The influence of the footing flexibility and the degree of soil non-homogeneity on the displacements, bending moments and contact stresses of a surface footing is examined over a wide range of governing parameters. In the case of anchor plates the influence of depth of embedment, degree of soil non-homogeneity and anchor flexibility on the anchor displacement is investigated.     

A method of analysis for horizontally embedded anchors in an elastic soil

A general method is presented for the analysis of horizontally embedded anchors in an elastic soil. Provision is made in the analysis for the consideration of anchor shape, layer depth, anchor–soil interface condition, breakaway of the anchor from the underlying soil and interaction between groups of anchors. Application of the analytical technique is illustrated for strip and circular anchors, and these solutions are presented in the form of influence charts which may be used directly in hand calculations to predict the elastic load deflection behaviour, of anchor plates for a wide variety of material and geometric conditions.     

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.     

Break out resistance of inclined anchors in sand

Inclined anchors are widely used in a variety of civil engineering problems to resist oblique loads, most relevant being in transmission towers and in rocks and dams for structural strengthening. In the present study, the breakout resistance of the inclined anchors in sand has been worked out using limit equilibrium approach. The breakout resistance has been calculated for different soil friction angles with varying relative depth ratio and anchor inclination. The break out factor increases continuously with the inclination of the anchor. A comparison of predicted values of break out resistance of anchors by the proposed analysis with the experimental values as reported by the other researchers showed reasonably good agreement.     

A theoretical estimate of the tilt of a surface foundation due to an inclined anchor load applied at the interior of the soil medium

This paper examines the problem of the interaction between a loaded rigid circular foundation located at the surface of an isotropic elastic halfspace and an inclined concentrated anchor load which is located at a finite depth along the axis of symmetry. Such inclined loads can be induced by, for example, anchor regions supporting earth retaining structures. The loaded rigid circular foundation resting in smooth contact with the elastic soil mass experiences a displacement and a tilt due to the action of the inclined anchor load. The magnitude of the rotational settlement is evaluated in exact closed form.     

An approximate analysis procedure for piled raft foundations

A piled raft foundation comprises both piles and a pile cap that itself transmits load directly to the ground. The aim of such a foundation is to reduce the number of piles compared with a more conventional piled foundation where the bearing effect of the pile cap, or raft, is ignored. This paper describes a ‘hybrid’ approach for the analysis of piled raft foundations, based on a load transfer treatment of individual piles, together with elastic interaction between different piles and with the raft. The numerical analysis is used to evaluate a simple approximate method of estimating the overall response of the foundation from the response of the component parts. The method leads to estimates of the overall foundation stiffness, the proportion of load carried by the pile group and the raft, and an initial assessment of differential settlements. Parametric studies are presented showing the effect of factors such as raft stiffness and pile spacing, length and stiffness, and a worked example is included demonstrating the accuracy of the approximate design approach.     

基于最小势能原理的桩锚支护结构空间变形分析

以矩形基坑桩锚支护结构为研究对象,通过分析现场实测数据和数值分析结果,归纳出了冠梁和支护桩的空间变形模式,进而建立了整个支护系统的能量表达式。利用最小势能原理,推导了支护桩桩顶最大位移的解析解,并分析了各主要支护参数对该位移的影响。研究结果表明：桩顶最大位移随着坡顶超载和桩间距的增大而线性增大,但随着锚杆刚度的增大而减小;当基坑深度系数逐渐增大时,桩顶最大位移也逐渐增大,但趋势渐缓;基坑长度对桩顶最大位移的影响也较大,但当其超过临界长度后,桩顶最大位移逼近最大值;同样,锚杆安设也具有临界高度,当处于该位置时,桩顶最大位移达到最小值。最后,利用上述研究成果对广州太平广场花园基坑进行了验证,并与现场监测结果作了对比,计算结果能够满足工程要求。     

Numerical Study of Behavior of Circular Footing on Geogrid-Reinforced Sand Under Static and Dynamic Loading

A series of axi-symmetry models using finite element analyses were performed to investigate the behavior of circular footings over reinforced sand under static and dynamic loading. Geogrid was modeled as an elastic element and the soil was modeled using hardening soil model which use an elasto-plastic hyperbolic stress–strain relation. Several parameters including number of geogrid layers, depth to the first geogrid layer, spacing between layers and load amplitude of dynamic loading are selected in this paper to investigate the influence of these parameters on the performance of reinforced systems under both static and dynamic loads. The numerical studies demonstrated that the presence of geogrid in sand makes the relationship between contact pressure and settlement of reinforced system nearly linear until reaching the failure stage. The rate of footing settlement decreases as the number of loading cycles increases and the optimum values of the depth of first geogrid layer and spacing between layers is found 20% of the footing diameter. Some significant observations on the performance of footing-geogrid systems with change of the values of parametric study are presented in this paper.     

