变刚度复合地基变形控制设计理论研究
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摘要
复合地基的受力机理复杂,影响地基变形的因素很多,诸如天然地基物理特性、桩身强度、桩间距、桩长、桩身尺寸、上部结构刚度等都会对复合地基的变形产生影响。针对这些问题,综合运用理论分析、数值模拟等方法,对不布桩模式下的地基变形情况进行了系统研究,对各种因素影响规律进行了分析。在此基础上,给出了控制复合地基变形的优化设计方法,最后通过工程实践证明该方法适用、经济,满足工程精度要求。
对地基单一受力区域三维分层中的桩基础,运用分层材料介质的广义Kelvin基本解的边界元法,就单桩位移和群桩共同作用进行了理论分析,并建立了分层地基中桩基础边值问题的边界积分方程；对地基相邻受力区域按照刚性基础分析,假定被影响刚性基础的基底与地基紧密接触,将接触面划分为n个矩形网格,在上部荷载与相邻区域基础荷载影响下,考虑基础埋深和建筑物高度对倾斜的影响,建立了刚性基础地基反力和整体倾斜基本方程,应用迭代法对相邻区域共同作用进行分析。
本文采用FLAC3D有限差分程序,考虑桩身长L、桩直径D、桩间距S、上部刚度K、复合地基的置换率m等影响因素,对应不同布桩模式建立了8组共39个数值模型,分别就均布荷载和非均布荷载两种受力模式下的地基变形特征展开系统数值模拟研究,并对各种影响要素进行理论分析。数值模拟研究结果表明：
(1)水平方向变形特征：①桩顶位置在所有变刚度模式下的各关键竖向变形均符合指数衰减特征,最大变形值位于荷载形心,最小值则位于基础端角,其次是板边。水平方向变形等值线均呈现同心圆形状,与基础形状及加载区域形状关系不密切。②桩底位置由于剪切位移的连续性,表现出较好的自适应调节能力,在所有变刚度模式中未出现变形突变,桩底变形情况受桩长影响最大,桩距、桩径对变形无影响,随土层深度增加,变形逐步过渡为平滑的碗形。
(2)竖向变形特征：①桩顶位置变形表现为“同心圆柱”,而且这种情况会一直持续到约桩长一半。②桩底位置由于不存在上部刚度约束,其变形情况与平面、竖向布桩形式有关。
(3)应力分布特征：①复合地基4个端角桩顶位置的主应力、竖向反力呈现高度应力集中,使得该范围复合地基进入承载力极限状态,但是变形受邻域影响仍会继续发展,变刚度模式对该范围调节能力有限。次一级应力集中现象出现板边中部,形成一个环绕基础的应力带；地基内部应力水平受地基竖向刚度变化影响较大,表现为随刚度加强而聚集；变桩长模式对调整应力分布最为有效的,变桩径、变桩距模式影响不大；②桩底位置应力特征表现为桩身将竖向荷载传递至土层深部,竖向应力水平在桩端位置有所提高。
(4)变桩长对地基变形调节能力最强。随着荷载形心区域桩长的增加,边缘区域和角点区域地基变形量都会明显减小；边缘区域和角点区域桩长增加同样会减小中心区域的地基变形量,且各个关键点的变形总量与复合地基的整体桩身体积置换率成线性反比关系。
(5)最佳控制地基变形的布桩模式为：在均布荷载计算模式下,中区、边区、角区的桩长(其他设计参数一致)满足5：4：3规律；在非均布荷载作用下的中区、边区、角区的理想桩长则是5：4：3乘以各自区域的荷载大小比例系数。
(6)桩径、桩距的调整导致复合地基应力水平的变化异常复杂；无论改变桩径、桩距对基础局部倾斜没有影响；变桩径模式提高了局部地基刚度,竖向反力向刚度较大区域聚集,桩土共同作用减弱,局部地基变形量反而有增大趋势。
在此基础之上以先“放”后“抗”为原则,本文给出了系统的变刚度复合地基设计解决方案。简单的归纳为：中、边、角；5：4：3；内强外弱；共同作用；整体考虑；相邻兼顾；反复迭代。
本文得到的一些规律性的结论和设计理念,在满足整体承载力前提下,对复合地基的变形控制、最小化变形差,降低基础和上部结构次应力,提高建筑物耐久性和使用寿命及开拓岩士工程设计思路等方面具有重要指导意义。
Composite foundation, which force mechanism is complex, has many influence factors for its deformation, such as the physical characteristics of natural foundation, pile strength, pile spacing, pile's length, pile's geometry dimension, the upper structure rigidity and so on. In view of these problems, theory analysis and numerical simulation methods were used to system research the foundation deformation under the condition of piles'different arrangements, and qualitative analysis was made to analysis the various Influence factors. Based on this, optimum design method was proposed to control the deformation of composite foundation. Engineering practice proves that the method is applicable and economic, which can satisfy the request of engineering.
