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.