Seismic bearing capacity of shallow strip footings

Seismic bearing capacity of shallow strip footings in soil has been obtained in the form of pseudo-static seismic bearing capacity factors N_cd, N_qd and N_d, denoting the cohesion, surcharge and unit weight components, respectively, by an extensive numerical iteration technique. Limit equilibrium method of analysis with composite failure surface is assumed. The validity of the principle of superposition is examined. Effects of both the horizontal and vertical seismic acceleration coefficients have been found to always reduce the ultimate bearing capacity significantly. Results obtained by the present method of analysis are compared with the available results and are found to be the least in the seismic case.     

Upper bound solutions of bearing capacity of strip footing by pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis of seismic bearing capacity of a strip footing using upper bound limit analysis. However, in the literature, the pseudo-static approach was frequently used by several researchers to compute the seismic bearing capacity factor theoretically, where the real dynamic nature of the earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of bearing capacity factor N _γE are determined for different magnitudes of soil friction angle, soil amplification and seismic acceleration coefficients both in the horizontal and vertical directions. The results obtained from the present study are shown both graphically as well as in the tabular form. It is observed that the bearing capacity factor N _γE decreases significantly with the increase in seismic accelerations and amplification. The results are thoroughly compared with the existing values in the literature and the significance of the present methodology for designing the shallow footing is discussed.     

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.     

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.     

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 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.     

A Simple Limit Equilibrium Approach for Calculation of Ultimate Bearing Capacity of Shallow Foundations on Two-Layered Granular Soils

The bearing capacity of shallow foundations in a non-homogeneous soil profile has been a challenging task in geotechnical engineering. In this paper, a limit equilibrium method is used for calculating bearing capacity factors of shallow foundations constructed on a two-layered granular soil profile. The main objective has been to determine the ultimate bearing capacity computed from equivalent bearing capacity factors N_q and N_γ and comparing that with numerical analysis using finite element methods. It will be shown that the data obtained form the developed method are well comparable with those obtained from FE approach, specially when the difference between shear strength parameters of layers is low which is a practical case for sedimentary soil profiles and also for artificially compacted soils. A computer program has been developed to investigate the influence of various parameters on bearing capacity factors.     

Pull-out behaviour of steel grid soil reinforcement embedded in silty sand

This paper investigates the pull-out behaviour (particularly the bearing resistance) of a steel grid reinforcement embedded in silty sand using laboratory tests and numerical analyses. It is demonstrated that the various common analytical equations for calculating the bearing component of pull-out resistance give a wide range of calculated values, up to about 200% disparity. The disparity will increase further if the issue of whether to use the peak or critical state friction angle is brought in. Furthermore, these equations suggest that the bearing resistance factor, N_q, is only a function of soil friction angle which is not consistent with some design guidelines. In this investigation, a series of large scale laboratory pull-out tests under different test pressures were conducted. The test results unambiguously confirmed that the N_q factor is a function of test pressure. A modified equation for calculating N_q is also proposed. To have more in-depth understanding of the pull-out behaviour, the tests were modelled numerically. The input parameters for the numerical analysis were obtained from laboratory triaxial tests. The analysis results were compared with the experimental results. Good agreement between experimental and numerical results was achieved if the strain-softening behaviour from peak strength to critical state condition was captured by the soil model used.     

Influence of random heterogeneity of the friction angle on bearing capacity factor Nγ

ABSTRACT

Probabilistic methods in geotechnical engineering have received a lot of attention during the last decade and different methodologies are used to capture the inherent variability of soil in different geotechnical engineering problems. In this paper, numerical simulations are conducted to obtain the bearing capacity factor, N_γ, for a purely frictional heterogenous soil where the friction angle is modelled as randomly distributed throughout the domain and the effect of its spatial variability on N_γ is investigated. A finite element method, based on the upper bound limit analysis was combined with random field theory and linear programming to develop a probabilistic analysis. Monte Carlo simulations were performed and the effect of the variability of the friction angle defined by statistical parameters on the bearing capacity factor was investigated. Results show that the mean bearing capacity factor N_γ of a footing on a spatially variable cohesionless soil is generally higher than the deterministic N_γ obtained from a constant mean value. Increasing the heterogeneity of the friction angle by an increase in the coefficient of variation generally increases this deviation. This can be explained by the nonlinearity of the relationship between N_γ and the friction angle.     

Failure modes and bearing capacity of strip footings on soft ground reinforced by floating stone columns

This study evaluates the failure modes and the bearing capacity of soft ground reinforced by a group of floating stone columns. A finite difference method was adopted to analyze the performance of reinforced ground under strip footings subjected to a vertical load. The investigation was carried out by varying the aspect ratio of the reinforced zone, the area replacement ratio, and the surface surcharge. General shear failure of the reinforced ground was investigated numerically without the surcharge. The results show the existence of an effective length of the columns for the bearing capacity factors N _c and N _γ. When certain surcharge was applied, the failure mode of the reinforced ground changed from the general shear failure to the block failure. The aspect ratio of the reinforced zone and the area replacement ratio also contributed to this failure mode transition. A counterintuitive trend of the bearing capacity factor N _q can be justified with a shift in the critical failure mode. An upper-bound limit method based on the general shear failure mode was presented, and the results agree well with those of the previous studies of reinforced ground. Equivalent properties based on the area-weighted average of the stone columns and clay parameters were used to convert the individual column model to an equivalent area model. The numerical model produced reasonable equivalent properties. Finally, a theoretical method based on the comparison of the analytical equations for different failure modes was developed for engineering design. Good agreement was found between the theoretical and numerical results for the critical failure mode and its corresponding bearing capacity factors.     

