THE SETTLEMENT OF A RIGID CIRCULAR FOUNDATION RESTING ON A HALF-SPACE EXHIBITING A NEAR SURFACE ELASTIC NON-HOMOGENEITY

The present paper examines the elastostatic problem pertaining to the axisymmetric loading of a rigid circular foundation resting on the surface of a non-homogeneous elastic half-space. The non-homogeneity corresponds to a depth variation in the linear elastic shear modulus according to the exponential form G(z)=G₁+G₂e^-ζz. The equations of elasticity governing this type of non-homogeneity are solved by employing a Hankel transform technique. The mixed boundary value problem associated with the indentation of the half-space by the rigid circular foundation is reduced to a Fredholm integral equation which is solved via a numerical technique. The numerical results presented in the paper illustrate the influence of the near-surface elastic non-homogeneity on the settlement of the foundation.     

Reliability of Conventional Settlement Evaluation for Circular Foundations on Stone Columns

The unit cell idealization has been long adopted in the settlement prediction of stone column-reinforced soils. This paper tests the accuracy of this modeling concept against trusted settlement values of engineering foundations. It is believed that in order to bestow the outcome of this study adequate generality different soil properties and foundation geometries need to be considered. It was, nevertheless, found impracticable to collect field settlement records for all the analyzed cases. The authors, therefore, appealed to the back analysis concept to construct a reliable mathematical model, calibrated against settlement records of full-scale field load test. This model, which is capable of reproducing the real field settlements, is then employed as a generic tool to obtain trusted settlement values for a variety of cases with essential geometrical similarity. The investigation revealed that the unit cell analysis may, in some cases, lead to erroneous estimation for the settlements of foundations with limited extents. Correction factors, dependent on the treated soil properties as well as the foundation size, are introduced.     

FLAC Based Numerical Studies on Dynamic Interference of Two Nearby Embedded Machine Foundations

This paper emphasizes on the dynamic interaction of two closely spaced embedded square or rectangular foundations under the action of machine vibration. One of the foundations is excited with a known vibration source placed on the top of it, called the active foundation. The objective is to study the effect of dynamic motion of the active foundation on the nearby passive foundation through a layered soil medium. The analysis is performed numerically by using the explicit finite difference code FLAC ^3D . The soil profile is assumed to obey the Mohr–Coulomb yield criteria with non-linear failure envelope. The analysis is performed under sinusoidal dynamic loading with varying amplitude. Under the dynamic excitation, the settlement behavior of the interacting foundations is studied by varying the spacing between the foundations. In addition, the variation of vertical normal and shear stress developed beneath the interacting foundations is also explored. The present theoretical investigation indicates that the settlement and vertical normal stress below the active foundation is generally found to be higher than that obtained for the passive foundation, whereas the shear stress response below the foundations follows the reverse trend.     

考虑三维变形的柔性和刚性基础沉降计算方法

传统的分层总和法不能考虑地基三维变形,计算基础沉降的误差非常大。为了减小分层总和法修正系数的范围,基于侧限压缩试验的e-p曲线,推导了能够考虑三维变形的柔性基础沉降算法。只要把传统算法的分层压缩量乘以一个修正系数,新算法就可以在分层总和法基础上考虑地基土的侧向变形。进一步地,通过调整基础底面的压力分布,推导了条形刚性基础沉降的近似算法。算例分析表明,考虑三维变形的沉降算法可以解决传统分层总和法在计算小尺寸基础时沉降过小的问题。计算表明,小尺寸刚性基础沉降计算结果比传统分层总和法大,大尺寸刚性基础沉降计算结果比传统分层总和法小,这可能是导致分层总和法修正系数范围过大的原因之一。应用文中方法有希望减小分层总和法的一部分误差。     

