Vertical uplift resistance of circular plate anchors in clays under undrained condition

The vertical uplift resistance of circular plate anchors, embedded horizontally in a clayey stratum whose cohesion increases linearly with depth, has been obtained under undrained ( = 0) condition. The axi-symmetric static limit analysis formulation in combination with finite elements proposed recently by the authors has been employed. The variation of the uplift factor (F_c) with changes in the embedment ratio (H/B) has been computed for several rates of increases of soil cohesion with depth. It is noted that in all the cases, the magnitude of F_c increases continuously with depth up to a certain value of H_cr/B beyond which the uplift factor becomes essentially constant. The proposed static limit analysis formulation is seen to provide acceptable results even for the two other simple chosen axi-symmetric problems.     

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.     

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (γH/c_o) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; γ = unit weight, H = height of the excavation and c_o = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.     

Horizontal Pullout Capacity of a Group of Two Vertical Strip Anchors Plates Embedded in Sand

The horizontal pullout capacity of a group of two vertical strip anchor plates placed along the same vertical plane in sand, has been determined by using the lower bound finite element limit analysis. The effect of vertical spacing (S) between the anchor plates on the magnitude of the total group horizontal failure load (P_uT) has been determined for different combinations of H/B, δ/ϕ and ϕ. The magnitude of P_uT has been obtained in terms of a group efficiency factor, η_γ, with respect to the failure load for a single vertical plate with the same H/B. The magnitude of η_γ becomes maximum corresponding to a certain critical S/B, which has been found to lie between 0.5 and 0.8. The value of η_γ for a given S/B has been found to become larger for greater values of H/B, ϕ, and δ.     

Bearing capacity of two interfering footings

By using an upper bound limit analysis in conjunction with finite elements and linear programming, the ultimate bearing capacity of two interfering rough strip footings, resting on a cohesionless medium, was computed. Along all the interfaces of the chosen triangular elements, velocity discontinuities were employed. The plastic strains were incorporated using an associated flow rule. For different clear spacing (S) between the two footings, the efficiency factor (ξ_γ) was determined, where ξ_γ is defined as the ratio of the failure load for a strip footing of given width in the presence of the other footing to that of a single isolated strip footing having the same width. The value of ξ_γ at S/B = 0 becomes equal to 2.0, and the maximum ξ_γ occurs at S/B = S_cr/B. For S/B?S_cr/B, the ultimate failure load for a footing becomes almost half that of an isolated footing having width (2B + S), and the soil mass below and in between the two footings deforms mainly in the downward direction. In contrast, for S/B>S_cr/B, ground heave was noticed along both the sides of the footing. As compared to the available theories, the analysis provides generally lower values of ξ_γ for S/B>S_cr/B. Copyright © 2007 John Wiley & Sons, Ltd.     

Upper bound limit analysis for finding interference effect of two nearby strip footings on sand

The ultimate bearing capacity of two closely spaced strip footings, placed on a cohesionless medium and loaded simultaneously to failure at the same magnitude of failure load, was determined by using an upper bound limit analysis. A logarithmic spiral radial shear zone, comprising of a number of triangular rigid blocks, was assumed to exist around each footing edge. The equations of the logarithmic spiral arcs were based on angles φ_L and φ_R rather than soil friction angle φ; the values of φ_L and φ_R were gradually varied in between 0 and φ. The ultimate bearing capacity was found to become maximum corresponding to a certain critical spacing between the footings. For spacing greater than the critical, the bearing capacity was found to decrease continuously with increase in the spacing. The extent of the spacing corresponding to which the ultimate bearing capacity becomes either maximum or equal to that of a single isolated footing increases with increase in φ. The results compare reasonably well with the available theoretical and experimental data.     

