Stability of anchored sheet wall in cohesive‐frictional soils by FE limit analysis

This study extends the limit analysis techniques used for the computation of strict bounds of the load factors in solids to stability problems with interfaces, anchors and joints. The cases considered include the pull‐out capacity of multi‐belled anchors and the stability of retaining walls for multiple conditions at the anchor/soil and wall/soil interfaces. Three types of wall supports are examined: free standing wall, simply supported wall and anchored wall. The results obtained are compared against available experimental and numerical data. The conclusion drawn confirms the validity of numerical limit analysis for the computation of accurate bounds on limit loads and capturing failure modes of structures with multiple inclusions of complex interfaces and support conditions. Copyright © 2012 John Wiley & Sons, Ltd.     

UPPER BOUND SOLUTION FOR PULLOUT CAPACITY OF ANCHORS ON SANDY SLOPES

By making use of limit analysis, an upper bound solution in a closed form for determining the ultimate pullout capacity of plate anchors buried in sandy slopes has been established. The anchor plate orientation has been considered either horizontal or parallel to the slope, with the pullout force applied perpendicular to the plate. It has been found that the pullout capacity for horizontal anchors, even on slopes, remains the same as that on horizontal ground surface as long as the average embedment ratio is kept constant. Whereas for anchors which are aligned parallel to the slope the collapse load decreases continuously with the increase in the inclination of slope. © 1997 John Wiley & Sons, Ltd.     

A perturbation method for optimization of rigid block mechanisms in the kinematic method of limit analysis

Collapse mechanisms consisting of sliding rigid blocks are used widely as the basis for computing bounds on limit loads in geotechnical and structural engineering problems. While these mechanisms are conceptually straightforward to analyze, evaluating kinematically admissible velocities for a particular arrangement of blocks can be a tedious process, and optimizing the geometry of the mechanism is often prohibitively cumbersome for more than a few blocks. In this paper, we present a numerical technique for evaluating and optimizing mechanisms composed of an arbitrary number of sliding triangular blocks, assuming plane strain and homogenous, ponderable material obeying the Mohr–Coulomb yield condition. In the proposed method, coordinates defining the vertices of the blocks are treated as unknowns, and the optimal geometry is found by successively perturbing the vertex coordinates and block velocities, starting initially from a user-specified arrangement of blocks. The method is applied to three different examples related to geotechnical engineering, each of which illustrate that the approach is an efficient way to evaluate bounds that are often close to the true limit load.     

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.     

Limit analysis slope stability with nonlinear yield condition

Kinematic approach of limit analysis is applied to stability of an infinite, homogeneous, free-of-surcharge slope of soil with a nonlinear Mohr–Coulomb yield condition. On operating with a linear yield condition that exceeds the actual nonlinear condition, upper bounds to stability factors are constructed. The solutions overestimate by less than 1% the stability factors given by Zhang and Chen¹ for a nonlinear condition.     

软土中张紧式吸力锚破坏标准模型试验与有限元分析

为了确定软土中张紧式吸力锚的破坏标准,采用自主研发的电动伺服加载装置,在荷载和位移控制方式下进行了张紧式吸力锚在最佳系泊点受静荷载作用的承载力模型试验。结果表明：不同的破坏模式,锚破坏时对应的位移也不同。当锚为竖向破坏时,对应锚沿系泊方向的位移约为0.6倍的锚径;当锚为水平破坏时,对应锚沿系泊方向的位移约为0.3倍的锚径。同时,按照模型试验所得的破坏标准确定的吸力锚的极限承载力与极限分析法的预测结果吻合较好。对足尺锚进行了有限元分析,将分析结果与极限分析法的预测结果进行比较,验证了模型试验所得位移破坏标准的合理性。     

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.     

Probabilistic stability assessment using adaptive limit analysis and random fields

For deterministic scenarios, adaptive finite element limit analysis has been successfully employed to achieve tight bounds on the ultimate load of a geotechnical structure in a much more efficient manner than a dense uniform mesh. However, no probabilistic studies have so far considered finite element limit analysis with adaptive remeshing. Therefore, this research explores the benefits of combining adaptive mesh refinement with finite element limit analysis for probabilistic applications. The outcomes indicate that in order to achieve tight bounds on probabilistic results (such as the probability of failure), the ultimate load in each individual simulation (e.g. factor of safety or bearing capacity) has to be estimated with a very high level of accuracy and this can be achieved more economically using adaptive mesh refinement. The benefits, assessed here for undrained conditions, are expected to be much more pronounced in the case of frictional soils and complex geometries.     

