Three-dimensional analysis of vertical square anchor plate in cohesionless soil

ABSTRACT

Vertical anchor plates are often provided to increase the performance of various geotechnical engineering structures such as sheet pile walls, bulkheads, bridge abutments and offshore structures. Hence, the safe design of such structures needs a better understanding of the 3D behaviour of the anchor plate. This paper presents and discusses the results obtained from a series of 3D finite-difference analyses of vertical square anchor plate embedded in cohesionless soil. The 3D model is found to closely predict experimental pullout load–displacement relationship. The failure mechanism observed in the numerical model is found to be very similar to the failure reported in experimental studies. For a given embedment depth, the stiffness of the breakout factor–displacement response substantially reduces with increase in anchor plate size. However, the ultimate reduction in anchor capacity is found to approximately 8% with an increase in anchor size from 0.1 to 1 m. Numerical analysis reveals that at deeper embedment depth, the friction angle of sand is the critical parameter in enhancing the performance of anchor plate. The obtained 3D model results are then compared with the published results and are found to be reasonably in good agreement with each other.     

土工格栅加筋砂土中水平锚板抗拔特性试验研究

土工格栅加筋能够有效改善锚板的抗拔承载力,然而锚板在上拔过程中的破坏机制及其影响因素尚需进一步研究。针对砂土中水平锚板的抗拔特性,开展了多组锚板上拔试验,分析了砂土密实度、锚板埋深、土工格栅布设层数和位置等因素的影响,结合粒子图像测速（particle image velocimetry,简称PIV）技术探究了锚板周边土体的变形破坏机制。研究结果表明：单层接触式格栅加筋对锚板的抗拔承载力有明显的提升,且其对土体性能的改善优于非接触式格栅加筋情况,其原因与土工格栅变形量和上覆土体重力有关;当采用双层土工格栅加筋时,下层格栅可充分发挥限制土体侧向变形和均化应力分布的作用,上层格栅相对而言贡献不大;采用土工格栅加筋后,锚-土界面附近土体的变形模式发生了明显的变化,其破坏面相比未加筋前向内侧收敛,且剪应变分布更为均匀。     

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.     

非均质地基浅埋水平条形锚板承载力上限分析

考虑地基土体的非均质特性,采用非线性Mohr-Coulomb强度准则及其关联流动法则构造了浅埋水平条形锚板的曲线型破裂机制与机动许可速度场,根据极限分析上限定理推导了条形锚板抗拔承载力的表达式。利用变分极值原理求得了锚板抗拔承载力及其上方土体破裂面的上限解,分析了锚板埋深、土体非均质和非线性强度特性对锚板抗拔承载特性的影响,并将该上限解与已有计算方法进行了对比。结果表明:锚板埋深、土体非均质和非线性强度特性对其抗拔承载力与破裂面特征具有明显的影响。锚板埋深和土体非均质系数越大以及土体非线性强度系数越小,锚板抗拔承载力和土体破裂面深度、宽度均是越大。该上限解与极限平衡和极限分析有限元方法的计算结果基本一致,验证了所采用的曲线型破裂机制和地基非均质变化规律有效性,为条形锚板设计提供了一定的参考。     

Three-dimensional numerical and analytical study of horizontal group of square anchor plates in sand

In this paper, numerical and analytical methods are used to evaluate the ultimate pullout capacity of a group of square anchor plates in row or square configurations, installed horizontally in dense sand. The elasto-plastic numerical study of square anchor plates is carried out using three-dimensional finite element analysis. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion. An analytical method based on a simplified three-dimensional failure mechanism is developed in this study. The interference effect is evaluated by group efficiency η, defined as the ratio of the ultimate pullout capacity of group of N anchor plates to that of a single isolated plate multiplied by number of plates. The variation of the group efficiency η was computed with respect to change in the spacing between plates. Results of the analyses show that the spacing between the plates, the internal friction angle of soil and the installation depth are the most important parameters influencing the group efficiency. New equations are developed in this study to evaluate the group efficiency of square anchor plates embedded horizontally in sand at shallow depth (H = 4B). The results obtained by numerical and analytical solutions are in excellent agreement.     

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。     

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.     