柔性和刚性浅基础的地基承载能力分析

为了研究刚性和柔性加载面下地基的破坏机制和极限承载力,着重对比分析了不考虑土体自重条件下柔性基础、基底完全光滑或完全粗糙的刚性基础的地基,采用关联流动的Mohr-Coulomb内切圆屈服准则,通过增量加载的有限元方法,全程模拟了地基由初始的线弹性状态逐渐过渡到塑性流动的极限破坏状态的过程。通过对这3种基础类型下地基的计算结果的对比分析,并结合国内外模型试验成果,得到如下结论：柔性和刚性浅基础地基在不考虑土体自重的条件下有相近的地基极限承载力,但基底水平面上竖向应力和位移的发展规律、临塑荷载及滑动面有着明显的区别。     

Analysis of rigid rafts supported by granular piles

Solutions for the magnitude and rate of settlement of rigid foundations supported by soil reinforced with granular piles are presented. An analytic solution using the theory of elasticity is developed for the settlement of the foundation and expressions for evaluating the moment and shear distributions across the foundation are given. A solution for the increase of the rate of settlement due to the presence of the granular piles has been found by a numerical solution of Biot's equations of consolidation.     

考虑不同基础埋深的沉降计算统一公式

通过对不同作用深度、不同长宽比矩形面积均布荷载角点下应力系数Mindlin解与Boussinesq解的分析比较,建立了二者之间的统计关系,利用“归一化函数”,引入“沉降计算深度修正系数”,并通过对北京地区数十个工程沉降实测值进行反分析得到“沉降计算经验系数”,提出了对不同埋深的天然地基与桩基都适用的“统一沉降计算公式”。     

Settlement of compacted ash fills

The coal ash is a by-product of coal-fired thermal power station. It is extensively used as a geo-material for landfill. The compacted ash is used as a structural fill if it is properly characterized for load-bearing capacity and settlement. The main objective of the present work is to characterize ash material and to evaluate its settlement characteristics. The ash is normally compacted by vibration at or near optimum moisture for its performance as structural fill. The overt characteristics of ashes are viewed similar to cohesionless soils. However, the mass behavior may have differences due to the subtle influence of chemical and physical processes involved in its formation. The empirical and analytical methods predicting settlement of footing under static loading require direct or indirect measurement of density and stress state in the deposit. In the present work, experimental investigations for settlement prediction were carried out on compacted coal ash produced at Ropar thermal power station in India, which was conveniently classified as ASTM class F ash. The settlement was experimentally obtained for the rigid plates having least dimension more than 0.3 m on ashes compacted at varying degree of compaction. The predicted settlement based on the observed data of coal ash using conventional techniques for soils was found to be conservative. A relationship between settlement and foundation size is proposed at varying compaction to obtain the settlement of compacted ash. At a higher degree of compaction, the settlement of a foundation may not exceed the allowable settlements in the working stress range.     

Dynamic stiffness for rectangular rigid foundations on a semi-infinite elastic medium

The present paper deals with the dynamic steady-state force-displacement relationships (complex stiffness) for rectangular rigid foundations resting on a semi-infinite medium, consisting of homogenous, isotropic, linear elastic materials. The foundations are considered to be excited under harmonic vertical and rocking vibration. This gives mixed boundary value problems which cannot be easily solved by analytical approaches. Therefore, a numerical method is proposed here. The method is based on quite, simple equations, and is straightforward in computation, compared with other methods. Although the proposed method gives just approximate solutions, it is satisfactory for engineering practices, and the soluations become highly accurate for a small value of ωB/V_s. The results obtained by the proposed method are compared with those of other methods to evaluate the accuracy of the results. The effects of length/width ratio and the area of the contact plane of the foundations are also discussed.     

