临近边坡的条形基础地基极限承载力数值分析

建筑物或构筑物基础临近边坡置放的情况在实际工程中十分普遍,但目前对于临近边坡基础的地基承载力及破坏模式尚缺乏深入研究。采用不连续布局优化（DLO）极限分析法建立数值模型,分析边坡几何尺寸、土体参数和基础位置对临坡条形基础的极限承载力和边坡破坏模式的影响,并对国内外现行规范推荐的计算方法进行评价。结果表明：极限承载力随边坡高度和边坡倾斜角的增大而减小,当坡高超过临界高度后,极限承载力将不受其影响;极限承载力随土体黏聚力和内摩擦角的增大而提高,滑动面随黏聚力的增大而变浅,随内摩擦角的增大而变深;极限承载力随基础与坡肩相对距离的增大而提高,当基础置放位置超过某临界距离后极限承载力不受边坡影响。在土体强度高、坡角较大时,《建筑地基基础设计规范》规定的临坡基础最小置放距离偏于危险,设计时仍需考虑边坡对承载力的减损作用;在土体强度较低、坡角较小时,规范规定值偏于保守。美国AASHTO规范对边坡地基极限承载力的取值在砂土边坡时较为可靠,但其仅适用于坡面破坏模式的情况;饱和黏土边坡的承载力曲线有悖于理论解,对临界距离的规定同样存在低估。     

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 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.     

土钉加固黏性土坡加载的离心模型试验研究

进行了不同坡度土钉加固边坡坡顶加载的离心模型试验,观测了土坡的破坏过程并测量土坡的位移场,研究了土钉加固黏性土坡的承载力、变形和破坏规律以及坡角对其破坏规律的影响。试验结果表明,坡顶荷载的增加引起土坡变形的增加,变形的集中产生和发展导致滑裂面的形成并使土坡发生破坏。土钉变形规律受加载阶段和加载底板的综合影响,坡顶荷载越大,接近坡顶的土钉弯曲挠度越大,钉土间的相互作用越强。土坡的坡角越大,承载力越低,土体呈现出更显著的向坡面位移的趋势。     

Bearing Capacity of Embedded Strip Footings on Cohesionless Soil Under Vertical and Horizontal Loads

In the last decades a few attention was given to the evaluation of the bearing capacity of embedded footing under inclined loads on a frictional soil. This paper focuses on a numerical study using the finite-difference code Fast Lagrangian Analysis of Continua (FLAC), to evaluate the bearing capacity of embedded strip footing on a frictional soil. The soil is modeled by an elasto-plastic model with a Mohr–Coulomb yield criterion and associative flow rule; the effect of non-associativity of the soil on the bearing capacity is also investigated. The effect of the embedment is estimated though a depth factor, defined as a ratio of the bearing capacity of a strip footing at a depth D to that of a strip footing at the ground surface. The inclination effect is estimated by inclination factors, defined as the ratio of the limit vertical load for a footing under inclined loading to that of the vertically loaded footing. Both swipe and probe analyses were carried out to identify the vertical force–horizontal force (V–H) failure envelope. The results have been compared with those 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.     

Reliability bearing capacity analysis of footings on cohesive soil slopes using RFEM

Reliability analysis of bearing capacity of a strip footing at the crest of a simple slope with cohesive soil was carried out using the random finite element method (RFEM). Analyses showed that the coefficient of variation and the spatial correlation length of soil cohesion can have a large influence on footing bearing capacity, particularly for slopes with large height to footing width ratios. The paper demonstrates cases where a footing satisfies a deterministic design factor of safety of 3 but the probability of design failure is unacceptably high. Isotropic and anisotropic spatial variability of the soil strength was also considered.     

Numerical analysis under seismic loads of soils improvement with floating stone columns

Geotechnical Engineering has developed many methods for soil improvement so far. One of these methods is the stone column method. The structure of a stone column generally refers to partial change of suitable subsurface ground through a vertical column, poor stone layers which are completely pressed. In general terms, to improve bearing capacity of problematic soft and loose soil is implemented for the resolution of many problems such as consolidation and grounding problems, to ensure filling and splitting slope stability and liquefaction that results from a dynamic load such as earthquake. In this study, stone columns method is preferred as an improvement method, and especially load transfer mechanisms and bearing capacity of floating stone column are focused. The soil model, 32 m in width and 8 m in depth, used in this study is made through Plaxis 2D finite element program. The clay having 5° internal friction angle with different cohesion coefficients (c 10, c 15, c 20 kN/m²) are used in models. In addition, stone columns used for soil improvement are modeled at different internal friction angles (? 35°, ? 40°, ? 45°) and in different s/D ranges (s/D 2, s/D 3), stone column depths (B, 2B, 3B) and diameters (D 600 mm, D 800 mm, D 1000 mm). In the study, maximum acceleration (a _max = 1.785 m/s²) was used in order to determine the seismic coefficient used. In these soil models, as maximum acceleration, maximum east–west directional acceleration value of Van Muradiye earthquake that took place in October 23, 2011 was used. As a result, it was determined that the stone column increased the bearing capacity of the soil. In addition, it is observed that the bearing capacity of soft clay soil which has been improved through stone column with both static and earthquake load effect increases as a result of increase in the diameter and depth of the stone column and decreases as a result of the increase in the ranges of stone column. In the conducted study, the bearing capacity of the soil models, which were improved with stone column without earthquake force effect, was calculated as 1.01–3.5 times more on the average, compared to the bearing capacity of the soil models without stone column. On the other hand, the bearing capacity of the soil models with stone columns, which are under the effect of earthquake force, was calculated as 1.02–3.7 times more compared to the bearing capacity of the soil models without stone column.     