Vertical Uplift Capacity of Equally Spaced Multiple Strip Anchors in Sand

The ultimate uplift resistance of a group of multiple strip anchors placed in sand and subjected to equal magnitudes of vertical upward pullout loads has been determined by means of model experiments. Instead of using a number of anchor plates in the experiments, a single anchor plate was used by simulating the boundary conditions along the planes of symmetry on both the sides of the anchor plate. The effect of clear spacing (s) between the anchors, for different combinations of embedment ratio (λ) of anchors and friction angle (ϕ) of soil mass, was examined in detail. The results were presented in terms of a non-dimensional efficiency factor (ξ_γ), which was defined as the ratio of the failure load for an intervening strip anchor of a given width (B) to that of a single strip anchor plate having the same width. It was clearly noted that the magnitude of ξ_γ reduces quite extensively with a decrease in the spacing between the anchors. The magnitude of ξ_γ for a given s/B was found to vary only marginally with respect to changes in λ and ϕ. The experimental results presented in this study compare reasonably well with the theoretical and experimental data available in literature.     

高密度电法反演分辨率数值模拟与分析

高密度电法在反演过程中,电极距相比电性异常体横向长度过大时,电性异常体在反演中无法得到约束;某电极距下,当电性异常体埋藏深度增加大到一定深度时,在反演中电性异常体也无法得到约束。针对以上两个问题,利用res2dmod正演软件建立模型,再利用res2dinv反演软件对模型进行反演,通过对比分析结果表明:温纳、偶极和微分三种装置分两种情况:如果电极距小于20m模拟条件下,对于埋藏深度为5m且剖面面积不同的电性异常高阻体(异常体电阻率=100Ω·m,围岩电阻率=10Ω·m),横向反演分辨率,温纳装置大于微分和偶极装置;电极距小于12.75m时,微分装置大于偶极装置,电极距大于12.75m时,偶极装置大于微分装置。如果电极距在2m^8m范围内,对于剖面面积为4×4(m2)的电性异常高阻体(异常体电阻率=100Ω·m,围岩电阻率=10Ω·m),其最大约束深度随电极距的增大而先增大后减小;相同电极距下,偶极装置的最大约束深度>微分装置的最大约束深度>温纳装置的最大约束深度。     

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.     

Stability of a long unsupported circular tunnel in soils with seismic forces

By using the lower-bound finite element limit analysis, the stability of a long unsupported circular tunnel has been examined with an inclusion of seismic body forces. The numerical results have been presented in terms of a non-dimensional stability number (γH/c) which is plotted as a function of horizontal seismic earth pressure coefficient (k _h) for different combinations of H/D and ?; where (1) H is the depth of the crest of the tunnel from ground surface, (2) D is the diameter of the tunnel, (3) k _h is the earthquake acceleration coefficient and (4) γ, c and ? define unit weight, cohesion and internal friction angle of soil mass, respectively. The stability numbers have been found to decrease continuously with an increase in k _h. With an inclusion of k _h, the plastic zone around the periphery of the tunnel becomes asymmetric. As compared to the results reported in the literature, the present analysis provides a little lower estimate of the stability numbers. The numerical results obtained would be useful for examining the stability of unsupported tunnel under seismic forces.     

The variation of Nγ with footing roughness using the method of characteristics

By using the method of characteristics, the effect of footing–soil interface friction angle (δ) on the bearing capacity factor N_γ was computed for a strip footing. The analysis was performed by employing a curved trapped wedge under the footing base; this wedge joins the footing base at a distance B_t from the footing edge. For a given footing width (B), the value of B_t increases continuously with a decrease in δ. For δ=0, no trapped wedge exists below the footing base, that is, B_t/B=0.5. On the contrary, with δ=?, the point of emergence of the trapped wedge approaches toward the footing edge with an increase in ?. The magnitude of N_γ increases substantially with an increase in δ/?. The maximum depth of the plastic zone becomes higher for greater values of δ/?. The results from the present analysis were found to compare well with those reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

Kinematic slices approach for uplift analysis of strip foundations

A kinematic method of slices has been used in this article to deal with the stability problems of strip foundations subjected to uplift loads. The method is based on the upper bound theorem of limit analysis and satisfies the kinematic admissiblility of the chosen collapse mechanism. Assuming the global rupture surface as an arc of logarithmic spiral, uplift factors F_c, F_q and F_γ separately for the effects of cohesion, surcharge and density have been determined. The effect of the yielding of soil mass with partial soil shear strength parameters along the slice interfaces on the results has been examined. The ultimate uplift capacity increases with increase in soil shear strength along the interfaces of slices. The results compare reasonably well with the various existing theories and reported experimental tests data. Copyright © 1999 John Wiley & Sons, Ltd.     