Interaction Effect of Group of Helical Anchors in Cohesive Soil Using Finite Element Analysis

In this paper, the interaction effect of a group of two and four symmetrical as well as asymmetrical helical anchors resting in homogeneous cohesive soil deposit with different helix configurations is determined using finite element analysis. The anchors were pulled to its ultimate failure controlling the displacement. Eight different types of anchor configuration were considered in the analysis, where mainly the number of helical plates, the depth of upper- and lower-most helical plates and the ratio of spacing between the helical plates to the diameter of the plate were varied. The variation of load–displacement curve for each anchor in the group was obtained and subsequently, the ultimate uplift capacity of each anchor was determined. The soil was assumed to follow Mohr–Coulomb failure criteria. The present theoretical observations are generally found in good agreement with those theoretical and experimental results available in the literature for single isolated helical anchor.     

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.     

岩质高挖方边坡锚杆参数优化设计研究

针对某220 kV变电站岩质高挖方边坡,采用极限平衡法和数值分析法,设置不同锚杆打入角度和长度方案对边坡的稳定性进行了计算对比分析,优化了锚杆设计参数,评价了坡顶位移监测、深层水平位移监测和锚杆应力监测对锚杆加固效果。结果表明,（1）随着锚杆打入角度的增加,边坡安全系数先增大后减小,存在最优锚固角度,确定22°为最优锚固角度;（2）边坡下部锚杆受力大于上部锚杆受力,设计时应有重点考虑下部锚杆参数。当边坡安全系数不满足设计要求时,应适当增大下部锚杆截面尺寸或增加锚杆长度;（3）各排锚杆应进行不等长设计,锚杆长度通过极限平衡法量取潜在滑动面到坡面的距离进行确定和验算;（4）现场监测结果显示优化设计后的锚杆参数加固效果良好,经济效益可观。     

Numerical simulation of ground anchors

A procedure of finite-element modeling and beam-column modeling of ground anchors was proposed in this study to investigate the load transfer mechanism in ground anchors. The procedure included the modeling of soil, grout, and strand tendon and the interface modeling of soil–grout and grout–strand in ground anchors. A series of finite element analyses and beam-column analyses were performed using the proposed models on ground anchors. The numerical predictions were compared with observed measurements in a field load test. The results indicated that the numerical simulation of load transfer mechanism on ground anchors can provide reasonable predictions.     

Performance of D-bolts Under Static Loading

D-bolt is a type of energy-absorbing rock bolt. It is made of a smooth steel bar with anchors spaced along the bolt length. A typical section between adjacent anchors is approximately 1-m long, but it can be adjusted to adapt to the rock conditions. The bolt is fully encapsulated with either cement or resin grout in a borehole. The anchors are firmly fixed into the grout, while the smooth bolt sections can freely deform to absorb deformation energy. Full-scale static pull tests were carried out at different testing facilities in two laboratories. The tests show that a smooth bolt section between anchors may elongate by 110–167 mm depending on the section length. Field trials of the D-bolt were conducted in deep metal mines. The measurements showed that the D-bolts were equally loaded within every anchor-between section, avoiding load peaks and premature bolt failure due to stress concentrations caused by fracture/joint opening. The field trials of rebar and D-bolts in a largely deformed mine tunnel showed that the D-bolts behaved satisfactorily, with only a few failed bolts, while a number of the rebar bolts failed at the thread.     

Upper bound limit analysis using finite elements and linear programming

This paper describes a technique for computing rigorous upper bounds on limit loads under conditions of plane strain. The method assumes a perfectly plastic soil model, which is either purely cohesive or cohesive-frictional, and employs finite elements in conjunction with the upper bound theorem of classical plasticity theory. The computational procedure uses three-noded triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the grid. The finite element formulation of the upper bound theorem leads to a classical linear programming problem where the objective function, which is to be minimized, corresponds to the dissipated power and is expressed in terms of the velocities and plastic multiplier rates. The unknowns are subject to a set of linear constraints arising from the imposition of the flow rulé and velocity boundary conditions. It is shown that the upper bound optimization problem may be solved efficiently by applying an active set algorithm to the dual linear programming problem. Since the computed velocity field satisfies all the conditions of the upper bound theorem, the corresponding limit load is a strict upper bound on the true limit load. Other advantages include the ability to deal with complicated loading, complex geometry and a variety of boundary conditions. Several examples are given to illustrate the effectiveness of the procedure.     

