非均质地基承载力及破坏模式的FLAC数值分析

利用基于Lagrangian显式差分的FLAC算法，通过数值计算，对黏结力随深度线性增长的非均质地基上条形基础和圆形基础的极限承载力及地基破坏模式进行了对比计算与系统分析。研究表明：（1）随着地基黏结力沿深度非均匀变化系数的增大，地基的破坏范围逐渐集中在地基表层和基础两侧：（2）即使地基的非均质程度较小，当将非均质地基近似地按均质地基考虑时，由此所估算的承载力可能过于保守；（3）地基承载力系数随黏结力沿深度非均匀变化系数的增大而非线性地增大。与数值解相比，skempton与Peck等近似公式均可能高估了非均质地基承载力。     

Bearing capacity of ring footings on cohesionless soil under eccentric load

This paper presents a study on the bearing capacity of eccentrically-loaded rough ring footings resting over cohesionless soil. To this aim, a series of 3D numerical simulations were performed using the finite difference method. In order to consider the effect of load eccentricity, reduction factor method is applied. In this method, the ratio of an eccentrically-loaded bearing capacity to the bearing capacity of the same footing under vertical load is defined. Comparison between the results of the numerical simulations with those of analytical solutions and experimental data indicates good agreement. A mathematical expression is also introduced for eccentrically-loaded ring footings.     

Bearing Capacity of Strip Footings Near Slopes

In the last decades a great attention was given by many authors to the evaluation of the static and seismic bearing capacity of footings near slopes. In this paper a model has been developed based on the limit equilibrium method, considering a circular surface propagates towards the slope until the sloping ground is reached. The bearing capacity is investigated considering either the distance of the footing from the edge of the slope and/or the effect of the footing embedment. A validation of the proposed model was made by a comparison with solutions taken from literature regarding the evaluation of the bearing capacity for a footing adjacent to a slope and for an inclined load. The loading conditions consist in vertical and horizontal stress on the footing and on the soil below the footing. Both the inertial and kinematic effects of the seismic loading have been analyzed, and a simple equation has been derived for the evaluation of the seismic bearing capacity. The static and seismic bearing capacity has been investigated as a function of the soil friction angle, of the seismic coefficient, of the sloping ground. Finally, the influence of the distance of the footing from the edge of the slope was taken into consideration in the evaluation of the bearing capacity, and a threshold distance at which the reduction of the bearing capacity due to the sloping ground vanishes has been defined.     

Drained bearing response of shallow foundations on structured soils

This paper examines the drained bearing response of circular footings resting on structured soil deposits. Numerical simulations have been carried out using a finite element formulation of the Structured Cam Clay model. A parametric study was conducted by varying the parameters that govern the behaviour of structured soils and guidelines are given for designers to identify when effects of the soil structure are important. Under fully drained conditions, deformation within the structured soil supporting the footing usually occurs as a local or punching shear failure due to high compressibility of the structured soil and the mobilised bearing pressure increases with the footing movement, without reaching an ultimate value. A novel approximate method is presented to obtain the load–displacement response of a rigid circular footing resting on the surface of a structured soil deposit. This requires the properties of the soil in the reconstituted state and two additional parameters, which govern the natural structure of the soil. The proposed method has been applied to a published case study, where plate load test results are given for rigid circular steel plates resting on structured soil deposits. Fair agreement is observed between the computed and experimental results, suggesting the approximate method may be useful in design studies of foundations on structured soil deposits.     

Interference of Multiple Strip Footings on Sand Using Small Scale Model Tests

By using small scale model tests, the interference effect on the vertical load-deformation behavior of a number of equally spaced strip footings, placed on the surface of dry sand, was investigated. At any stage, all the footings were assumed to (i) carry exactly equal magnitude of load, and (ii) settle to the same extent. No tilt of the footing was permitted. The effect of clear spacing (s) among footings on the results was explored. A new experimental setup was proposed in which only one footing needs to be employed rather than a number of footings. The bearing capacity increases continuously with decrease in spacing among the footings. The interference effect becomes further prominent with increase in soil friction angle. In contrast to an increase in the bearing capacity, with decrease in spacing of footings, an increase in the footing settlement associated with the ultimate state of shear failure was observed. The present experimental observations were similar to those predicted by the available theory, based on the method of characteristics. As compared to the theory, the present experimental data, however, indicates much greater effect of interference especially for larger spacing among footings.     

