Evaluation of Stone Columns Installation on Fundamental Frequency of Site with Finite Elements Method

Installation of stone columns is one of the proper and known methods for the improvement of weak soils. Stone column construction are employed to improve the bearing capacity, slope stability, and drainage rate, as well as reducing the settlement and liquefaction potential of the soft soil. In geotechnical earthquake engineering, stone columns are generally used to control the liquefaction potential of loose granular soils. However, the seismic performance of these inclusions has been partially studied and requires more researches. On the other hand, it is important to estimate a fundamental frequency of site for the seismic design of buildings and infrastructures and considers the basis of site classifications in seismic codes.
In this paper, the effects of stone column construction on the fundamental frequency of the sites are studied numerically. Finite element analysis was performed using ABAQUS. The analysis is a modal analysis through the calculation of eigenvalues. Analyses was carried out in 3D and 2D in some cases. According to the modal analysis of the problem, the behavior of the soil and stone column are considered linear elastic. Additionally, the shear wave velocity and density of the soil and stone columns are assumed constant in depth. The results demonstrated that stone columns construction can increase the fundamental frequency of the site to four times. The fundamental frequency amplification factor of the site (α) can be defined according to the dimensionless parameters including stone column to soil shear wave velocity, height to diameter, distance to diameter, and stone column arrangements.
The results indicated that α decreased with a rise in the ratio of the stone column height to diameter. Stone column arrangements are either square or triangle. When the triangle and square arrangements is used, zones of influences by each column as a regular hexagon and square, respectively. A comparison of the stone column arrangements demonstrated that, in triangle arrangement, α was greater than the corresponding value in square arrangement. The reason behind this is that in triangle arrangements, the zones of influence of each column is greater than the similar value in the square arrangement. Depending on the height of the column and depth of the bedrock, stone columns can be constructed as end bearing with their end on the bedrock or as floating with free end in the soil. The results indicate that, in floating stone columns, the effects of stone columns on α with respect to the condition where the stone column was end bearing, was considerably insignificant. In the following, tri-variant relation was determined for α. This relation was achieved using the Evolutionary Polynomial Regression (EPR). This method utilizes multi-objective genetic programming to derive regression equations by constructing symbolic models. Two-thirds of the data chosen to operate as training data and the other was used as testing data. The statistical parameters showed the good correlation and high accuracy of the derived relation for training and    testing data. In the following, the problem is done in plane strain condition (2D). For this purpose, stone columns which were in a row, were assumed as equivalent strips and these strips were supposed as a set of considerable rigid retaining walls in the soil profile. Similar to the 3D case, α can be presented by the values of dimensionless parameters. Finally, a 2D equivalent method for simplification of the 3D actual problem will be presented by examining the various cases. The results suggest that in the case the inertial moment of stone columns in 3D equal to 2D, relatively good approximation exists between the actual 3D and the equivalent 2D results.