For serviceability limit state of geotechnical structures at a specific site, the scatter among the load-displacement curves of bored piles, floating anchors or CFG piles is considered, and the set of regression parameters obtained by fitting these test curves is treated as a random variable. On the basis of theoretical framework of the geometric reliability method, a Gaussian Copula function is used to facilitate the transformation of random variables from the standard normal space to the original physical space, and then an inverse reliability algorithm based on probability density contours (PDCs) is constructed. In this algorithm, if one parameter of a normal probability density distribution is unknown, such as the mean or coefficient of variance, the PDC of the random variables can be derived when a target reliability index is specified. If the PDC is bounded by the limit state equation, the unknown mean value or coefficient of variance for the random variable under a given target reliability index is solved, and the corresponding safety factor is derived. While a non-normal marginal distribution is followed by random variables, the geometric configuration of the PDC can be still approximated by a set of discrete points, and the inverse reliability analysis is also applicable. The proposed algorithm is mainly used to solve problems with statistical parameters of random variables missing or incomplete. When the target reliability index is specified, the safety factor can be calibrated according to the importance hierarchy of the structure.