Soil–pipe interaction due to tunnelling: Assessment of Winkler modulus for underground pipelines

One of the key problems in the implementation of Winkler models to analyze tunnelling effects on existing pipelines lies in the assessment of subgrade modulus under external soil displacement. In this paper, an expression of the Winkler subgrade modulus for a pipeline buried at arbitrary depth and subjected to free soil displacement with arbitrary curve shape is given. Using superposition principle and the Fourier integral, the subgrade modulus of an infinite beam resting on the surface of an elastic half space and buried infinitely are obtained respectively. Then the influence of embedment depth is estimated based on Mindlin and Kelvin solution. The validity of the proposed subgrade modulus is verified by comparison with the results from an elastic continuum solution and two centrifuge model tests for the responses of buried pipeline due to nearby tunnelling. Thereafter, parametric studies are shown to assess the accuracy of the proposed subgrade modulus by comparing with an elastic continuum solution in homogeneous and non-homogeneous soil stratum and the amount of error is estimated.     

Settlement of inhomogeneous consolidating soils—II: The symmetrically loaded mass

We continue our study of the consolidation of inhomogeneous clay soils with an analysis of the response of a soil mass, whose shear modulus increases linearly with depth, to axially symmetric pressure on its surface. This extends the work reported in Part I on the corresponding one-dimensional problem of a clay column, and generalizes researches of Gibson and coworkers on the elastic model of the soil (i.e., the initial response). Because of great mathematical complexity when Poisson's ratio is allowed to assume arbitrary values, we have confined ourselves (as did Gibson in several of his papers) to variations of the modulus from a zero surface value, this being in reasonable accord with published test results on London clay. The deflection of points within this region, the deflection relative to the central one (that is, the shape of the deformed loading area), as well as the absolute deflection of surface points exterior to the load.     

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.     

斜坡浅埋水平条形锚板抗拔承载力的极限分析

针对山区和丘陵等复杂地形下浅埋锚板抗拔承载力计算问题,基于极限分析上限定理、非线性Mohr-Coulomb强度准则及其关联流动法则,构造了斜坡浅埋水平条形锚板的曲线型破裂机制和机动许可速度场,采用变分极值原理获得了其上方土体破裂面方程和抗拔承载力的上限解,分析了斜坡倾角和锚板埋深对锚板抗拔承载力的影响。结果表明:随着斜坡倾角的增大,锚板抗拔承载力逐渐减小,此时其上方两侧土体破裂面不再对称且整体向下坡侧偏移;锚板抗拔承载力及其上方两侧土体破裂面宽度均随着埋深增大而增加;锚板埋深越小,斜坡倾角对其抗拔承载力的影响越大,应在计算中予以考虑,以更合理地反映斜坡浅埋水平条形锚板的抗拔承载特性。     

Shape detection of multiple subsurface cavities by particle filtering with elastic wave propagation

A numerical technique for detecting the number and shape of subsurface cavities is presented, applying the particle filter and the parametric level set method to elastic wave propagation under the ground. When subsurface cavities exist, the elastic wave propagating in the ground is reflected at the boundary faces of the cavities. Observing the velocity of the reflection wave at the surface of a ground that includes multiple cavities and parameterizing the shape of the cavities by the parametric level function, both the number and the shape of the cavities can be identified by the particle filter. Numerical experimentation for detecting multiple cavities is conducted with synthetic observation data. The results show that the proposed technique enables the number of cavities to be identified by the number of peaks in the posterior probabilistic distribution function and solves geometric inverse problems by estimating the shape of the cavities through the parameter identification of the level set function.     

某基坑锚杆失效事故的原因分析

针对沿海软土地区一大型基坑中深达8.10 m的冷冻机房基础在基坑开挖过程中发生锚杆失效基坑坍塌事故,从挖土深度考虑不足、不良地质作用、锚杆施工间距超过设计要求、卸土放坡范围不足、锚杆抗拔承载力取值过高等5个方面进行了事故原因分析和模拟工况单元内力计算比较,指出了5大原因综合作用下增加的锚杆拉力设计值大大超过锚杆抗拔承载力而引发锚杆失效,基坑失稳破坏。     

Pseudostatic Seismic Response Analysis of a Pile Group in a Soil Slope

This paper presents a simple approximate pseudostatic method for estimating the maximum internal forces and horizontal displacements of a pile group located in a soil slope. The method is extension of an existing similar method developed by the authors for the case of a horizontal ground surface. The method employed for horizontal ground case involves two main steps: first, the free-field soil movements caused by the earthquake are computed; Then, the response of the pile group is analyzed based on the maximum free-field soil movements as static movements, as well as a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. This newly developed methodology takes into account the effects of group interaction and soil yielding. Simple modifications are applied to take into account the effect of slope on seismic deformations of the pile group, making use of the Newmark sliding block method. The applicability of the approach and the developed program is verified by comparisons made with both experimental shaking table tests and the results of a more refined analysis of a pile-supported wharf. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment and horizontal displacement for many practical cases, despite its relative simplicity. The simplifying assumptions and the limitations as well as reliability of the methodology are discussed, and some practical conclusions on the performance of the proposed approach are suggested.     

