Modeling the Stress-Strain Curve of Elastic-Plastic Materials

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

Numerical Simulation and Analysis of the Three-Step Excavation of an Extra-Large Cross-Section and a Low Flat-Ratio Railway Tunnel

The Xinbaishiyan tunnel in the reconstruction Chengdu-Kunming railway Ermeishan-Mipan section mainly runs through dolomite with dolomitic limestone, with an excavation area of 260 m2, a maximum span of 22.3 m, a maximum height of 14.4 m, a vector height of 7 m, and a rise-span ratio of 0.31. The tunnel has an extra-large cross-section and it is a low flat-ration railway tunnel. This paper mainly describes the the finite element analysis for this tunnel excavation that was used to guide the construction. Finite element software was used to model the tunnel according to the engineering geological conditions of the tunnel. These engineering geological conditions included the rock mass, system bolts, middle pipe shed, steel arch and shotcrete, grouting layer, second lining and so on. Nonlinear construction phase analysis was adopted. The results showed that the maximum vertical deformation of the tunnel vault and the middle of the invert was about 34 mm. The vertical deformation of the tunnel could be divided into an acceleration deformation section, linear deformation section, deceleration deformation section, and stable deformation section. The maximum horizontal deformation in the middle of the side wall was about 12.3 mm. Under the effect of the initial support, the equivalent stress of the side wall gradually increased with the excavation of the steps and the increase of the support structure. The axial force of the bolt in the middle of the side wall was larger than that in other places and the axial force of the middle pipe shed went along with the excavation of the tunnel in waves. The steel arch and the shotcrete had the maximum effective stress at the arch shoulder, which played the role of the deformation and pressure for the surrounding rock. During the construction, the length and height of the three-step method had to be set reasonably. The middle pipe shed and the system bolt supported the rock mass together. In the construction of the extra-large cross section and the flat tunnel, there was no need to set up temporary support, which was convenient for mechanical excavation.

GROUND SUBSIDENCE MONITORING WITH MT-InSAR AND MECHANISM INVERSION OVER XI’AN, CHINA

The ancient Xi’an, China, has been suffering severe land subsidence and ground fissure hazards since the 1960s, which has affected the safety of Subways. Multi-sensor SAR data are conducted to monitor the latest complex ground deformation and its influence on subway line No.3 over Xi’an. Annual deformation rates have been retrieved to reveal the spatiotemporal evolution of ground subsidence in Xi’an city from 2013 to 2017. Meanwhile, the correlation between land subsidence and ground fissures are analyzed by retrieving the deformation differences in both sides of the fissures. Besides, the deformation along subway line No. 3 is analyzed, and the fast deformation section is quantitatively studied. Finally, a flat lying sill model with distributed contractions is implemented to model the InSAR deformation over YHZ subsidence center, which manifests that the ground deformation is mainly caused by groundwater withdrawal.