In light of pile foundation of 3D layered foundation with single stressed region, generalized Kelvin basic solution's BEM about layered properties media was used to made theory analysis on the cooperation work between single pile displacement and pile groups, and boundary integral equation was established about pile foundation's boundary value problem in layered foundation, in which the integrate on layered properties'interface was not included. The foundation adjacent stressed region was analysized according to rigid foundation, assuming basement and foundation soil of rigid foundation were close contact, under the influence of upper loads and adjacent foundation load, the surface contact was divided into n rectangular grids. Considering embedded depth of foundation and building height impact on inclination, subgrade reaction and overall inclination of rigid foundation basic equation is presented, and iterative method is obtained by the analysis above.
Three-dimensional finite-difference software FLAC3D, considering pile's length L, pile spacing S, Poisson ratio of natural foundation soil and displacement ratio of composite foundation, was adopted for the simulation of deformation characteristic of ground soil, in this paper. Depending on different arrangements of piles,39 numerical models (8 groups) were set. A series of numerical simulations on loading mode of nonuniform load and uniform load were respectively carried out, and qualitative analysis of various influence factors was conducted.
The numerical simulation showed that the horizontal deformation of the location of composite foundation pile head, variable stiffness in all modes of vertical deformation of the key features are in line with exponential decay, the maximum deformation in the load centroid, the minimum is located in the base-side corner, followed by is the edge. Horizontal contour deformation showed a concentric shape, and it is not close to the foundation shape and the loading area shape; the vertical deformation of the continuity of the shear displacement showed better adaptive ability in the pile location, and all variable stiffness does not appear in the deformation mode of mutation, the pile length have the greatest impact on the pile bottom deformation. Pile spacing and pile diameter has no effect on the deformation, and the gradual deformation of a smooth transition is going to be the bowl shape with the increase of soil depth.
Vertical deformation of pile top position is characterized as "concentric cylindrical", and this situation will continue until about half the pile length; and the bottom of the pile is in relation to the flat pile in the form the form of vertical pile because there is no upper bound stiffness.
Through numerical simulations show that stress distribution on pile top position:the basic four horns including principal stress and the vertical force appears highly stress concentration, makes the scope of composite foundation bearing capacity limit state into, but the deformation of neighborhood influence will continue to develop, the scope of variable stiffness mode adjust ability is limited, Sub-tissue stress concentration phenomenon appear in central plate edge, forming a foundation with the stress around, Internal stress level ground by vertical stiffness foundation changes for greater influence over stiffness and strengthening, varied length of piles to adjust the stress distribution pattern is the most effective and varied diameter of piles, varied distance of piles has little effect. The pile bottom position stress characteristics show that pile body make the vertical load transfer to the deep layer, the vertical stress level in the pile tip is somewhat increased.
Variable pile height has strong adjusted ability on foundation deformation. With the load area length of pile centroid increases, the edge area and corner area will significantly reduce the amount of ground deformation; the increase of the pile length of the edge area and comer area will reduce the ground deformation of the central area, and the key points of each total deformation and the overall composite foundation pile volume replacement ratio have linear inverse relationship.
Optimal control by numerical simulation of the pile foundation deformation mode:in the uniform load calculation mode, the central, border, corner area of the pile length (consistent with other design parameters) is to satisfy the law 5:4:3; in non-uniform loads under the area, border, corner area the ideal length of pile is to satisfy the law 5:4:3 multiplied by the size of their respective regional load scale factor.
Stress level of composite foundation varies complicatedly on the grounds that pile diameter and pile spacing are adjusted. While often adjustment of pile diameter and pile spacing have no effect on local foundation inclination, model of pile with varying diameter improves local foundation stiffness,and regions of larger stiffness gather to accumulate vertical force gradually, and pile-soil interaction weakens gradually and deformation quantity of local ground foundation shows an increasing tendency.
Based on the principle of valuation after resistance, this paper presents some effective solutions to designs of varying stiffness composite foundation.Specifically,it can be classified into seven essential points:medium-edge-angle, five to four to three, strongly inner weakly outer,interaction,considered as a whole,consideration of adjacent elements and repeated iteration.
