Bearing capacity factors of circular foundations for a general c–ϕ soil using lower bound finite elements limit analysis

By using the lower bound limit analysis in conjunction with finite elements and linear programming, the bearing capacity factors due to cohesion, surcharge and unit weight, respectively, have been computed for a circular footing with different values of ?. The recent axisymmetric formulation proposed by the authors under ?=0 condition, which is based on the concept that the magnitude of the hoop stress (σ_θ) remains closer to the least compressive normal stress (σ₃), is extended for a general c–? soil. The computational results are found to compare quite well with the available numerical results from literature. It is expected that the study will be useful for solving various axisymmetric geotechnical stability problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Relevance vector machine applied to slope stability analysis

This paper examines the potential of relevance vector machine (RVM) in slope stability analysis. The nonlinear relationship between slope stability and its influence factors is presented by the relevance vector learning mechanism based on a kernel‐based Bayesian framework. The six input variables used for the RVM for the prediction of stability slope are density (γ), friction angle (C), friction coefficient (?), slope angle (?_r), slope height (H), and pore water pressure (r_u). Comparison of RVM with some other methods is also presented. RVM has been used to compute the error bar. The results presented in this paper clearly highlight that the RVM is a robust tool for the prediction of slope stability. The experimental results show the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

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.     

Stability of long circular tunnels in sloping ground

Assessment of tunnel stability has become increasingly crucial as more and more tunnels are built in difficult terrains such as sloping ground. The required support pressure on the tunnel walls associates both tunnel stability and liner design considerations. The present analysis attempts to find a uniform internal pressure which can support a circular tunnel built in a sloping ground with a particular level of stability in cohesive-frictional soils. The lower bound finite element limit analysis has been applied to find the required minimum uniform internal support pressure presented as a non-dimensional term p/c; where p is the minimum normal internal pressure on the tunnel boundary to avoid collapse and c is the cohesion of soil. The variation of p/c is presented for a range of normalised embedment depth of tunnel (H/D), stability number (γD/c), internal friction angle of soil (?) and slope angle (β); where H is the crown depth of the tunnel, D is the tunnel diameter and γ is the unit weight of soil. Appropriate comparisons have been carried out with available literature. Failure patterns of the tunnel have also been studied to understand the extent and the type of failure zone which may generate during the collapse.     

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.     

Use of a non-associated flow rule for determining the stability of a vertical circular excavation

An axisymmetric lower bound limit analysis technique in combination with the finite elements has been used to investigate the effect of considering a non-associated flow rule on the stability number (γH/c) for a vertical circular unsupported excavation in a general cohesive–frictional soil medium, where (1) H is the excavation height, (2) γ defines the unit weight of the soil mass, and (3) c indicates the cohesion of the soil mass. The results are derived for different magnitudes of dilative coefficient (η), friction angle (?), and normalized excavation height (H/b), where b = the radius of the excavation. The results clearly indicate the increase in γH/c with an increase in η value. It is expected that the charts provided in this note will be quite helpful for the practicing engineers.

     

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.     

Application of statistical learning algorithms to ultimate bearing capacity of shallow foundation on cohesionless soil

This study employs two statistical learning algorithms (Support Vector Machine (SVM) and Relevance Vector Machine (RVM)) for the determination of ultimate bearing capacity (q_u) of shallow foundation on cohesionless soil. SVM is firmly based on the theory of statistical learning, uses regression technique by introducing varepsilon‐insensitive loss function. RVM is based on a Bayesian formulation of a linear model with an appropriate prior that results in a sparse representation. It also gives variance of predicted data. The inputs of models are width of footing (B), depth of footing (D), footing geometry (L/B), unit weight of sand (γ) and angle of shearing resistance (?). Equations have been developed for the determination of q_u of shallow foundation on cohesionless soil based on the SVM and RVM models. Sensitivity analysis has also been carried out to determine the effect of each input parameter. This study shows that the developed SVM and RVM are robust models for the prediction of q_u of shallow foundation on cohesionless soil. Copyright © 2010 John Wiley & Sons, Ltd.     

Determination of passive earth pressure with lower bound finite elements limit analysis and modified pseudo-dynamic method

ABSTRACT

The present study deals with the determination of passive earth pressure under seismic condition by following the lower bound finite elements limit analysis and modified pseudo-dynamic methodology. In accordance with the lower bound finite elements formulation, the stress field was modelled using a three-noded triangular elements, while the passive pressure was determined via linear optimisation. The parametric study was performed, for a vertical rigid retaining wall, by varying the magnitude of seismic acceleration in horizontal direction (k_h) between 0 and 0.3, while the vertical seismic acceleration (k_v) was kept equal to 0 or 0.5 k_h. Furthermore, the damping coefficient for dry cohesionless backfill was kept ξ = 10%. The obtained results in various cases were found to be in good agreement with those found in the literature. It is expected that this method can be further used for solving other important geotechnical stability problems.     

