Bearing capacity of strip foundations with structural skirts

A modified bearing capacity equation is proposed for skirted strip foundations on dense sand. A series of tests on foundation models were carried out to study the factors that affect the bearing capacity of foundations with skirts. Several factors including foundation base friction, skirt depth, skirt side roughness, skirt stiffness and soil compressibility were studied and incorporated in the equation. The results obtained from the proposed equation were compared with the results obtained from Terzaghi, Meyerhof, Hansen and Vesic bearing capacity equations for foundations without skirt. Comparison shows that the use of structural skirts can improve the bearing capacity by a factor of 1.5 to 3.9 depending on the geometrical and structural properties of the skirts and foundation, soil characteristics and interface conditions of the soil-skirt-foundation system. This revised version was published online in July 2006 with corrections to the Cover Date.     

Bearing Capacity of Eccentrically–Obliquely Loaded Footings Resting on Fiber-Reinforced Sand

This paper presents the method proposed to calculate the bearing capacity of a square footing under oblique and eccentric oblique loading condition (satisfying both shear failure and settlement criteria) resting on fiber reinforced sand layer underlain by sand with geosynthetic/fabric sheet at the interface. Large direct shear tests were carried out to investigate the shear strength parameters of sand and randomly distributed fiber reinforced sand (RDFS) and soil-plastic fabric sheet bond. The ultimate bearing capacity of RDFS was determined using direct shear results. Non-dimensional charts proposed by Kumar (Behaviour of eccentrically–obliquely loaded footing on reinforced earth slab. Ph.D. thesis, University of Roorkee, Roorkee, India, 2002) were used to consider the contribution of plastic fabric sheet in increasing the bearing capacity. Also, for calculating the settlement, horizontal deformation and tilt at a given pressure the regression analysis of plate load test data have been carried out. The predicted values of ultimate bearing capacity, settlement, horizontal deformation and tilt are compared with the experimental values which are in good agreement with each other. There appeared to be an increase in the residual shear strength and angle of internal friction of RDFS.     

Experimental Study of Bearing Capacity of Granular Soils,Reinforced with Innovative Grid-Anchor System

The pull-out resistance of reinforcing elements is one of the most significant factors in increasing the bearing capacity of geosynthetic reinforced soils. In this research a new reinforcing element that includes elements (anchors) attached to ordinary geogrid for increasing the pull-out resistance of reinforcements is introduced. Reinforcement therefore consists of geogrid and anchors with cubic elements that attached to the geogrid, named (by the authors) Grid-Anchor. A total of 45 load tests were performed to investigate the bearing capacity of square footing on sand reinforced with this system. The effect of depth of the first reinforcement layer, the vertical spacing, the number and width of reinforcement layers, the distance that anchors are effective, effect of relative density, low strain stiffness and stiffness after local shear were investigated. Laboratory tests showed that when a single layer of reinforcement is used there is an optimum reinforcement embedment depth for which the bearing capacity is the greatest. There also appeared to be an optimum vertical spacing of reinforcing layers for multi-layer reinforced sand. The bearing capacity was also found to increase with increasing number of reinforcement layer, if the reinforcement were placed within a range of effective depth. The effect of soil density also is investigated. Finally the results were compared with the bearing capacity of footings on non-reinforced sand and sand reinforced with ordinary geogrid and the advantages of the Grid-Anchor were highlighted. Test results indicated that the use of Grid-Anchor to reinforce the sand increased the ultimate bearing capacity of shallow square footing by a factor of 3.0 and 1.8 times compared to that for un-reinforced soil and soil reinforced with ordinary geogrid, respectively.     

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.     

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.     

Developing artificial neural network models to predict allowable bearing capacity and elastic settlement of shallow foundation in Sharjah,United Arab Emirates

This research proposes the use of artificial neural network to predict the allowable bearing capacity and elastic settlement of shallow foundation on granular soils in Sharjah, United Arab Emirates. Data obtained from existing soil reports of 600 boreholes were used to train and validate the model. Three parameters (footing width, effective unit weight, and SPT blow count) are considered to have the most significant impact on the magnitude of allowable bearing capacity and elastic settlement of shallow foundations, and thus were used as the model inputs. Throughout the study, depth of footing was limited to 1.5 m below existing ground level and water table depth taken at the level of the footing. Performance comparison of the developed models (in terms of coefficient of determination, root mean square error, and mean absolute error) revealed that the developed artificial neural network models could be effectively used for predicting the allowable bearing capacity and elastic settlement. As such, the developed models can be used at the preliminary stage of estimating the allowable bearing capacity and settlements of shallow foundations on granular soils, instead of the conventional methods.     

砂-黏土双层地基极限承载力的数值研究

在实际工程中,常见天然的或通过人工换填形成的上部砂土、下部黏土的层状地基,目前关于这种双层地基极限承载力和破坏机制研究还不够深入。通过有限差分法建立双层地基数值模型,分析基底粗糙程度、砂土剪胀角和超载对地基破坏模式及极限承载力的影响,并根据有限差分法计算结果对强度加权平均法、应力扩散法和冲剪破坏法等现有实用计算方法的估算正确性进行评价。研究结果表明,基底粗糙程度对极限承载力的影响随着砂土内摩擦角的增大而减小;当剪胀角较小时,剪胀角变化对承载力的影响更为明显;当下层黏土强度较小时,超载的作用更明显。强度加权平均法由于低估破坏面影响深度导致砂土层权重较大,计算结果偏大;应力扩散法忽略了砂土剪切强度,在砂土层较厚时出现低估;冲剪破坏法由于可较为精确地计算砂土破坏面上抗剪强度和被动土压力,是3种实用方法中计算最准确的,当砂土厚度和黏土强度较大时,建议按太沙基经验公式对下卧黏土进行局部剪切破坏修正后确定极限承载力。     

