Stability analysis of a deep buried elliptical tunnel in cohesive–frictional (c–ϕ) soils with a nonassociated flow rule

The stabilities and associated collapse mechanisms of deep buried unlined elliptical tunnels in cohesive–frictional (c–[Formula: see text]) soils with the action of soil weight are investigated by the “upper-bound finite element method with rigid translatory moving elements” (UBFEM–RTME). The soil masses are assumed to obey the Mohr–Coulomb yield criterion and a nonassociated flow rule. Upper-bound stability coefficients (γcrD/c, where γcr is critical unit weight; D is tunnel height; c is cohesion) are deduced for different values of friction angles ([Formula: see text]), dilatancy coefficients (ψ/[Formula: see text], where ψ is dilation angle), and dimensionless spans (B/D, where B is span). The obtained collapse mechanisms do not extend to the ground surface and are primarily composed of a series of mutually movable rigid blocks. The γcrD/c values increase while the collapse zones decrease with an increasing [Formula: see text] and ψ/[Formula: see text] and a decreasing B/D.

Model of deformation of concrete based on flow plasticity theory for analysis of durability of plain concrete and reinforced concrete bridge constractions

The purpose of research - perfection of mathematical approaches to an estimation of durability of reinforced concrete structures. The method of research used in work is based on known positions of theories of plasticity with nonassociated flow rule and double isotropic hardening. Result of work are the basic mathematical dependences of nonlinear model of concrete on the basis of the nonassociated flow rule, and algorithm of their application for an estimation of durability of concrete and reinforced concrete bridge structures. The nonassociated flow rule is used. For the description of nonlinear compressibility of a material at the three-dimension stress state, additional loading surfaces and the plastic potential, are entered. The strength surface of durability is presented in the principle stresses space in the form of the closed volume (cap model). The loading surface is under construction as similar of a strength surface. Complexity of the received mathematical model is compensated by opportunities of calculation of designs at nonproportionate loadings. The model can be built in the general model of deformation of concrete and reinforced concrete with cracks, including - in view of cyclic and long term loadings. The practical importance consists in applicability of model for forecasting durability of statically indefinable concrete and ferro-concrete designs having damages in the form of cracks.

Problems on Yield Criterion and Dilatancy of Limit Analysis Finite Elements to Bearing Capacity of Geomaterials

The theoretical basis of classic geotechnical engineering stability problems is limit analyis thereom. Incremen-tal loading finite elements and strength reduction finite elements were put forward by Zienkiewicz in 1975 and the meth-ods are called by the authors Limit Analysis Finite Elements (abbreviation LAFE for short). It has been successfully ap-plied to slope engineering, and used to bearing capacity problems foundations. The LAFE method is still in initial stage, with problems in engineering practice. Key problems on yield criterion and dilatancy angle were also discussed in detail. The paper proved again that same ultimate bearing capacity and slip line are obtained in slip line field theory under asso-ciated and nonassociated flow rule, with the only difference of velocity vector direction. Meanwhile, the dilatancy angle should be φ/2 when nonassociated flow rule is employed under plane strain, and corresponding volumetric strain is zero. Thus the correctness of the theoretical solution in literature [19] is proved, and LAFE method is also proved a very prom-ising approach in solving bearing capacity problems of foundations. Rigorous theoretical basis is available for finite ele-ments incremental loading to solve the bearing capacity problems of foundations, and the approach is simple to use. In the numerical simulation process, not only the ultimate bearing capacity and load-displacement curve are obtained, but also the failure mechanism proved same as the one by traditional limit analysis approach is achieved. Only the yield criterion matched with practical engineering problems can generate a precise result. Under plane strain the results by Mohr-Coulomb inscribed circle yield criterion (DP3) for associated flow rule, and Mohr-Coulomb match yield criterion (DP5) for nonassociated flow rule are close to the accurate theoretical solution by Prandtl. The achievements can be applied in practical geotechnical engineering purposes.