Bearing capacity of strip and circular footings in sand using finite elements

Design of shallow foundations relies on bearing capacity values calculated using procedures that are based in part on solutions obtained using the method of characteristics, which assumes a soil following an associated flow rule. In this paper, we use the finite element method to determine the vertical bearing capacity of strip and circular footings resting on a sand layer. Analyses were performed using an elastic–perfectly plastic Mohr–Coulomb constitutive model. To investigate the effect of dilatancy angle on the footing bearing capacity, two series of analyses were performed, one using an associated flow rule and one using a non-associated flow rule. The study focuses on the values of the bearing capacity factors N_q and N_γ and of the shape factors s_q and s_γ for circular footings. Relationships for these factors that are valid for realistic pairs of friction angle and dilatancy angle values are also proposed.     

Bearing capacity of two close strip footings on soft clay reinforced with geotextile

For many years ago, the beneficial effects of using reinforcement to improve the property of soil have been demonstrated. Over the last three decades, the use of polymeric reinforcement such as geotextile has increased in geotechnical engineering. Among the possible applications, earth reinforcement techniques have become useful and economical techniques to solve many problems in geotechnical engineering practice, such as improve the bearing capacity and settlement characteristics of the footing. This research presents the effect of geotextile inclusion on the bearing capacity of two close strip footings located at the surface of soft clay. A broad series of finite element analysis were performed on two footings with width of 1 and 2 m using two-dimensional plane strain model using the computer code Plaxis (ver 8). Only one type of soft clay was used for the analysis, and the soil was represented by two yielding criteria including hardening soil model and Mohr–Coulomb model, while reinforcement was represented by elastic element, and at the interface between the reinforcements and soft clay, interface elements have been used. A wide range of boundary conditions, including unreinforced and reinforced cases, was analyzed by varying parameters such as number of geotextile layers, vertical spacing of layers, depth to topmost layer of geotextile, tensile stiffness of geotextile layers, and distance of between two footings. From numerical results, the bearing capacity ratio and the interference factor of the foundations have been estimated. On the basis of the analysis performed in this research, it can be concluded that there is a best distance between footings and optimum depth for topmost layer to achieve maximum bearing capacity for closely spaced strip footings. The bearing capacity was also found to increase with increasing number of reinforcement layers if the reinforcements were placed within a range of effective depths. In addition, the analysis indicated that increasing reinforcement stiffness beyond a threshold value does not result in a further increase in the bearing capacity.     

圆形基础地基极限承载力计算

利用临界滑动场法计算了浅埋圆形基础的地基承载力,并提供了系数N、Nq和Nc的计算表格和曲线,同时分析了侧面土压力对N、Nq的影响。通过建立土体条块极限平衡方程,推导了计算地基承载力的递推关系式。首先,设定土体计算范围,并划分条块和设置状态点; 其次,根据递推公式和推力极值原理计算各个状态点的参数,并搜索临界滑面; 最后,根据搜索出的临界滑面计算地基承载力。通过与已有系数计算值或模型试验的比较,验证了该方法的合理性。研究结果表明:N、Nq和Nc与其他学者的计算值相近; 相同情况下侧面土压力越大系数N、Nq越小。该方法是临界滑动场法在地基承载力研究中的推广应用,原理简单、易于编程,可为深入研究圆形基础地基承载力的计算提供参考。     

Numerical study of the bearing capacity for two interfering strip footings on sands

Current studies of bearing capacity for shallow foundations tend to rely on the hypothesis of an isolated footing. In practice a footing is never isolated; it is mostly in interaction with other footings. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua (FLAC), to evaluate the bearing capacity for two interfering strip footings, subjected to centered vertical loads with smooth and rough interfaces. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion and associative flow rule. The interference effect is estimated by efficiency factors, defined as the ratio of the bearing capacity for a single footing in the presence of the other footing to that of the single isolated footing. The efficiency factors have been computed individually to estimate the effects of cohesion, surcharge, and soil weight using Terzaghi’s equation, both in a frictional soil with surcharge pressures and in a cohesive-frictional soil with surcharge pressures. The results have been compared with those available in the literature.     

Bearing Capacity of Shallow Foundation on Two Clay Layers by Numerical Approach

Natural soils are often deposited in layers. The estimation of the bearing capacity of the soil, using conventional bearing capacity theory based on the properties of the top layer, introduces significant inaccuracies if the thickness of the top layer is comparable to the width of the rigid footing placed on the soil surface. Saturated normally consolidated and lightly overconsolidated clays indicate that under undrained condition the cohesion of soil mass increases almost linearly with depth. A few theoretical studies have been proposed in the literature to incorporate the variation of cohesion with depth in the computation of the ultimate bearing capacity of strip and circular footings. In this paper, after reviewing previous works, numerical computations using the FLAC code (Fast Lagrangian Analyses of Continua) are reported to evaluate the two layered clays effect on the bearing capacity beneath rigid strip footing subject to axial static load. The results of the bearing capacity relating to the relative thickness of the top layer, the strength ratio of the soil two-layered clays and the rates of the increase of soil cohesion with depth are presented in Tables and graphs. The obtained results are compared with previous published results available in the literature.     

