| Vibrating grouting method is a new way to treat weak foundation. The sand of foundation is made destructive by vibrating load at first, and as a result its strength is weakened in this destructive area. Under the condition of high pressure, the grout is easier to be poured into the foundation. From what is said above, we know that vibration is important to the grouting method. In this paper, the author studies the sand response under the vibrating load carefully to provide the vibrating grouting method with good parameters.At first, the sand is studied through the dynamic tri-axial experiment, in which we use a computer-controlled system which is advanced in our country. With the data recorded by computer, the author studies the experiment progress in detail, which includes the development of pore press, strain, strength of the sand, etc. Connecting the development of these phenomena with the development of stress path, the author finds new mechanism which can explain the phenomena in the experiment. What is more, according to the dynamic test of the sand, there appears a steady state at the last phase of the development of strain and stress path, in which the strength of the sand is studied because it is an important parameter in evaluating the stability of sand against liquefaction.Secondly, the dynamic constitutive relation was studied through the dynamic tri-axial test. According to the different behavior of stress status in the experiment, the progress is divided into four phases. A new sand constitutive relation connecting the relationship between stress and strain with the stress path is set up to reflect these phases, at the same time the phenomenon of shear contraction, shear dilatation and unloading shrink are taken into account in this constitutive relation. Extracting the merit of the nonlinear model and plastic-elastic model, it is simple and effective. The computation results show that the dynamic constitutive relation can reflect most of the phenomena in the process of experiment . Thirdly, because there is local large deformation in the sand breakage under vibrating load in the destructive phase, small deformation theory is not appropriate; therefore, large deformation analysis theory is applied to this process. Based on the research of many predecessors, the author sets up a computation pattern of the saturated sand deduced from energy theory. In this pattern a new kind of infinite boundary element is developed to reduce wave reflection on the boundary. By this method, a simple and convenient numerical way is worked out and dissipation of the pore press, damping can be taken into account. It can not only solve the problem of material nonlinearity, but also be suitable for the problem of large deformation.Based on the work of Dr. Yang Guolin, a finite element program is worked out according to the finite element theory. The data to be imputed can be generated by software Super-Sap93, which can simplify the work of data preparation. In this program, the material nonlinearity and geometry nonlinearity are taken into account; what is more, it can calculate two-dimensional stress, strain and axial symmetry problems of foundation, tunnel, etc. Aftercontrasting tri-axial experiment data with the computational result of the program, we can see that the program works well.Fourthly, with the finite element program, the author analyzes the relationship between the load magnitude or frequency and range of breakage or pore pressure. This can provide appropriate parameters for the method of vibrating grouting.Fifthly, adopting the compressible porous medium, the author adduced dynamic theory of liquid saturated porous medium to analyze the displacement and force in the sand when there is dynamic load below the earth surface. Supposed to be axial symmetry, the problem is put into the cylindrical coordinate, and through the Laplace-Hankel transformation, the equations are turn into differentia equations of constant coefficient. In the analyzing progress, dynamic transfer matrix is used t...
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