横-竖立体加筋地基中附加应力的分析计算

建立了横-竖立体加筋（H-V筋）地基的有限元模型,通过分析地基中的竖向应力分布、水平向位移分布以及筋-土界面相互作用,发现横-竖立体加筋地基中的竖向应力在筋材下方出现扩散和重分布,并逐渐向土体下部传递,使得土体中整体的应力分布更加均匀;同时,横-竖筋材中的竖筋类似于一个侧壁,其提供的垂直侧向力约束了介于竖筋间的土体,限制了土体的侧向水平位移,使得地基中筋材上部土体的侧向水平位移变小。基于有限元模拟对横-竖立体加筋地基加固机制的认识,将横-竖立体筋视为作用在地基上的一维弹性地基梁,通过弹性地基梁理论,根据弗拉曼解推导求解了横-竖立体加筋地基中任意一点竖向附加应力的计算表达式。将模型计算结果与有限元模拟所得结果进行对比发现两者吻合良好。     

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.     

Influence of size of granulated rubber on bearing capacity of fine-grained sand

Nowadays, in most of the advanced and developing countries, waste tires have caused serious environmental problems such as fire and environmental contamination. For reusing them in an appropriate and beneficial way, waste tires have been utilized as a lightweight fill material in geotechnical engineering applications such as highway embankments. In this study, Babolsar fine-grained sand and granulated rubber with sizes in the ranges of 1 to 4, 1 to 9, and 4 to 9 mm were used. A series of model footing tests on reinforced sand with different sizes of granulated rubber were carried out. According to the results, 4- to 9-mm granulated rubber had the highest effect on enhancement of bearing capacity and reduction of fine-grained sand settlement. The results showed that sand-granulated rubber mixtures with granulated rubber in the range of 4 to 9 mm and content of 10% by weight of mixture can increase the bearing capacity of sand up to 50%. In addition, for this mixture, a series of laboratory tests were conducted to determine the optimum width and depth of the reinforcement layer consisting of sand-granulated rubber mixture. The results indicate that the optimum width and the most effective depth of this mixture are 5B and 1B, respectively (where B is the footing width).     

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.     

Closely spaced rectangular footings on reinforced sand

In this paper, an analysis has been presented for calculating the pressure of an adjacent rectangular footing resting on reinforced sand for a given settlement. An approximate method has been suggested to compute the ultimate bearing capacity of adjacent footings resting on reinforced earth slab. The computation of normal force on the reinforcement area and estimation of interfacial friction coefficient at different layer levels are two essential steps in computation of pressure ratio. The process has been simplified by presenting suitable charts in non-dimensional form that can be directly used by practicing engineers.     

Performance of surface footing on geocell-reinforced soft clay beds

This paper presents the results of laboratory model tests carried out to develop an understanding of the behaviour of geocell-reinforced soft clay foundations under circular loading. Natural silty clay was used in this study. The geocells were prepared using biaxial polymer grid. The performance of the reinforced bed is quantified using non-dimensional factors i.e., Bearing capacity improvement factor (I_f) and Percentage reduction in footing settlement (PRS). The test results demonstrate that the geocell mattress redistributes the footing load over a wider area thereby improving the performance of the footing. The load carrying capacity of the clay bed is increased by a factor of up to about 4.5 times that of unreinforced bed. From the pressure-settlement responses, it is observed that the geocell-reinforced foundation bed behaves as a much stiffer system compared to the unreinforced case indicating that a substantial reduction in footing settlement can be achieved by providing geocell reinforcement in the soft clay bed. The maximum reduction in footing settlement obtained with the provision of geocell mattress of optimum size placed close to the footing is around 90%. Further improvement in performance is obtained with provision of an additional planar geogrid layer at the base of the geocell mattress.     

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.     

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.     

Effects of base geogrid on geocell-reinforced foundation beds

The effect of a base geogrid layer below the geocell mattress in sand, sand overlying soft clay, and soft clay foundation beds has been studied using a series of laboratory scale load tests. A rigid circular model footing was used to apply static monotonic loading on the foundation beds with and without geocell reinforcement. The model test results show that the provision of an additional layer of planar geogrid at the base of the geocell mattress further increases the performance of the footing in terms of bearing capacity and reduction in surface heave of the foundation bed. It is also observed that the beneficial effect of the base geogrid layer becomes negligible with increasing height of the geocell mattress beyond the influence of the depth of the footing. Strain measurements in the base geogrid layer indicate that it is more effective with the limited heights of the geocell mattress. The earth pressure cells embedded in the subgrade soil provide evidence that when the base geogrid is provided below the geocell mattress, the footing pressure is distributed more uniformly over an extended area.     

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.     

Transient loading-related settlement of a square foundation on geogrid-reinforced sand

Summary Laboratory model test results are presented that determine the effectiveness of using layers of geogrids as reinforcement in sand to reduce the settlement of square surface foundations subjected to transient loading. The model tests were conducted with only one type of geogrid at one relative density of compaction of sand. The maximum intensity of the transient load applied always exceeded the static ultimate bearing capacity of the foundation when supported by unreinforced sand. The settlement reduction factors for various depths of reinforcement have been determined.     

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.     

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.