非完全粗糙平板锚旋转安装过程中的丢失埋深研究

吸力贯入平板锚被用于系泊深海浮式结构,实际应用中必须预估平板锚旋转安装过程中的丢失埋深。采用大变形有限元方法探索非完全粗糙平板锚在正常固结黏土中的旋转过程。大变形有限元法通过网格重剖避免平板锚大幅值平动和转动引起的土体单元扭曲。根据平板锚旋转到达的埋深,实时更新“锚-土”界面上的摩擦剪切强度。将数值模拟结果与离心机模型试验进行对比验证,表明高岭土中平板锚表面的粗糙系数约为0.3。平板锚丢失埋深随粗糙系数的减小而增大,但粗糙系数对丢失埋深的影响受平板锚厚度比和拉力偏心比的耦合作用。厚度比和偏心比越小,粗糙系数对丢失埋深的影响越显著。     

Effect of shape on holding capacity of plate anchors buried in soft soil

Plate anchor is one of the most common varieties of anchors used in the construction and maintenance work of various on-land and offshore structures. An accurate estimation of the uplift capacity of anchor foundations is necessary for an economical design as well as for the safety and stability of structures. This paper outlines the effect of shape of anchor plates on their breakout capacity, through a series of model tests. Both shallow and deep anchor behaviours were investigated under conditions developing suction force and without suction force. The results of these tests are presented in terms of load-displacement behaviour, variation of breakout factors (with and without suction force) with depth of embedment, the critical embedment depth of anchors and variation of suction force with embedment ratio. Further, the variations of breakout factor ratio with aspect ratio and embedment ratio are reported. Based on the experimental results and the model test results of other investigators an empirical relationship has been suggested to determine the shape factor and holding capacity of plate anchors buried in saturated cohesive soils.     

浅埋平板圆锚竖向拉拔极限承载力计算方法

采用自制可视化试验装置开展了平板圆锚的拉拔模型试验,基于数字照相测量技术对极限拉拔下锚周土体的位移变形场进行了量化分析。在本次试验的埋深比范围内,极限承载力随埋深比增加而非线性增大,但增长速率逐渐减缓;观测到的锚周土体滑动面与地面、锚板所围区域整体呈现出“底大、顶小、径长”的倒喇叭形状;滑动面可用两条直线段来近似描述;极限拉拔力学模型由一个截面直径上小下大的倒圆台和一个等截面圆柱体组成。根据极限平衡条件推导建立了砂土中浅埋平板圆锚竖向拉拔极限承载力的计算方法,该方法对4组试验数据的计算较其他4种方法与试验实测值更为接近,且离散性更小,效果较好。     

Uplift response of symmetrical anchor plates in reinforced cohesionless soil

The uplift response of symmetrical anchor plates with and without geogrid reinforcement layers has been evaluated in model tests and numerical simulations using PLAXIS. Many parameters of the reinforcement layers were used to reinforce the sandy soil over circular, square, and rectangular symmetrical anchor plates of various sizes. In the current research, different parameters, such as relative density of sand and embedment ratios, in conjunction with geogrid reinforcement layer parameters including size, number of layers, and the proximity of the layer to the circular anchor plate, were investigated in a scale model. The failure mechanism and the associated rupture surface were observed and evaluated. Test results showed that using geogrid reinforcement layers significantly improves the uplift capacity of symmetrical anchor plates. It was found that inclusion of one geogrid layer resting directly on top of the symmetrical anchor plate was more effective in enhancing the symmetrical anchor capacity than the layer itself. It was also found that the inclusion of one geogrid layer on the symmetrical anchor plate improved the uplift capacity more than the same symmetrical anchor plate embedded without a reinforcement layer. The single geogrid layer was also more effective in enhancing the uplift capacity compared to the multiple geogrid layer reinforcement approach. In general, the results show that the uplift capacity of symmetrical anchor plates in loose and dense sand can be significantly increased by the inclusion of geogrid layers. It was also observed that the inclusion of geogrid layers reduces the requirement for a higher L/D ratio to achieve the required uplift capacity. The results of the laboratory and numerical analysis are found to be in agreement in terms of the breakout factor and failure mechanism pattern.     