In this paper, some regularity conclusions and design concept are obtained. On the premise of general bearing capacity satisfied, conducting a study is of important directive significance in deformation control of composite foundation, minimization of deformation difference, reduction of secondary stress for foundation and superstructure, improvement of durability and service life for building and development plans of main design ideas for geotechnical engineering.
对地基单一受力区域三维分层中的桩基础,运用分层材料介质的广义Kelvin基本解的边界元法,就单桩位移和群桩共同作用进行了理论分析,并建立了分层地基中桩基础边值问题的边界积分方程；对地基相邻受力区域按照刚性基础分析,假定被影响刚性基础的基底与地基紧密接触,将接触面划分为n个矩形网格,在上部荷载与相邻区域基础荷载影响下,考虑基础埋深和建筑物高度对倾斜的影响,建立了刚性基础地基反力和整体倾斜基本方程,应用迭代法对相邻区域共同作用进行分析。
本文采用FLAC3D有限差分程序,考虑桩身长L、桩直径D、桩间距S、上部刚度K、复合地基的置换率m等影响因素,对应不同布桩模式建立了8组共39个数值模型,分别就均布荷载和非均布荷载两种受力模式下的地基变形特征展开系统数值模拟研究,并对各种影响要素进行理论分析。数值模拟研究结果表明：
(1)水平方向变形特征：①桩顶位置在所有变刚度模式下的各关键竖向变形均符合指数衰减特征,最大变形值位于荷载形心,最小值则位于基础端角,其次是板边。水平方向变形等值线均呈现同心圆形状,与基础形状及加载区域形状关系不密切。②桩底位置由于剪切位移的连续性,表现出较好的自适应调节能力,在所有变刚度模式中未出现变形突变,桩底变形情况受桩长影响最大,桩距、桩径对变形无影响,随土层深度增加,变形逐步过渡为平滑的碗形。
(2)竖向变形特征：①桩顶位置变形表现为“同心圆柱”,而且这种情况会一直持续到约桩长一半。②桩底位置由于不存在上部刚度约束,其变形情况与平面、竖向布桩形式有关。
(3)应力分布特征：①复合地基4个端角桩顶位置的主应力、竖向反力呈现高度应力集中,使得该范围复合地基进入承载力极限状态,但是变形受邻域影响仍会继续发展,变刚度模式对该范围调节能力有限。次一级应力集中现象出现板边中部,形成一个环绕基础的应力带；地基内部应力水平受地基竖向刚度变化影响较大,表现为随刚度加强而聚集；变桩长模式对调整应力分布最为有效的,变桩径、变桩距模式影响不大；②桩底位置应力特征表现为桩身将竖向荷载传递至土层深部,竖向应力水平在桩端位置有所提高。
(4)变桩长对地基变形调节能力最强。随着荷载形心区域桩长的增加,边缘区域和角点区域地基变形量都会明显减小；边缘区域和角点区域桩长增加同样会减小中心区域的地基变形量,且各个关键点的变形总量与复合地基的整体桩身体积置换率成线性反比关系。
(5)最佳控制地基变形的布桩模式为：在均布荷载计算模式下,中区、边区、角区的桩长(其他设计参数一致)满足5：4：3规律；在非均布荷载作用下的中区、边区、角区的理想桩长则是5：4：3乘以各自区域的荷载大小比例系数。
(6)桩径、桩距的调整导致复合地基应力水平的变化异常复杂；无论改变桩径、桩距对基础局部倾斜没有影响；变桩径模式提高了局部地基刚度,竖向反力向刚度较大区域聚集,桩土共同作用减弱,局部地基变形量反而有增大趋势。
在此基础之上以先“放”后“抗”为原则,本文给出了系统的变刚度复合地基设计解决方案。简单的归纳为：中、边、角；5：4：3；内强外弱；共同作用；整体考虑；相邻兼顾；反复迭代。
本文得到的一些规律性的结论和设计理念,在满足整体承载力前提下,对复合地基的变形控制、最小化变形差,降低基础和上部结构次应力,提高建筑物耐久性和使用寿命及开拓岩士工程设计思路等方面具有重要指导意义。
Composite foundation, which force mechanism is complex, has many influence factors for its deformation, such as the physical characteristics of natural foundation, pile strength, pile spacing, pile's length, pile's geometry dimension, the upper structure rigidity and so on. In view of these problems, theory analysis and numerical simulation methods were used to system research the foundation deformation under the condition of piles'different arrangements, and qualitative analysis was made to analysis the various Influence factors. Based on this, optimum design method was proposed to control the deformation of composite foundation. Engineering practice proves that the method is applicable and economic, which can satisfy the request of engineering.
