【作者】 张敏；

【导师】 吕爱钟；

【作者基本信息】 华北电力大学(北京) ， 水利工程， 2022， 硕士

【摘要】 随着建筑物高度和密集程度的不断增加,加强对地基在建筑物基础作用下的研究成为当下值得重视的工作。对于上方作用有浅埋条形基础,下方卧有基岩的弹性土层,当基岩的刚度相较于土层足够大时,可以认为土层与基岩接触面的位移为零。本文在土层与上方基础接触面的位移给定的前提下,对地基内土层的应力和位移场进行了求解。根据平面弹性的复变函数理论,地基内的应力与位移场可以由两个解析函数给出。利用保角变换将物理平面上有限厚度的层状地基映射为象平面上的单位圆内域,解析函数在单位圆内域可以写为只含有正幂次项的幂级数的形式,幂级数的系数由土层上方和下方的应力与位移边界条件确定。在具体计算时,使用边界配点法建立起关于幂级数系数的线性方程组,通过求解线性方程组确定解析函数。将解析方法得到的结果和ANSYS数值方法的结果进行了比较,发现两者的结果吻合的较好,由此可以证明本文推导过程的正确性。主要研究内容和结论如下:(1)对于单个条形基础作用下的土层,根据保角变换和复变函数理论,对条形基础与地基接触面的应力分布以及土层内部各处的应力和位移进行了研究,并通过算例讨论了接触面不同位移模式以及不同土层厚度对土层应力的影响。发现当位移边界条件给定时,土层同一点的应力会随着土层厚度的增大而减小。在基础作用的附近土体,其应力的分布会受到土层厚度的影响。当土层与条形基础接触面的位移模式不同时,会使土层的应力分布有很大差别,特别在接触面上。本文研究的两种位移模式中,刚性基础均匀沉降的基底压力呈抛物线式分布,而可变形基础的基底压力分布较为均匀,基底中间部分应力较两端稍大。(2)对于相邻条形基础作用下的土层,考虑条形基础间相互干涉作用的影响,对条形基础与地基接触面的应力分布以及土层内部各处的应力和位移进行了研究,并通过算例讨论了不同土层厚度、距宽比(相邻基础的净间距与基础宽度的比值)、沉降差以及基础宽度不等对土层应力的影响。随着距宽比的增大,基础产生相同位移的合力增大,但增大的幅度却越来越小,且不同基础宽度下相同距宽比的基础合力比值是不同;相邻基础之间间距越大,沉降差允许值越大,作用在相邻基础上的合力之差越大;对于宽度不等的相邻基础,研究发现虽然作用在宽度大的基础合力较大,但却是宽度小的基础附近土体应力较大。更多还原

【Abstract】 As the height and density of buildings growing,strengthening the research on the foundation under the action of building footing has become a work worthy of attention at present.Consider an elastic soil layer with a shallow-buried strip footing at the upper boundary and bedrock at the lower boundary,the displacement along the contact surface between the soil layer and the bedrock can be considered as zero when the bedrock is sufficiently rigid relative to the soil layer.In this paper,the stress and displacement fields in the soil layer are solved on the premise that the displacement on the contact surface between the soil layer and the strip footing is given.The stress and displacement fields in the foundation can be given by two analytical functions according to the complex variable method of plane elasticity.The soil layer with the finite thickness on the physical plane is mapped onto the inner domain of the unit circle on the image plane based on the conformal transformation.The analytical function in the unit circle domain can be written as a power series containing only positive power terms.The coefficients of which can be determined by the stress and displacement boundary conditions on the upper and lower boundaries of the soil layer.In calculation,the linear equations about the power series coefficients are established by using the boundary collocation method,and the analytical function is determined by solving the linear equations.The obtained results of the analytical solution are compared with the results of the numerical method based on ANSYS.It is found that the two results are in good agreement,which can prove the correctness of the derivation process in this paper.The main research contents and conclusions are as follows:(1)For the soil layer under the action of a single strip footing,the stress distribution of the contact surface between the foundation and the strip footing and the stress and displacement in the soil layer are studied according to the conformal transformation and complex variable function theory.The effects of different displacement modes of contact surface and different soil layer thickness on soil stress are discussed through examples.It’s found that the stress at the same point of the soil layer will decrease with the increase of the thickness of the soil layer when the displacement boundary condition is given.The stress distribution will be different in the soil layer close to the footing area for different soil thicknesses.If the displacement mode of the contact surface between the soil layer and the strip footing is different,the stresses distribution in the soil layer will be changed greatly,especially for the stresses on the contact surface.In the two displacement modes studied in this paper,the base pressure of uniform settlement induced by rigid footing presents a parabolic distribution.However,the base pressure distribution is more uniform for deformable footing,and the stress in the middle part of the base is slightly larger than that at both ends.(2)For the soil layer under the action of adjacent strip footings,considering the influence of mutual interference between strip footings,the stress distribution on the contact surface between strip footing and foundation and the stress and displacement in various parts of the soil layer are studied.The effects of different soil layer thickness,spacing width ratio(the ratio of net spacing between footings to footing width),differential settlement and unequal footing width on soil stress are discussed through examples.With the increase of the distance width ratio,the resultant force of the footing to produce the same displacement will increase,but the increasing range is smaller and smaller.The ratio of the resultant force of the footing with the same distance width ratio is different under different footing widths.The greater the spacing between adjacent footings,the greater the allowable value of settlement difference,and the greater the difference of resultant force acting on adjacent footings.For adjacent footings with different widths,it is found that although the resultant force acting on the footing with large width is larger,the soil stress near the footing with small width is larger.更多还原