Abstract: In this paper, the extended precise integration method is used to solve the plane strain problem of transversely isotropic multilayered soils. Extended precise integration method is of high accuracy and efficiency, which is an effective method to solve differential equations. Compared with analytical methods, it can save a lot of time for theoretical derivation. Starting with the governing equations of elasticity in Cartesian coordinates, the matrix differential equation in the Fourier transform domain is derived. Then, the establishment and combination of adjacent layer elements are introduced, and the extended precise integration solution of multilayered soils subjected to internal loads can be obtained further. The comparison with existing results verifies the accuracy and correctness of this method, and numerical examples are presented to elucidate the influence of transverse isotropy, stratification and load position. It turns out that the vertical displacement decreases with the increase of modulus ratio n, and increases with the increase of modulus ratio m. Besides, soils above the loading point is more sensitive to change of load position, while the modulus of upper soils is more important to the results of vertical displacement, and stratification of the soils has more significant influence on vertical displacement compared with vertical stress.

Key words: transverse isotropy, layered soil, plane strain, extended precise integration method