瞬态面波预测单桩承载力模型研究

总结了现有单桩竖向承载力检测技术存在的一些问题,结合实例提出了一种预测单桩承载力的间接方法———瞬态面波法。剪切波速与标贯击数之间也存在着相关关系,通过标贯击数建立起剪切波速与桩侧摩阻力及桩端阻力的相关模型,应用瞬态面波测试技术可快速检测桩周土剪切波速,确定单桩承载力。     

土钉支护基坑抗隆起稳定性计算方法研究

以基坑隆起破坏的根本原因是地基承载力不足为前提,运用Terzaghi地基极限承载力理论,推导了土钉支护条件下基坑抗隆起稳定性的计算方法。采用地基土单侧滑动失稳破坏假设,同时考虑了单侧滑动体上竖向抗剪力对抵抗基坑隆起所起的作用。通过基本算例,对影响基坑抗隆起稳定性的参数进行了讨论,并得出了各抗隆起安全系数与各因素之间的部分变化规律。与现有的基坑抗隆起稳定性计算方法对比分析表明,所建议的方法在实际工程应用中是可行的。     

Hierarchy of earthquakes in the Baikal rift system: implications for lithospheric stress

We investigated space-time lithospheric stress patterns of the Baikal rift system according to the hierarchy of earthquakes using mechanisms of 265 K_P ≥ 10 events recorded from 1950 to 1998 and seismic moments of 802 K_P ≥ 11 events from 1968 to 1994. The lithosphere of the region was confirmed to undergo rifting with mostly normal-slip events, while local areas of frequent strike-slip and reverse motions may record stress heterogeneity. The dominance of rifting, although being evident in the stress dynamics, is unstable, which is indicated by increase in strike-slip and reverse motions to as many as normal slip events in the latest 1980s–earliest 1990s. The lithospheric stress patterns inferred from seismic-moment data are generally consistent with those derived from the classical focal mechanism method. The suggested approach of seismic zoning according to earthquake slip geometry may provide a more reliable background for successful mitigation of seismic hazard in the region.     

Reflections on frequency dependence in earthquake-source inversions

The corner frequency of the spectrum of particle acceleration in a seismic wave radiated by an earthquake source marks the transition between the low-frequency band, in which the spectrum rises as frequency squared, and the high-frequency band, in which the spectrum is flat. These two distinct bands are controlled by different characteristics of faulting. The low-frequency range is governed by the value of slip alone, while the high-frequency range is controlled by both the total slip and slip velocity. This distinction explains why inversions of geodetic and shorter-period seismic data sense different characteristics of source process and are not generally comparable. Neglect of the sensitivity of seismic data to both slip and its rate may lead to false images of the inverted slip on the fault, as these characteristics trade off with each other. A recent example of the 2011 M _w 9.0 Tohoku-oki, Japan, earthquake demonstrates that the observed “frequency-dependent” variations in the rupture process over the fault plane should not be considered unique to this particular event but rather a natural consequence of the frequency-dependent inversion.     

考虑地震影响的地基极限承载力的理论解析解

本文根据塑性力学中的滑移线法，建立了地震力作用下的地基土的滑移线应力议程，并在考虑地基土的自重和不计其自重的情况，推导出此时地基土的极限承载力的理论解析解。     

Seismic vertical uplift capacity of horizontal strip anchors using pseudo-dynamic approach

This paper presents the pseudo-dynamic analysis to determine the seismic vertical uplift capacity of a horizontal strip anchor using upper bound limit analysis. However, in the literature, the pseudo-static approach was used by few researchers to compute the seismic vertical pullout resistance, where the real dynamic nature of earthquake accelerations cannot be considered. Under the seismic conditions, the values of the unit weight component of uplift factor f_γE are determined for different magnitudes of soil friction angle, soil amplification, embedment ratio and seismic acceleration coefficients both in the horizontal and vertical directions. It is observed that the uplift factor f_γE decreases significantly with the increase in seismic accelerations and amplification but increases with the increase in embedment ratio. The results are compared with the existing values in the literature and the significance of the present methodology for designing the horizontal strip anchor is discussed. In presence of vertical earthquake acceleration and amplification of vibration, the present values of f_γE compare reasonably well with the existing pseudo-static values obtained by modifying the horizontal acceleration coefficient.     

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     

Do faults preserve a record of seismic slip: A second opinion

Exhumed fault zones offer insights into deformation processes associated with earthquakes in unparalleled spatial resolution; however it can be difficult to differentiate seismic slip from slow or aseismic slip based on evidence in the rock record. Fifteen years ago, Cowan (1999) defined the attributes of earthquake slip that might be preserved in the rock record, and he identified pseudotachylyte as the only reliable indicator of past earthquakes found in ancient faults. This assertion was based on models of frictional heat production (Sibson, 1975, 1986) providing evidence for fast slip. Significant progress in fault rock studies has revealed a range of reaction products which can be used to detect frictional heating at peak temperatures less than the melt temperature of the rock. In addition, features formed under extreme transient stress conditions associated with the propagating tip of an earthquake rupture can now be recognized in the rock record, and are also uniquely seismic. Thus, pseudotachylyte is no longer the only indicator of fossilized earthquake ruptures.We review the criteria for seismic slip defined by Cowan (1999), and we determine that they are too narrow. Fault slip at rates in the range 10⁻⁴−10¹ m/s is almost certainly dynamic. This implies that features reproduced in experiments at rates as low as 10⁻⁴ m/s may be indicators of seismic slip. We conclude with a summary of the rock record of seismic slip, and lay out the current challenges in the field of earthquake geology.     

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 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.