THEORY OF STOCHASTIC MEDIUM AND ITS APPLICATION IN SURFACE SUBSIDENCE DUE TO EXCAVATION

Research on the stochastic theory and its application have been conducted in China for 40 years.This paper emphasizes on the basic theory of stochastic medium and its practice in predicting the ground movements and deformations induced by underground and open pit mining,near surface excavation of tunnel and so on.

Predictions of ground surface settlement for shield tunnels in sandy cobble stratum based on stochastic medium theory and empirical formulas

This paper focuses on the prediction of ground surface settlement induced by shield tunnelling in sandy cobble stratum.Based on the stochastic medium theory,an analytical solution to predict the surface settlement is developed considering the difference between soil and tunnel volume loss.Then,the effects of tunnel geometries,influence angle and volume loss on the characteristics of surface settlement are discussed.Through back analysis,a total of 103 groups of field monitoring data of surface settlement induced by shield tunnelling in sandy cobble stratum are examined to investigate the statistical characteristics of the maximum settlement,settlement trough width and volume loss.An empirical prediction is presented based on the results of back analysis.Finally,the analytical solution and empirical expression are validated by the comparisons with the results of model tests and field monitoring.Results show that the soil at ground surface has an overall dilative response for most of the shield tunnelling in sandy cobble stratum.In addition,the developed analytical solution is applicable and reasonable for surface settlement prediction.Meanwhile,the proposed empirical formula also shows good per-formance in some cases,providing an approach or a reference for engineering designers to preliminarily evaluate the surface settlement.

Prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum

This study focuses on the analytical prediction of subsurface settlement induced by shield tunnelling in sandy cobble stratum considering the volumetric deformation modes of the soil above the tunnel crown.A series of numerical analyses is performed to examine the effects of cover depth ratio(C/D),tunnel volume loss rate(h t)and volumetric block proportion(VBP)on the characteristics of subsurface settle-ment trough and soil volume loss.Considering the ground loss variation with depth,three modes are deduced from the volumetric deformation responses of the soil above the tunnel crown.Then,analytical solutions to predict subsurface settlement for each mode are presented using stochastic medium theory.The influences of C/D,h t and VBP on the key parameters(i.e.B and N)in the analytical expressions are discussed to determine the fitting formulae of B and N.Finally,the proposed analytical solutions are validated by the comparisons with the results of model test and numerical simulation.Results show that the fitting formulae provide a convenient and reliable way to evaluate the key parameters.Besides,the analytical solutions are reasonable and available in predicting the subsurface settlement induced by shield tunnelling in sandy cobble stratum.

THE ERGODICITY OF STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS WITH LVY JUMP

In this article,we first prove the existence and uniqueness of the solution to the stochastic generalized porous medium equation perturbed by Lévy process,and then show the exponential convergence of（pt）t≥0 to equilibrium uniform on any bounded subset in H.

Mechanism of grout bulb expansion and its effect on ground uplifting

In order to study the uplifting effect of compensation grouting on ground surface and the upper structures,the ground heave induced by stratum expansion was considered as a stochastic process and the stochastic medium theory was applied to determine the heave and deformation of ground surface under uniform and non-uniform expansion models of spherical grout bulb.The corresponding calculating formulas and simplified methods were derived based on the hypotheses of radial expansion.Then,a numerical model,in which radial velocity was imposed on the outer nodes of grout bulb to simulate the expansion process reaching a required volume strain,was established simultaneously.This new method avoids repeated trial calculation needed in the traditional method which applies a "fictitious" expanding pressure in the grouting elements.The results show that the numerical solutions have good consistency with the theoretical ones.Meanwhile,though the heave resulting from non-uniform expansion is larger than that from uniform expansion for shallow grouting,both of them tend to be convergent with the increasing of grouting depth.

Prediction of ground surface displacement caused by grouting

Ground surface displacement caused by grouting was calculated with stochastic medium theory. Ground surface displacement was assumed to be caused by the cavity expansion of grouting, slurry seepage, and slurry contraction. A prediction method of ground surface displacement was developed. The reliability of the presented method was validated through a comparison between theoretical results and results from engineering practice. Results show that the present method is effective. The effect of parameters on uplift displacement was illustrated under different grouting conditions. Through analysis, it can be known that the ground surface uplift is mainly caused by osmosis of slurry and the primary influence angle of stratum β determines the influence range of surface uplift. Besides, the results show that ground surface uplift displacement decreases notably with increasing depth of the grouting cavity but it increases with increasing diffusion radius of grout and increasing grouting pressure.

The new method of prediction on mining subsidence and deformation

A new probability function of mining overlying strata and subsidence is put forward that has a general statistical significance based on the ideal stochastic medium displacement model. It establishes a new system of prediction on horizontal mining subsidence and deformation, which gives a new method for prediction on mining subsidence and deformation.

Stochastic Generalized Porous Media Equations with Levy Jump

In this paper, we first prove the existence and uniqueness of a general stochastic differential equation in finite dimension, then extend the result to the infinite dimension by the classical Galerkin method. As an application, we prove the existence and uniqueness of the generalized stochastic porous medium equation perturbed by Levy process.