Abstract: Groundwater distribution and determination of rock mass permeability parameters are very important in the process of underground engineering construction. Based on analysis of the objective function of underdetermined problem, and through the use of fitness function and the principle of geological statistics and variation function optimization, we obtain a class of hydrogeological problems' penalty function for solving formation permeability coefficient, which provides an optimized evaluation criterion to solve the problem of inverse analysis of underdetermined problem. Also, a mathematical model of optimized back analysis combined with particle swarm optimization (PSO) algorithm is established, and a new method to evaluate formation permeability coefficient is proposed using back analysis of the drilling head change from packer permeability test. At Nanjing Shang Yuanmen subway station, we conduct packer permeability test to get drilling head height on-site, and obtain permeability coefficient of the layer by using back analysis numerical calculation to optimize the penalty function. Detection of the resistivity cross-hole CT is conducted to verify the accuracy of the method, and drilling in-situ permeability tests verify the accuracy of the method to obtain numerical results. The results show that calculation accuracy reached 90% after analysis optimization by a penalty function, which proves that the method helps in getting comprehensive formation hydrogeological information. The method is important for the follow-up governance, which is expected to have certain reference significance for similar projects.

Key words: penalty function, particle swarm optimization (PSO), evaluation criterion, packer permeability test, back analysis, seepage field