砂土中群锚锚周土体变形特性模型试验研究

群锚是常见的基础形式应用较为广泛,由于群锚之间的相互作用,群锚上拔过程中锚周土体的变形破坏机制比较复杂。采用非接触式数字图像相关方法（DIC）对群锚上拔过程开展模型试验研究,分析了群锚上拔过程中上拔力-位移关系曲线特征和锚周土体变形破坏机制。试验结果表明,密实度和埋深对群锚上拔力-位移关系曲线特征具有显著影响,在相同密实度、相同埋深率下浅埋与深埋群锚与同条件下的单锚具有相似的上拔力-位移关系曲线特征;群锚抗拔承载力具有明显的叠加效应,且砂土密实度、埋深和锚间距等参数因素对群锚效应具有显著影响。通过变形场的研究,得出了砂土密实度、埋深以及锚间距对群锚效应的影响规律。     

Modelling of the mechanical interaction between anchored wire meshes and granular soils

In this paper a theoretical and numerical analysis of the mechanical interaction between an anchored deformable facing structure and the underlying granular soil is presented. The reinforcement system is mainly composed of wire meshes, geosynthetics, bars/ties, and spike steel plates. This is usually employed for stabilising potentially unstable slopes. The punching process that can occur locally is described by considering the complex interaction mechanisms arising among the different system elements and the soil. For the sake of simplicity, the soil stratum and the anchor are assumed to be horizontal and vertical, respectively. A simplified displacement-based approach is introduced with the main goal of evaluating both the maximum force that can be applied on the anchor and the correlated penetration of the spike plate within the soil. The approach is validated by means of experimental laboratory test results already available in the literature. Finally, in order to stress the role of the spike plates' spacing and the soil stiffness in influencing the mechanical response of the system, the numerical results of parametric analyses are discussed.     

Modeling soil desiccation cracking by analytical and numerical approaches

An energy approach is proposed as a complement to the stress approach commonly considered for investigating soil desiccation cracking. The elastic strain energies before and after crack initiation are estimated by both numerical and analytical solutions. The energy released by cracking is then compared with the fracture energy to discuss crack initiation conditions. This leads to combined energy and stress conditions for crack initiation following Leguillon's theory. An approximate analytical solution is derived from a variational formulation of the porous elastic body equations. A cohesive zone model and finite element code are used to simulate crack propagation in an unsaturated porous body. This analysis shows that the energy criterion is reached before the stress criterion, and this can explain unstable crack propagation at the beginning. The approximate analytical solution allows predicting correctly the crack depth and opening in its initiation stage.     

Pseudostatic approach for seismic analysis of pile group

This paper evaluates a simple approximate pseudostatic method for estimating the maximum internal forces and horizontal displacements of pile group subjected to lateral seismic excitation. The method involves two main steps: (1) computation of the free-field soil movements caused by the earthquake, and (2) the analysis of the response of the pile group based on the maximum free-field soil movements (considered as static movements) as well as a static loading at the pile head, which depends on the computed spectral acceleration of the structure being supported. The methodology takes into account the effects of group interaction and soil yielding at pile–soil interface. The applicability of this approach has been validated by a similar approach for single piles and then verified by both experimental centrifuge models of pile-supported structures and field measurements of Ohba-Ohashi Bridge in Japan. It is demonstrated that the proposed method yields reasonable estimates of the pile maximum moment, shear, and horizontal displacement for many practical cases despite of its simplicity. Limitations and reliability of the methodology are discussed and some practical conclusions on the performance of the proposed approach are presented.     

Topography and volume effects on travel distance of surface failure

The authors investigated factors affecting the travel distance of a surface failure and developed a simple model for estimating the distance based on soil properties and topographic factor. The authors conducted field surveys and various soil tests for a number of surface failures that occurred during torrential rain at the end of August 1998 in southern Fukushima Prefecture, Japan. The authors studied the effects of various factors such as landslide volume, pore-water pressure, slope inclination, and the internal friction near the slip surfaces on the travel distances. The analyses showed no clear relationship between landslide volume and equivalent coefficient of friction, which was likely attributable to the very small range of volume compared to other studies on catastrophic landslides. The effect of excess pore-water pressure was likely negligible because undrained conditions were not to be maintained at the shallow flow depths. A positive correlation was shown between slope inclination and equivalent coefficient of friction. This correlation was attributable to two factors, one was positive correlation between the internal friction on the slip surface and slope inclination, and the other was the kinetic energy dissipation of moving mass that occurred at the inclination changing point between a slope and a sedimentary flat surface. The authors then developed a predictive model for critical flow inclination of landslide by installing the factors of soil properties and slope inclination factors. The model predicted equivalent coefficient of frictions, which were very similar to the observed values, thus verifying the effectiveness of the model.