In light of pile foundation of 3D layered foundation with single stressed region, generalized Kelvin basic solution's BEM about layered properties media was used to made theory analysis on the cooperation work between single pile displacement and pile groups, and boundary integral equation was established about pile foundation's boundary value problem in layered foundation, in which the integrate on layered properties'interface was not included. The foundation adjacent stressed region was analysized according to rigid foundation, assuming basement and foundation soil of rigid foundation were close contact, under the influence of upper loads and adjacent foundation load, the surface contact was divided into n rectangular grids. Considering embedded depth of foundation and building height impact on inclination, subgrade reaction and overall inclination of rigid foundation basic equation is presented, and iterative method is obtained by the analysis above.
Three-dimensional finite-difference software FLAC3D, considering pile's length L, pile spacing S, Poisson ratio of natural foundation soil and displacement ratio of composite foundation, was adopted for the simulation of deformation characteristic of ground soil, in this paper. Depending on different arrangements of piles,39 numerical models (8 groups) were set. A series of numerical simulations on loading mode of nonuniform load and uniform load were respectively carried out, and qualitative analysis of various influence factors was conducted.
The numerical simulation showed that the horizontal deformation of the location of composite foundation pile head, variable stiffness in all modes of vertical deformation of the key features are in line with exponential decay, the maximum deformation in the load centroid, the minimum is located in the base-side corner, followed by is the edge. Horizontal contour deformation showed a concentric shape, and it is not close to the foundation shape and the loading area shape; the vertical deformation of the continuity of the shear displacement showed better adaptive ability in the pile location, and all variable stiffness does not appear in the deformation mode of mutation, the pile length have the greatest impact on the pile bottom deformation. Pile spacing and pile diameter has no effect on the deformation, and the gradual deformation of a smooth transition is going to be the bowl shape with the increase of soil depth.
Vertical deformation of pile top position is characterized as "concentric cylindrical", and this situation will continue until about half the pile length; and the bottom of the pile is in relation to the flat pile in the form the form of vertical pile because there is no upper bound stiffness.
Through numerical simulations show that stress distribution on pile top position:the basic four horns including principal stress and the vertical force appears highly stress concentration, makes the scope of composite foundation bearing capacity limit state into, but the deformation of neighborhood influence will continue to develop, the scope of variable stiffness mode adjust ability is limited, Sub-tissue stress concentration phenomenon appear in central plate edge, forming a foundation with the stress around, Internal stress level ground by vertical stiffness foundation changes for greater influence over stiffness and strengthening, varied length of piles to adjust the stress distribution pattern is the most effective and varied diameter of piles, varied distance of piles has little effect. The pile bottom position stress characteristics show that pile body make the vertical load transfer to the deep layer, the vertical stress level in the pile tip is somewhat increased.
Variable pile height has strong adjusted ability on foundation deformation. With the load area length of pile centroid increases, the edge area and corner area will significantly reduce the amount of ground deformation; the increase of the pile length of the edge area and comer area will reduce the ground deformation of the central area, and the key points of each total deformation and the overall composite foundation pile volume replacement ratio have linear inverse relationship.
Optimal control by numerical simulation of the pile foundation deformation mode:in the uniform load calculation mode, the central, border, corner area of the pile length (consistent with other design parameters) is to satisfy the law 5:4:3; in non-uniform loads under the area, border, corner area the ideal length of pile is to satisfy the law 5:4:3 multiplied by the size of their respective regional load scale factor.
Stress level of composite foundation varies complicatedly on the grounds that pile diameter and pile spacing are adjusted. While often adjustment of pile diameter and pile spacing have no effect on local foundation inclination, model of pile with varying diameter improves local foundation stiffness,and regions of larger stiffness gather to accumulate vertical force gradually, and pile-soil interaction weakens gradually and deformation quantity of local ground foundation shows an increasing tendency.
Based on the principle of valuation after resistance, this paper presents some effective solutions to designs of varying stiffness composite foundation.Specifically,it can be classified into seven essential points:medium-edge-angle, five to four to three, strongly inner weakly outer,interaction,considered as a whole,consideration of adjacent elements and repeated iteration.
In this paper, some regularity conclusions and design concept are obtained. On the premise of general bearing capacity satisfied, conducting a study is of important directive significance in deformation control of composite foundation, minimization of deformation difference, reduction of secondary stress for foundation and superstructure, improvement of durability and service life for building and development plans of main design ideas for geotechnical engineering.
引文
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