高速公路扩建工程软基拓宽的沉降监测与分析

高速公路拓宽建设中新老路基特别是软土路基的固结沉降与力学性质的差异将引起严重的路面开裂,因而控制其差异沉降、防止拼接处路面开裂成为扩建工程软基处理中的技术关键。针对采用薄壁管桩和粉喷桩处理的软基路段,选取具有典型地质条件及较高填方的断面,通过埋设地面沉降板,对拓宽路基及新老路堤结合部进行了为期9个月的沉降动态监测。监测结果表明,拓宽路基的累计沉降及差异沉降均很小,后期沉降速率小于控制标准,为新老路基差异沉降的评价提供了依据;薄壁管桩用于处理埋深大、层厚大的拓宽软基及粉喷桩用于处理埋深浅、层厚较小的拓宽软基具有各自的适用性,拓宽后的新老路基已形成整体性强的复合地基,达到了路基拓宽的理想效果。     

Lithospheric flexural modelling of the seaward and trenchward of the subducting oceanic plates

ABSTRACT

Based on a two-segment plate flexural modelling, we investigated the effective elastic thickness of global subducting oceanic lithosphere. Our results show that for the plate age of 0 to 50 Ma, the seaward effective elastic thickness T _e ^M values are located between 600 and 900°C isotherms, and do not track any isotherm, while the majority of the trenchward effective elastic thickness T _e ^m values are located between 300 and 600°C isotherms. For the plate age older than 50 Ma, T _e ^M values basically matches the 600°C isotherm with some fluctuations for the age older than 110 Ma, while T _e ^m values mainly fall between 200 and 400°C isotherms. The reduction in effective elastic thickness (T _e ^M-T _e ^m) varies from 2.6 to 30.1 km, or 11–68% of seaward T _e ^M. Thus, the absolute value of the decrease in the effective elastic thicknesses (T _e ^M-T _e ^m) increases with the plate age, while the percentage reduction in the effective elastic thickness (1-T _e ^m/T _e ^M) has no obvious relationship with the age, but more related to the curvature of bending plate. Almost all bending-related earthquakes occurred above the T _e ^M line, but many normal-faulting earthquakes are deeper than the T _e ^M-T _e ^m line, implying that the plate may still retain some thickness of an elastic property core in the areas (depth) where earthquakes occur.     

碎石环梁与混凝土环梁超大储罐强夯地基沉降变形对比研究

地层沉降及不均匀沉降控制是储罐建造安全性保障的重要环节。本文重点分析了加设碎石环梁强夯地层的沉降变形特征,综合比较了碎石环梁与混凝土环梁加固储罐地基土的环向、径向沉降与不均匀沉降差异;指出地层差异能影响两类环梁基础的地基土加固效果;考察了碎石环梁弹性模量改变对储罐地基土沉降规律的影响;比较了截面为矩形的混凝土环梁与梯形碎石环梁对储罐地层的加固效果;并给出了碎石环梁加固储罐地基土的工程建议。研究成果可为类似工程建设提供借鉴参考。     

Fundamental results concerning the settlement of a rigid foundation on an elastic medium due to an adjacent surface load

This paper examines the interaction between a rigid circular foundation resting in smooth contact with an isotropic elastic halfspace and a concentrated surface load which acts at a finite distance from the foundation. Owing to the action of the external load the rigid foundation experiences an extra settlement and a tilt. The expressions for the extra settlement and the tilt are evaluated in exact closed form. It is also shown that these deformations due to the external load satisfy Betti's reciprocal theorem. The auxiliary solution required for the application of the reciprocal theorem is derived from the analysis of the problem of a rigid circular foundation resting in smooth contact with an elastic medium and subjected to an eccentric load. The, results developed for the interaction between the rigid circular foundation and the external concentrated load are utilized to generate, among others, solutions for the settlement and tilt induced at a rigid foundation due to its interaction with uniformly or non-uniformly distributed loads with circular and square plan shapes.     