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 state boundary surface model for improving the dilatancy simulation of granular material in reinforced anchors

It is acknowledged that for extending the experimental results to real scale design, it is necessary to use an appropriate numerical analysis. The good analysis in geotechnical problems needs to adopt a suitable constitutive model for the materials. This paper presents a modeling approach to investigate the complex behavior of granular trench and reinforcement system. For this purpose, an experimental and numerical investigation has been carried out on the behavior of pullout resistance of an embedded anchor (circular plate) with and without geogrid reinforcement layers in stabilized loose and dense sand using a granular trench. Different parameters have been considered, such as number of geogrid layers, embedment ratios, relative density of soil, and height ratios of granular trench. Finite element analysis with Hardening Soil Model was utilized for sand and CANAsand constitutive model was used for granular trench to investigate failure mechanism and the associated rupture surfaces. Results showed that, when soil was improved with the granular-geogrid trench, the uplift force significantly increased, but in geogrid-reinforced granular trench condition, the ultimate pullout resistance at failure increased as the number of geogrid layers increased up to the third layer, the fifth layer had a negligible effect in comparison with the third layer of reinforcement. The ultimate uplift capacity of anchor plate and the variation of surface deformation for all the tests indicated a close agreement between the experimental and numerical models.     

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.     

基于Hoek-Brown破坏准则的浅埋条形锚板抗拔力上限分析

现有的锚板极限承载力研究大多是采用线性或非线性Mohr-Coulomb破坏准则在砂质地基中进行的,然而Mohr-Coulomb破坏准则并不适合分析岩质地基中的抗拔结构。采用Hoek-Brown破坏准则构建了一个曲线型的破坏机制,根据极限分析上限定理求出了条形锚板抗拔力的表达式。通过变分计算,得到了极限状态下条形锚板的抗拔力和岩体破裂面的上限解。为了证明所采用方法的有效性,当材料参数B =1时,采用与Mohr-Coulomb破坏准则等效的土体参数,计算了曲线型破坏机制下条形锚板的极限抗拔力,并与已有计算结果进行了比较。结果表明,采用曲线型破坏机制得到的锚板极限抗拔力与直线型多块体破坏机制的结果基本一致,证明了所采用的曲线形破坏机制是正确的。参数研究表明：在其他参数不变的情况下,锚板极限抗拔力和破坏面都随岩体参数B的增大而减小。     

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.     

The axial loading of a rigid circular anchor plate embedded in an elastic half-space

The present paper examines the axisymmetric problem related to the loading of a rigid circular anchor plate which is embedded in bonded contact with an isotropic elastic half-space. A Hankel transform development of the governing equations is used to reduce the associated mixed boundary value problem to a set of coupled Fredholm integral equations of the second kind. These equatons are solved in a numerical fashion to generate results of engineering interest. In particular, the results indicate the influence of the depth of embedment on the axial stiffness of the rigid anchor plate.     

基于统一强度理论的锚杆挡土墙可靠度分析

将基于统一强度理论的岩土材料参数c、φ值引入到锚杆的抗拔力及规范推荐的粘性土广义库伦土压力中,以此建立锚杆挡土墙的功能函数。考虑岩土参数全部为正态分布与对数正态分布的两种情况,分别采用设计验算点法和JC法对一工程实例编制了考虑中主应力影响的可靠度计算程序。计算结果表明:锚杆挡土墙的可靠指标随中主应力影响系数b的增大而增大,且参数变异系数越小,增量越大;参数为对数正态分布的可靠指标比参数为正态分布时大,且两者的差量随b的增大而增大。     

砂土中扩体锚杆承载特性模型试验研究

在25个室内模型试验基础上,研究了均质砂土中竖向拉拔扩体锚杆的几何尺寸及埋深对其承载特性的影响。试验结果表明,根据深径比的不同,扩体锚杆可以分为浅埋与深埋扩体锚杆2种形式,它们在拉拔过程中均经历了土体弹性变形阶段、非扩体锚固段-土界面剪切破坏阶段、土体弹塑性变形阶段以及剪切破坏阶段,破坏特征分别表现为整体剪切破坏与局部剪切破坏。通过扩体锚杆与普通拉力型锚杆模型试验对比发现：与普通拉力型锚杆相比,扩体锚杆极限承载力、承载比与安全性均有大幅度提高。而通过增大扩体锚固段直径的方式提高扩体锚杆承载力的优势较为明显。此外,根据承载比分析,扩体锚杆存在最优扩体锚固段直径,因此,在实际工程中应寻找一个满足需要的最优扩体锚固段尺寸以取得较好的经济效益。     

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.