Stability of eccentrically loaded footings on slopes

The stability of eccentrically loaded strip footings on slopes was investigated using the method of finite element analysis based on the theory of elasto-plasticity. The analysis was done for two different soils involving three levels of slope angle, six footing locations, and two levels of load eccentricity plus central vertical loading. The strip footing analysed was a 3-ft (0.9 m) wide reinforced concrete footing embedded to a depth of 3 ft (0.9 m). The analysis focused on footing settlement, plastic yielding of soil, and ultimate bearing capacity. The results of analysis show that the influence of load eccentricity on footing pressure vs. footing centre settlement is negligibly small. However, the progressive soil yielding and ultimate bearing capacity are greatly affected by load eccentricity. Furthermore, the effect of load eccentricity differs considerably with the load location relative to the footing centre and slope crest. The ultimate bearing capacity for the eccentric load located on the slope side is significantly greater than that for the load located on the other side of the footing centre. For a 2(H): 1(V) slope in silty clay, the effect of slope on footing stability decreases with increasing footing location from slope crest as would be expected, and diminishes when the footing is located from the crest at about 5-times the footing width.     

Estimation of bearing capacity for multiple footings in sand

In the present study, the effects of multiple-footing configurations in sand on bearing capacity were investigated using field plate load tests and finite element analyses. Both strip and spread footings were considered in the finite element analyses. In each case, different footing distances were applied for the purposes of comparison among all of the results. From these results, it was observed that the load responses of multiple footings are similar to those of the single footing at distances greater than three times the footing width. Design equation and correlation parameters, necessary for quantifying the values of the bearing capacity ratio for the different multiple-footing configuration, were derived. Experimental test results from the literature were selected and used in verifying the proposed method.     

Application of a non-coaxial soil model in shallow foundations

The influence of a non-coaxial model for granular soils on shallow foundation analyses is investigated. The non-coaxial plasticity theory proposed by Rudnicki and Rice (J. Mech. Phys. Solids 1975, 23, 371–394) is integrated into a Drucker–Prager model with both perfect plasticity and strain hardening. This non-coaxial model is numerically implemented into the finite-element program ABAQUS using a substepping scheme with automatic error control. The influence of the non-coaxial model on footing settlement and bearing capacity is investigated under various loading and boundary conditions. Compared with the predictions using conventional coaxial models, the non-coaxial prediction results indicate that the settlement of a footing increases significantly when the non-coaxial component of plastic strain rate is taken into consideration, although ultimate footing bearing capacities are not affected significantly. The non-coaxial model has a different effect on footing settlements under different loading and boundary conditions. In general, the discrepancies between coaxial and non-coaxial predictions increase with increasing rotation of principal stresses of the soil mass beneath a footing. It can be concluded that if the non-coaxial component of plastic strain rate is neglected in shallow foundation problems using the finite-element method, the results tend to be non-conservative when designs are dominated by settlement of footings.     

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.     

上拔扩底基础与地基土体承载特性差异性分析

工程中多采用基础上拔静载试验中基础顶部荷载-位移曲线获取基础的承载力,忽略了基础周围土体的变形破坏过程,而实际工程中均是基础周围地基土体发生破坏。为研究扩底基础与其周围土体在抗拔承载特性方面的差异,以黄土地基中的9个扩底基础为研究对象,通过现场全尺寸基础的上拔静载试验,分别获得基础顶部与地表的上拔荷载-位移曲线,并进一步对基顶与地表处的荷载-位移曲线变化特征、抗拔承载力取值进行对比分析。结果表明,两处的荷载-位移曲线变化特征相似,相同上拔荷载作用下地表处的位移量均小于基础处位移量,差异以初始弹性阶段变形最为突出;两者在弹性极限荷载QL1取值方面,相差较大,但随着地基基础由弹性向塑性发展,差异逐渐减小,两者塑性极限荷载QL2取值基本相同。结合上拔扩底基础的破坏模式,分析出上述差异主要由于基础与周围土体之间变形不协调所致,加载初期基础顶部的上拔位移包括基础拔出量和上部土体压缩量,当上部土体压密后压缩变形消失,地基基础成为一个整体,上拔基础与周围土体的变形趋于协调。     

