SUMMARYThis paper presents two hybrid stress four-node tetrahedron solid elements which are equipped with the rotational d.o.f.s proposed by Allman. Inasmuch Allman's rotation is employed, the elements are plagued by zero-energy rotation modes which induce no strain. A modi"ed Hellinger}Reissner functional that treats the rotation and the skew symmetric stress as independent "elds is employed to formulate a stabilization scheme. Particular e!ort has been made to reduce the number of stress modes to minimum without sacri"cing the frame invariance and proper rank of the element. The computational cost of the element is reduced by adopting orthogonal constant and non-constant symmetric stress modes. Numerical benchmark tests indicate that accuracy of the element with the minimum number of stress modes is close to another multi-"eld element which, however, is not frame invariant and exhibits unsuppressed zero-energy deformation modes.
In this paper, hybrid variational principles are employed for piezoelectric "nite element formulation. Starting from eight-node hexahedral elements with displacement and electric potential as the nodal d.o.f.s, hybrid models with assumed stress and electric displacement are devised. The assumed stress and electric displacement are chosen to be contravariant with the minimal 18 and seven modes respectively. The pertinent coe$cients can be condensed at the element level and do not enter the system equation. A number of benchmark tests are exercised. The predicted results indicate that the assumed stress and electric displacements are e!ective in improving the element accuracy. 1999 Academic Press 0022-460X/99/380519#29 $30.00/0 522 K. Y. SZE AND Y. S. PAN
In order to study the design of incomplete well point for groundwater extraction in open cut foundation pit in which the inner and outer aquifers are not completely isolated and the change mechanism of ground subsidence due to dewatering in the foundation pit, an open cut foundation pit for a subway station on Chengdu Metro Line 6 is taken as an example; meanwhile, the typical sandy pebble soil strata are also considered as a research object in this paper. Firstly, a new method for designing groundwater extraction in the open cut foundation pit is presented and applied to the practical project. The dewatering funnel curve is derived based on Dupuit’s assumption, and the ground subsidence around the foundation pit due to groundwater extraction is calculated using the stratification summation method as well as considering the effect of seepage force. The finite difference software FLAC3D is employed to simulate the groundwater extraction process in the foundation pit, and the simulation of groundwater extraction by single well point and group well points is also carried out and the unapparent effect of group well points is obtained. The comparison among on-site monitoring, theoretical calculation, and numerical simulation shows that these values have the same trend in indicating ground subsidence, and the conventional stratification summation method is conservative, and the algorithm considering the effect of seepage force is more accurate. Therefore, the ground subsidence curve caused by groundwater extraction in the foundation pit is presented. The above research methods and results can be applicable for practical engineering and be used to guide the design and construction of groundwater extraction in the foundation pit by using the open cut method in sandy pebble soil strata.
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