Vertical deformation of rigid foundations of arbitrary shape on layered soil media

A numerical procedure is described for the analysis of vertical deformation of smooth, rigid foundations of arbitrary shape on homogeneous and layered soil media. The contact area at the interface of the foundation and soil medium is approximated by square subdivisions. The response of the system is then obtained from the superposition of the influence of the individual subdivisions. The flexibility influence coefficients are based on equivalent smooth, rigid circular areas with the same contact area as the square subdivisions. For foundations on a homogeneous, isotropic elastic half-space, the flexibility coefficients are given analytically by the integrated forms of the Boussinesq's solution. For a layered soil medium, the flexibility coefficients are determined from an axisymmetric finite element analysis which is essentially two dimensional. Thus, there is no necessity for a full three-dimensional finite element analysis. Comparison with solutions obtained using the integral transform technique for smooth, rigid rectangular foundations on a homogeneous, isotropic elastic half-space shows good agreement. Parametric solutions are presented for the response of rectangular foundations on some ‘typical’ soil profiles. The use of a simplified method to estimate the settlement of rectangular foundations on a layered soil medium by superposing solutions for homogeneous, elastic strata is discussed.     

Relations between load and settlement of circular foundations on or in a dense sand expressed by a function of diameter and depth

When load acts on a circular foundation on or in a dense sand, average contact pressure on the lower surface of the foundation is q and settlement of the foundation is s. Diameter and depth of the foundation are B and D_f. When the sand, B and D_f are given, we can know the relation between q and s/B by, e.g. a loading test, i.e. the relation is determined by B and D_f for the sand. Using the results of numerical analyses, we express a relation between q and s/B up to s=0.1B by functions of a single variable which is a linear combination of B and D_f. Consequently when two foundations have different B's and different D_f's but have the same value of the variable, the relations are the same. Then we examine whether the functions can express the results of eleven tests of model foundations of wide range of B and/or D_f. In all the tests, the relations are expressed with sufficient accuracy. Copyright © 2005 John Wiley & Sons, Ltd.     

油罐基础不均匀沉降主要影响因素的敏感性分析

在上部均布荷载作用下柔性基础基底压力是均匀分布的,基底以下土体在同一深度附加应力呈现中间大、周围小的分布规律,导致基础沉降中间大、周围小。刚性基础的沉降是均匀的,必然导致基底压力的分布为周围大、中间小。软基上的油罐筏板基础是具有一定刚度的基础,但并非刚性基础,因而基底压力分布应该介于柔性基础和刚性基础之间,沉降为中间大、周围小的不均匀分布。基于ABAQUS有限元分析,结合工程实际情况,采用UH模型作为土体本构模型进行了模拟分析,对筏板厚度、地基刚度等影响基础不均匀沉降的主要因素进行敏感性分析,探求变刚度地基在油罐基础不均匀沉降中的影响规律。     

Field and Laboratory Tests Investigating Settlements of Foundations on Weathered Keuper Marl

Measured settlements of buildings on the weathered Keuper Marl appeared to be much smaller than calculated settlements, which were based on stiffness modulus from standard oedometer tests. Therefore, both special triaxial K ₀-tests and oedometer tests were carried out for an accurate determination of stiffness moduli. Modulus obtained in the triaxial K ₀-tests were at least two to three times the values obtained in the oedometer tests. To verify observations from the laboratory tests, the loads and the settlements of two single footings on weathered Keuper mudstone have been measured during construction of a building over 1 year. Also, a large scale footing load test with measurements of deformations were conducted on the weathered Keuper mudstone. The measured settlements of the two single footings and the tested foundation were compared with the settlements based on conventional calculations with moduli from oedometer tests and triaxial K ₀-tests. Up to a foundation pressure of σ_v = 500 kN/m2 the calculated settlement based on E _S-modulus obtained from triaxial K ₀-tests was found to correspond well to the measured deformation. For foundation pressure beyond 500 kN/m2, the foundation response was highly non-linear and it could not be described any more with the linear-elastic model. Therefore the footing load test was also simulated by FEM analyses.     