氢化物发生-电感耦合等离子体发射光谱法测定铀矿地质样品中痕量硒

采用氢化物发生技术测定地质样品中的硒时,需要考虑样品的溶解、Se价态的预还原以及抑制共存离子的干扰。本文采用硝酸-盐酸-氢氟酸-高氯酸体系快速溶解样品,直接加入浓盐酸煮沸将六价硒还原为四价硒,将氢化物发生器与电感耦合等离子体发射光谱仪联用测定了铀矿地质样品中的痕量硒。样品中除了Cu2+其他离子的含量均不干扰硒的测定,通过在试液中加入铁盐溶液或在硼氢化钠还原剂中加入铁氰化钾抑制了Cu2+的干扰。方法检出限为0.12μg/L,精密度(RSD)小于5%。与前人报道的方法相比,本方法检出限较低,操作简单快速,冲洗30 s可消除记忆效应,适合批量铀矿地质样品中痕量硒的测定。     

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.     

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.     

X射线荧光光谱法分析不同类型岩石中10种主量元素的测试能力验证

以28个不同类型岩石标样作外标,用玻璃熔片法制样,采用经验系数法进行基体校正,建立了X射线荧光光谱法(XRF)测定不同类型岩石中硅铝钙镁等10种主量元素的分析方法。该方法被用于参与GeoPT分析测试能力验证,15年来分析了23个不同类型的岩石验证样品。经验证该方法对SiO_2、Al_2O_3、K_2O和CaO具有非常好的分析效果(所有测定结果的|Z|2);对于MgO、MnO、TiO_2和Na_2O四个元素,尽管各有一个样品的分析结果的|Z|2,这主要是样品与标样的基体差异较大造成了低含量样品测定结果超差,但依然可获得好的分析效果;当TFe_2O_31.0%,P_2O_5含量在0.08%~0.80%区间时,分析结果的|Z|2,满足分析期望。总体上所建立的XRF分析方法稳定,可满足应用地球化学实验室测试不同类型岩石中10种主量元素的分析期望。     

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.     

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.     

基于遗传算法的BP神经网络模型在岩心扫描仪测定海洋沉积物多种组分中的应用研究

海洋沉积物样品成分复杂,由于基体效应的影响,利用岩心扫描仪开展X射线荧光光谱分析只能得到目标元素的强度信息,不利于该方法在成矿机制和古环境等研究领域更好地发挥作用。本文采用岩心扫描仪测定海洋沉积物中的铝硅钾钙钛锰铁钒铬铜锌铷锶钇和铅15种元素,尝试引入BP神经网络模型利用其非线性拟合能力校正基体效应。实验表明,以水系沉积物、海洋沉积物和岩石国家标准物质以及定值海洋沉积物样品为训练样本,采用遗传算法优化BP神经网络的初始权值和偏置,可以有效校正除硅之外的14种元素基体效应的影响,实现了岩心扫描仪XRF测量结果由强度到浓度的转化。本方法的精密度为0.6%~6.8%(RSD,n=11),国家标准物质和海洋沉积物实际样品中15种组分的预测值与参考值的相对偏差在0.5%~17.5%之间,适合于海洋沉积物中多种主次量组分的快速分析,拓展了岩心扫描仪的功能。     

Use of multivariate statistical analysis to determine the relationship between the magnetic properties of urban topsoil and its metal, S, and Br content

Multivariate statistical analysis has been used for detailed examination of the relationship between the magnetic properties of Xuzhou urban topsoil, for example concentration-dependent properties (mass magnetic susceptibility (χ), susceptibility of anhysteretic remanent magnetization (χ _ARM), saturation isothermal remanent magnetization (SIRM), soft remanent magnetization (SOFT), and frequency-dependent magnetic susceptibility (χ _FD)) and feature-dependent properties (S _{−100 mT} ratio, SIRM/χ ratio and F _{300 mT} ratio), and the concentrations of metals (Ti, Fe, Cr, Al, Ga, Pb, Sc, Ba, Li, Cd, Be, Co, Cu, Mn, Ni, V, Zn, Mo, Pt, Pd, Au, As, Sb, Se, Hg, Bi, Ag, and Sn), S, and Br in the soil. The results show that SIRM/χ ratios correlate best with the heavy metals (Hg, Cr, Sb, As, and Bi) which are mainly derived from coal-combustion emissions whereas χ _FD correlates best with the metals (Al, Ti, V, Be, Co, Ga, Mn, and Li) which principally originate from soil parents. Concentration-dependent magnetic properties (χ _ARM, χ, SIRM, and SOFT) correlate well with elements (Se, Pb, Cu, Zn, Fe, Ag, Sc, Ba, Mo, Br, S, Cd, Ni, etc.) which are mainly derived from road-traffic emissions. For the same chemical element, χ _ARM, SIRM, and SOFT values are frequently better correlated than χ values, and χ _ARM values are the best indicators of the concentrations of these elements associated with traffic emissions in this study area. In addition, S _{−100 mT} ratios significantly correlate positively with Se, Sc, Pb, Cu, Zn, Mo, and S whereas F _{300 mT} ratios only correlate positively with Pt and negatively with Fe. These results confirm the suitability of different magnetic properties for characterizing the concentrations of heavy metals, S, and Br in Xuzhou urban topsoil.