Bearing capacity of foundations on rock mass using the method of characteristics

The method of stress characteristics has been used for computing the ultimate bearing capacity of strip and circular footings placed on rock mass. The modified Hoek‐and‐Brown failure criterion has been used. Both smooth and rough footing‐rock interfaces have been modeled. The bearing capacity has been expressed in terms of nondimensional factors N_σ0 and N_σ, corresponding to rock mass with (1) γ = 0 and (2) γ ≠ 0, respectively. The numerical results have been presented as a function of different input parameters needed to define the Hoek‐and‐Brown criterion. Slip line patterns and the pressure distribution along the footing base have also been examined. The results are found to compare generally well with the reported solutions.     

Behaviour of model footing on pond ash

This paper focuses on the effective utilization of pond ash, as foundation medium. A series of laboratory model tests have been carried out using square, rectangular and strip footings on pond ash. The effects of dry density, degree of saturation of pond ash, size and shape of footing on ultimate bearing capacity of shallow foundations are presented in this paper. Local shear failure of a square footing on pond ash at 37% moisture content (optimum moisture content) is observed up to the values of dry density 11.20 kN/m³ and general shear failure takes place at the values of dry density 11.48 kN/m³ and 11.70 kN/m³. Effects of degree of saturation on ultimate bearing capacity were studied. Experimental results show that degree of saturation significantly affects the ultimate bearing capacity of strip footing. The effect of footing length to width ratio (L/B), on increase in ultimate bearing capacity of pond ash, is insignificant for L/B ≥ 10 in case of rectangular footings. The effects of size of footing on ultimate bearing capacity for all shapes of footings viz., square, rectangular and strip footings are highlighted.     

Pressure–settlement characteristics of rectangular footings on reinforced sand

A method has been proposed to obtain the pressure–settlement characteristics of rectangular footings resting on reinforced sand based on constitutive laws of soils. The confining effect of the reinforcement provided in the soil at different layers has been incorporated in the analysis by considering the equivalent stresses generated due to friction at the soil– reinforcement interface. The prerequisite of the method is the value of ultimate bearing capacity, which can be obtained from the approaches already available in literature. The value of settlement may be read directly from pressure–settlement curves for the given pressure intensity. Therefore, the rectangular footing resting on reinforced sand can be proportioned satisfying shear failure and settlement criteria.     

Effective width rule in calculations of bearing capacity of shallow footings

The classical solution to the bearing capacity problem predicts the limit load on symmetrically loaded shallow strip footings. A useful hypothesis was suggested by Meyerhof to account for eccentricity of loading, in which the footing width is reduced by twice-the-eccentricity to its ‘effective’ size. This hypothesis sometimes has been criticized as being overconservative. This paper examines Meyerhof’s suggestion and presents the bearing capacity of eccentrically loaded footings calculated using the kinematic approach of limit analysis. It is found that the effective width rule yields a bearing capacity equivalent to that calculated based on the assumption that the footing is smooth. For more realistic footing models and for cohesive soils the effective width rule is a reasonable account of eccentricity in bearing capacity calculations. Only for significant bonding at the soil-footing interface and for large eccentricities does the effective width rule become overly conservative. For cohesionless soils, however, the effective width rule may overestimate the best upper bound. This overestimation increases with an increase in eccentricity. ©     

Behavior of Shallow Strip Footing on Twin Voids

This paper numerically examines the bearing capacity and failure mechanism of a shallow strip foundation constructed above twin voids. The voids may refer to caves, caverns, underground aqueduct or tunnels due to water seepage, chemical reaction or deliberately excavated in soil deposit. The ability of numerical model to accurately predict the system behavior is evaluated by performing verification analyses on existing researches. Subsequently, a parametric study carried out to reveal the influence of size of footing/voids and their location (i.e. depth, spacing, eccentricity) on the bearing capacity of footing. To clarify the failure mechanism, the distribution of shear strain in the soil for different scenarios is assessed. The parametric study provided a new framework to determine the bearing capacity and the mode of failure for footings on voids. Based on the results, a criterion can be issued to avoid collapse of footing/voids regarding the shape, location and size of voids. The results can also be used to design construction of a footing on existing voids while the acquired failure mechanisms can be appointed to develop analytical solutions for this problem. Results demonstrated that a critical depth for voids and a critical distance between them exist where the influence on the ultimate bearing capacity of footing disappears.