According to the characteristics of geotechnical and underground engineering structures

the variational principle employing modified Reissner functional into which independent rotation field has been introduced. The rotation field is interpolated by true rotation at each node. The rational type of incompatible fields of 4-node element is discussed. The incompatible displacement functions being suitable for arbitrary quadrilateral element are denoted. An internal parameter type incompatible element with rotational degrees of freedom is established and the numerical computation formulae are developed. The element of this paper is proved to pass the patch test. The compatibility with beam elements with rotation freedoms can be easily made. From the computational examination questions as well as the underground tunnel engineering example

it is shown that the numerical results by using the computation model of this paper have good accuracy. A perfect numerical method is developed for analyses and computations of geotechnical and underground engineering structures.