Collapse loads for rectangular foundations by three-dimensional upper bound limit analysis using radial point interpolation method

A three-dimensional kinematic limit analysis approach based on the radial point interpolation method (RPIM) has been used to compute collapse loads for rectangular foundations. The analysis is based on the Mohr-Coulomb yield criterion and the associated flow rule. It is understood that the internal plastic power dissipation function and flow rule constraints can be expressed entirely in terms of plastic strain rates without involving stresses. The optimization problem has been solved on basis of the semidefinite programming (SDP) by using highly efficient primal-dual interior point solver MOSEK in MATLAB. The results have been presented in terms of the variation of the shape factors with changes in the aspect ratio (L/B) of the footing for different values of soil internal friction angle (ϕ). Computations have revealed that the shape factors, s_c and s_q, due to effects of cohesion and surcharge increase continuously with (1) decrease in L/B and (2) increase in ϕ. On the other hand, the shape factor s_γ, due to the effect of soil unit weight, increases very marginally with an increase in L/B up to (1) ϕ = 25° for a rough footing and (2) ϕ = 35° for a smooth footing. Thereafter, for greater values of ϕ, the variation of s_γ with L/B has been found to be quite similar to that of the factors s_c and s_q. The variations of (1) nodal velocity patterns, (2) plastic power dissipation, and (3) maximum plastic shear strain rates have also been examined to interpret the associated failure mechanism.     

Bearing capacity of strip foundations reinforced with geogrid sheets by using upper bound finite‐element limit analysis

By using the upper bound finite‐elements limit analysis, with an inclusion of single and two horizontal layers of reinforcements, the ultimate bearing capacity has been computed for a rigid strip footing placed over (i) fully granular, (ii) cohesive‐frictional, and (iii) fully cohesive soils. It is assumed that (i) the reinforcements are structurally strong so that no axial tension failure can occur, (ii) the reinforcement sheets have negligible resistance to bending, and (iii) the shear failure can take place between the reinforcement and soil mass. It is expected that the different approximations on which the analysis has been based would generally remain applicable for reinforcements in the form of geogrid sheets. A method has been proposed to incorporate the effect of the reinforcement in the analysis. The efficiency factors, η_c and η_γ, to be multiplied with N_c and N_γ , for finding the bearing capacity of reinforced foundations, have been established. The results have been obtained (i) for different values of ? in case of fully granular and cohesive‐frictional soils, and (ii) for different rates at which the cohesion increases with depth for a fully cohesive soil. The optimum positions of the reinforcements' layers have also been determined. The effect of the reinforcements' length on the results has also been analyzed. As compared to cohesive soils, the granular soils, especially with higher values of ?, cause a much greater increase in the bearing capacity. The results compare reasonably well with the available theoretical and experimental data from literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Bearing capacity factor Nc under ϕ=0 condition for piles in clays

Bearing capacity factor N_c for axially loaded piles in clays whose cohesion increases linearly with depth has been estimated numerically under undrained (?=0) condition. The study follows the lower bound limit analysis in conjunction with finite elements and linear programming. A new formulation is proposed for solving an axisymmetric geotechnical stability problem. The variation of N_c with embedment ratio is obtained for several rates of the increase of soil cohesion with depth; a special case is also examined when the pile base was placed on the stiff clay stratum overlaid by a soft clay layer. It was noticed that the magnitude of N_c reaches almost a constant value for embedment ratio greater than unity. The roughness of the pile base and shaft affects marginally the magnitudes of N_c. The results obtained from the present study are found to compare quite well with the different numerical solutions reported in the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

The influence of horizontal confinement on the bearing capacity factor Nγ of smooth strip footing