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.     

Ultimate Bearing Capacity Prediction of Eccentrically Inclined Loaded Strip Footings

Extensive laboratory model tests have been carried out on a strip footing resting over dry sand bed subjected to eccentrically inclined load to determine the ultimate bearing capacity (Patra et al. in Int J Geotech Eng 6(3):343–352, 2012a.  https://doi.org/10.3328/IJGE.2012.06.03.343-352, Int J Geotech Eng 6(4):507–514, b.  https://doi.org/10.3328/IJGE.2012.06.04.507-514). Similarly, lower bound calculations based on finite element method were performed to compute the bearing capacity of a strip footing subjected to an eccentric and inclined load lying over a cohesionless soil with varying embedment depth and relative density (Krabbenhoft et al. in Int J Geomech ASCE, 2014.  https://doi.org/10.1061/(ASCE)GM.1943-5622.0000332). The load may be applied in two ways namely, towards the center line and away from the center line of the footing. Based on the results (both experimental and numerical analyses), a neural network model is developed to predict the reduction factor that will be used in computing the ultimate bearing capacity of an eccentrically inclined loaded strip footing. This reduction factor (RF) is the ratio of the ultimate bearing capacity of the footing subjected to an eccentrically inclined load to the ultimate bearing capacity of the footing subjected to a centric vertical load. A thorough sensitivity analysis is carried out to evaluate the parameters affecting the reduction factor. Based on the weights of the developed neural network model, a neural interpretation diagram is developed to find out whether the input parameters have direct or inverse effect on the output. A prediction model equation is framed with the trained weights of the neural network as the model parameters. The predictions from ANN, and those from other approaches, are compared with the results computed from both experimentation and FEM analyses. The ANN model results are found to be more accurate and well matched with other results.     

An analytical model of the strip footing reinforced with geogrid

The ultimate bearing capacity of a strip footing on soil reinforced with geogrids has been studied analytically. The reinforcing mechanism of the soil bearing on lateral surfaces and shearing over soils through the apertures of the grids was considered. The passive resistance against transverse ribs of geogrid was calculated using the Prandtl mechanism. The proposed equation incorporated the traditional Nγ factors, unit weight of soil, soil shear strength angle, footing width, and the geometry of the geogrid. The accuracy of theoretical predictions was verified by the experimental and analytical results from the existing literatures. The mean bias of the theoretical model was found to be about 10%.     

Bearing capacity computation for a ring foundation using the stress characteristics method

The stress characteristics method (SCM) has been used to compute the bearing capacity of smooth and rough ring foundations. Two different failure mechanisms for a smooth footing, and four different mechanisms for a rough footing have been considered. For a rough base, a curvilinear non-plastic wedge has been employed below the footing. The analysis incorporates the stress singularities at the inner as well as outer edges of the ring footing. Bearing capacity factors, N_c, N_q and N_γ are presented as a function of soil internal friction angle (ϕ) and the ratio (r_i/r_o) of inner to outer radii of the footing.     

Bearing capacity of a strip foundation on a sand layer overlying a smooth rigid stratum

The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N _q and N = bearing capacity factors for a semi-infinite layer - N _qs and N _s= bearing capacity factors for a finite layer - H _o /B= limiting depth - D _r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q _u= bearing capacity - = unit weight of sand     

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.     

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.     

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.     

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.     

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.     

基于非对称双侧破坏模式的临坡地基承载力上限分析

临坡地基已成为一种广泛的地基形式。针对临坡条形基础地基破坏模式的非对称性特点,首先引进双侧破坏模式的研究思路,重点考虑临坡地基基础两侧滑块大小和同一滑块几何形状的双重非对称性特征,构建了临坡条形基础地基非对称双侧破坏模式,为临坡地基承载力分析奠定了坚实基础;然后在此基础上,引进极限上限分析和优化理论,建立了临坡条形基础地基承载力分析的模型与方法,该方法不仅可考虑地基破坏模式,还可考虑基础与坡顶距离对临坡地基承载力的影响,而且还可较好地蜕化为平地地基承载力的分析;最后通过工程实例计算,并与现有相关分析方法进行对比分析,表明该方法的可行性与合理性以及普遍适用性。     

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.