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.     

均质黏土中圆形平板锚的抗拉承载力分析

基于网格重新生成和场变量映射的大变形有限元模型,探索了立即脱离和无脱离两种典型条件下均质黏土中圆形平板锚的抗拉承载力。与小变形有限元比较,大变形分析克服了锚周围土体初始网格畸变的不利影响,能够追踪平板锚整个拔出过程中抗拉力的变化。通过具体算例,考察平板锚表面摩擦性质和上覆土重等因素对立即脱离工况承载力的影响程度,指出有重土中深锚的承载力小于无重土中对应的承载力与上覆土重之和,其上限是无脱离条件下的承载力。计算结果表明：土重对无脱离条件下的承载力影响很小,进而给出了无脱离承载力系数与初始埋深的关系曲线。     

Numerical analysis of an experimental pipe buried in swelling soil

This paper investigates the pipe–soil interaction for pipes buried in expansive soil when subjected to swelling soil movement due to increase in moisture content. A laboratory experiment has been undertaken on a plastic pipe in a large-scale pipe box. A three dimensional numerical model is developed to analyse the pipe response, using FLAC^3D computer program. The pipe is assumed to behave as a linearly elastic material, while the soil is modelled as a nonlinear material with Mohr–Coulomb failure criterion. The water flow and soil/pipe deformations are decoupled, where water flow is calculated using simplified capillary rise theory on the basis of measurements made. A reasonably good agreement between the experimental results and model predictions is reported.     

Serviceability limit state design for uplift of helical anchors in clay

Presently, no displacement-based design methodology exists for helical anchors subjected to tensile or uplift loading. This study investigates the statistical and probabilistic aspects of the load-displacement uncertainty associated with a database of thirty-seven uplift loading tests of helical anchors founded within cohesive soils. Initially, an ultimate resistance model is identified, and the semi-empirical uplift breakout factor statistically characterized. A relationship between ultimate resistance and slope tangent capacity is established, and used to form the basis for normalizing the load-displacement response. Hyperbolic and power law models are statistically evaluated for use in serving as a reference load-displacement model; the hyperbolic curve was selected based on goodness-of-fit statistics. Monte Carlo reliability simulations are used to establish an equivalent-deterministic load factor that associates the selected load factor with a probability of exceeding a pre-determined allowable uplift displacement, given uncertainty in the undrained shear strength, ultimate resistance model, transformation uncertainty, uncertainty in the allowable displacement, and variability in uplift loading. A practical example is provided to show the intended use of this probabilistic helical anchor displacement model.     

Active and passive arching stresses in c′-ϕ′ soils: A sensitivity study using computational limit analysis

Vertical soil arching, commonly known as the “trapdoor mechanism,” is a pervasive phenomenon in various geotechnical applications that can be evaluated through a variety of analytical and numerical approaches, most of which exist due to a variety of proposed arching mechanisms, many of which are focused on either purely frictional or cohesive soils. This study investigates the realized arching mechanisms and associated loads for trapdoors under both active and passive arching conditions in c′-ϕ′ soils through a series of dimensionless charts using both upper and lower bound limit analyses. An associated sensitivity analysis demonstrates that arching loads are highly dependent on collapse mechanism, a function of not only geometry, but soil shear strength, with cohesion affecting the realized mechanism and arching loads.     

软岩地基中大直径布袋桩抗拔试验研究

西北地区深大基础工程日益增多,兼顾基础抗浮和耐久性问题的研究空白,借助西宁火车站综合改造工程,引入大直径布袋桩技术,有效解决了基础抗浮和耐久性问题;选择6根试桩进行了现场单桩抗拔载荷试验,最大加载量为9 060 kN;运用MATLAB软件分别拟合出3种抗拔极限承载力预测函数模型的曲线,同时运用PLAXIS软件对不同等级荷载桩-土位移进行模拟,并与实测的荷载-位移曲线对比分析。研究发现：双曲线和幂函数模型较适合此类抗拔桩极限承载力预测;本地区类似地基预测大直径缓变形抗拔桩极限荷载所需的极限位移标准应由0.030D减小为0.025D;仅根据土层的物理力学特征确定抗拔桩桩周土的极限摩阻力不够完善,至少还要考虑埋深不同对具有相似物理力学特征土层性质的影响。