On the Ratios between Elastic Modulus and Uniaxial Compressive Strength of Heterogeneous Carbonate Rocks

The ratios M _R = E/σ _c for 11 heterogeneous carbonate (dolomites, limestones and chalks) rock formations collected from different regions of Israel were examined. Sixty-eight uniaxial compressive tests were conducted on weak-to-strong (5 MPa < σ _c < 100 MPa) and very strong (σ _c > 100 MPa) rock samples exhibiting wide ranges of elastic modulus (E = 6100–82300 MPa), uniaxial compressive strength (σ _c = 14–273.9 MPa), Poisson's ratio (ν = 0.13–0.49), and dry bulk density (ρ = 1.7–2.7 g/cm³). The observed range of M _R = 60.9–1011.4 and mean value of M _R = 380.5 are compared with the results obtained by Deere (Rock mechanics in engineering practice, Wiley, London, pp 1–20, 1968) for limestones and dolomites, and the statistical analysis of M _R distribution is performed. Mutual relations between E, σ _c, ρ, M _R for all studied rocks, and separately for concrete rock formations are revealed. Linear multiple correlations between E on the one hand and σ _c and ρ on the other for Nekorot and Bina limestone and Aminadav dolomite are obtained. It is established that the elastic modulus and M _R in very strong carbonate samples are more correlated with ρ−σ _c combination and ε _a max, respectively, than in weak to strong samples. The relation between M _R and maximum axial strain (ε _a max) for all studied rock samples (weak-to-strong and very strong) is discussed.     

On the optically biaxial character and heterogeneity of anthracites

The results of the study of optical properties of 13 anthracites from different parts of the world are presented in this paper. Measurements of reflectance values were made on non-oriented vitrinite grains for a minimum of 300 points per sample. The reconstruction of Reflectance Indicating Surfaces (RIS) were made by Kilby's method [Kilby, W.E., 1988. Recognition of vitrinite with non-uniaxial negative reflectance characteristics. Int. J. Coal Geol. 9, 267–285; Kilby, W.E., 1991. Vitrinite reflectance measurement — some technique enhancements and relationships. Int. J. Coal Geol. 19, 201–218]. It was found that the use of Kilby's method for strongly anisotropic materials like anthracites did not give unambiguous results. Some improvement in Kilby's method, consisting of the division of the cumulative cross-plot into several elemental components, is suggested. Each elemental cross-plot corresponds to a textural class of anthracite, which is characterized by the values of RIS main axes R_MAX^(k), R_INT^(k) and R_MIN^(k) (k=1,2,…n; n — number of classes). The global texture of anthracite is characterized as a RIS with main axes calculated as the weighted means of , and for each class of this anthracite.The division of cumulative Kilby's cross-plot on elemental components makes possible the calculation of new coefficients H_t and H₁₀ characterizing the heterogeneity of the structure and texture of anthracites. The results of our study show that all anthracites have biaxial negative textures, but their heterogeneity varies in a wide range of H_t and H₁₀ coefficients depending upon the individual coal basin.     

Dynamic Response of Pile Reinforced Soils and Piled Foundations

The rigid-pile soil-improvement technique aims to increase the bearing capacity of the soil and decrease the settlement of the surface structure. The most remarkable difference of this technique from the deep-foundation system is the soil layer between the pile heads and the structure. This soil layer, called the mattress, is made of compacted granular materials and participates in the load transfer through arching and shear mechanisms. In order to understand the dynamic behavior of rigid-pile reinforced soils, tri-dimensional finite-element analyses of a soil-pile-slab system, a soil-pile-mattress-slab system, and a soil-pile-mattress-embankment system are presented in this paper. Different geometric configurations are studied in terms of dynamic impedances. The soil, piles, mattress, and embankment are represented as continuum solids, and the slab is represented by structural plate-type elements. The horizontal and vertical impedances of pile foundations are presented and the results are compared with studies in the literature. This study shows the influence of the mattress stiffness, the geometrical configuration, and head/tip fixity conditions on the dynamic response of the foundation system. A comparison between rigid piles and pile foundations is then presented.