We studied the upper-bound ultimate bearing capacity of smooth strip shallow footings with symmetrical and asymmetrical horizontal confinements on purely frictional sand within the framework of upper-bound limit analysis. The subsoil follows the associated flow rule, and no surcharge on the soil surface is assumed. The contact between the soil and the horizontal confinement walls is assumed to be perfectly rough. The upper-bound solutions for the objective functions are obtained using nonlinear sequential quadratic programming. The results for the different internal friction angles φ are provided in terms of the variation of two parameters, namely, the bearing capacity factor N_γ and the correction factor of bearing capacity K_γ, with respect to the change in the clear spacing between the edge of smooth footing and the rigid vertical walls. The values of N_γ and K_γ increase with φ and decrease with the clear spacing between the edge of the smooth footing and the rigid vertical walls. N_γ and K_γ are more sensitive to this confining effect as φ increases. The numerical results, a comparative analysis with the results from previous studies, and design charts are also included.     

Bearing capacity of interfering multiple strip footings by using lower bound finite elements limit analysis

The ultimate bearing capacity of a number of multiple strip footings, identically spaced and equally loaded to failure at the same time, is computed by using the lower bound limit analysis in combination with finite elements. The efficiency factor (ξ_γ), due to the component of soil unit weight, is computed with respect to changes in the clear spacing (S) between the footings. It is noted that the failure load for a footing in the group becomes always greater than that of a single isolated footing. The values of ξ_γ for the smooth footings are found to be always lower than the rough footings. The values of ξ_γ are found to increase continuously with a decrease in the spacing between footings. As compared to the available theoretical and experimental results reported in literature, the present analysis provides generally a little lower values of ξ_γ.     

Determination of stability of slope using Minimax Probability Machine

This article examines the capability of Minimax Probability Machine (MPM) for the determination of stability of slope. MPM is constructed within a probabilistic framework. This study uses MPM as classification and regression tools. Unit weight (γ), cohesion (c), angle of internal friction (φ), slope angle (β), height (H) and pore water pressure coefficient (r_u) have been used as inputs of the MPM model. The outputs of MPM are stability status of slope and factor of safety (F). The results of MPM have been compared with the artificial neural network models. The experimental results demonstrate that the developed MPM is a promising tool for the determination of stability of slope.     

Uplift capacity of pile group anchors

Experimental investigations on model single pile anchor and pile group anchors of configuration 2 × 2 subjected to uplift loads were conducted on dry Ennore sand, obtained from Madras, India. The embedment length to shaft width ratios, L/d = 20 and L/d = 30, and enlarged base width to shaft width ratios, B/d = 1,2,3, center to center spacing of pile anchors in the groups, 3d, 4d, 6d and 8d were used. The load displacement response, ultimate resistance and variation of group efficiency with L/d, B/d and spacing have been studied quantitatively and qualitatively. For short pile group anchors (L/d = 20), the isolation spacing appears to be at a spacing of about 4d to 6d and 8d for B/d = 1 and B/d = 2 and 3, respectively. For long pile group anchors (L/d = 30), the isolation spacing appears to be at a spacing of about 4d, 6d and 8d for B/d = 1, 2 and 3, respectively. The analytical model of limit equilibrium method has been proposed to predict the net uplift capacity of pile group anchors. The predicted results compare reasonably well with the experimental results.     

Response of saturated porous media to cyclic thermal loading

The response of a semi‐infinite saturated porous medium subjected to a harmonic thermal loading on its free face is studied herein. The pressure diffusion equation that governs the fluctuation of the interstitial pressure is established. It allows us to obtain prevalent parameters, i.e. the thermal and fluid mass diffusivities and the coefficient of relative bulk variation. Closed‐form solutions of the maximum fluid pressure P_max and its location x_cr are derived. It is shown that the location x_cr of P_max is localized and depends on the diffusivity ratio and the frequency of the thermal loading while the magnitude of P_max depends on the diffusivity ratio and the thermal amplitude. Master curves for x_cr and P_max versus diffusivity ratio are built. It follows that three regimes can be distinguished: namely, thin spalling, thick spalling or in‐depth cracking and no cracking. Copyright © 2003 John Wiley & Sons, Ltd.