Theoretical analysis of the spatio-temporal evolution of the bulk-strain field based on a rheologic inclusion model

Based on the theoretical expression of the three-dimension rheologic inclusion model, we analyze in detail the spatio-temporal changes on the ground of the bulk-strain produced by a spherical rheologic inclusion in a semi-infinite rheologic medium. The results show that the spatio-temporal change of bulk-strain produced by the hard inclusion has three stages of different characteristics, which are similar to most of those geodetic deformation curves, but those by a soft inclusion do not. The α-stage is a long stage in which the precursors in both the near source region and the far field develop from the focal region to the periphery. The β-stage indicates a very rapid propagation of the precursors, so that they almost appear everywhere. During the γ-stage, the precursors in the far-field converge from the periphery, and the precursors in the near source region develop outwards. The theoretical results have been used to explain tentatively the stage characteristics of the spatio-temporal change of earthquake precursors.

A MIXED MODE FRACTURE CRITERION BASED ON THE MAXIMUM TANGENTIAL STRESS IN BRITTLE INCLUSION

A closed-form solution for predicting the tangential stress of an inclusion located in mixed mode Ⅰ and Ⅱ crack tip field was developed based on the Eshelby equivalent inclusion theory. Then a mixed mode fracture criterion, including the fracture direction and the critical load, was established based on the maximum tangential stress in the inclusion for brittle inclusioninduced fracture materials. The proposed fracture criterion is a function of the inclusion fracture stress, its size and volume fraction, as well as the elastic constants of the inclusion and the matrix material. The present criterion will reduce to the conventional one as the inclusion having the same elastic behavior as the matrix material. The proposed solutions are in good agreement with detailed finite element analysis and measurement.

3-D rheologic model of earthquake preparation (I)—Displacement field

Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelas-tic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model.

3-D rheologic model of earthquake preparation (Ⅱ): Strain field and its applications

On the basis of the three-dimensional elastic inclusion model, the analytic expression of viscoelastic strain field is derived, i.e., the analytic expression of viscoelastic strain at an arbitrary point (x, y, z) in x-axis, y-axis and z-axis produced by three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model, namely the normal strains exx(r, t), eyy(r, t) and ezz(r, t), the shear strains exy(r, t) and eyx(r, t), eyz(r, t) and ezy(r, t), exz(r, t) and ezx(r, t), and the bulk-strain q (r, t). By computing the spatial-temporal variation of bulk strain on the ground produced by a spherical rheologic inclusion in a semi-infinite rheologic medium, we obtained some significant results that the bulk-strain variation with time produced by a hard inclusion has three stages (a, b, g) with different characteristics, which are similar to those of most geodetic deformation curves, but not the case for those by a soft inclusion. It is meaningful that these theoretical results have been applied to explain preliminarily the characteristics of stage variation of spatial-temporal evolution, the pattern and quadrant distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to found the physical model of earthquake precursors and a reference to predict physically the earthquakes.

3-D rheologic model of earthquake prepa-ration (III): Precursor field

On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point （x, y, z） in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.

On the physical model of earthquake precursor fields and the mechanism of precursors＇timespace distribution──origin and evidences of the strong body earthquake──generating model

According to the requirement of the project 'Establishment of the Physical Model of Earthquake PrecursorFields',this paper elucidates the train of thinking for research on the project and some scientific problems whichmust be studied i, the elucidation emphasizes that the core of this project is to study the conditions and processesof the generation of strong earthquakes. The paper first outlines the origin and development of the'strong-bodyearthquake-generating model' proposed by the author in the 1980;and then proves the reasonableness of themodel from three aspects, namely: deep structures, mechanical analysis and rock fracture experiments. Bystudying the tomographic image for the northern part of North China, it can be seen that the sources of strongearthquakes are all distributed in high-velocity bodies,or in the contact zone between high-velocity and lowvelocity bodies but nearer to the high-velocity body. It has been affirmed through studies of the mechanical modelsof hard and soft inclusions that the existence of a hard inclusion is an imPOrtant condition for the high concentration of large amounts of strain energy. A lot of theoretical and experimental studies have been made to investigate the conditions for rock instability; the results have consistently indicated that rock instability,sudden fracture and stress drop would be possible only if the stiffness of the source body is greater than the environmentalstiffness.

An anisotropic micromechanics model for predicting the rafting direction in Ni-based single crystal superalloys

An anisotropic micromechanics model based on the equivalent inclusion method is developed to investigate the rafting direction of Ni-based single crystal superalloys. The micromechanical model considers actual cubic structure and orthogonal anisotropy properties. The von Mises stress, elastic strain energy density, and hydrostatic pressure in dif- ferent inclusions of micromechanical model are calculated when applying a tensile or compressive loading along the [001] direction. The calculated results can successfully pre- dict the rafting direction for alloys exhibiting a positive or a negative mismatch, which are in agreement with pervious experimental and theoretical studies. Moreover, the elastic constant differences and mismatch degree of the matrix and precipitate phases and their influences on the rafting direction are carefully discussed.

On seismic strengthening area before strong and great shocks and its mechanism

By systematically studying seismic strengthening areas before 85 earthquakes with M>=6.0 in China, some results have been extracted. 1) Earthquake active strengthening area exists universally before strong shock or great earthquake; 2) The size of the strengthening area and its appearing time will increase when the earthquake magnitude increases; 3) The rate between the size of seismic strengthening area and the size of the source region decreases when earthquake magnitude increases; 4) The appearing time of the earthquake active strengthening region in the eastern part of China is longer than that in the western part of China. The above characteristics have been preliminarily explained qualitatively and half-quantitatively by applying the strong body earthquake generating model and the hard inclusion theory. Then applying the seismic strengthening area, we have obtained long-term predictions of 2 earthquakes, so the seismic strengthening area before strong earthquake or great earthquakes is a universal phenomenon, which has some mechanical base.

Quadrant characteristics of earthquake precursors and its theoretical analysis

On the basis of quadrant features of the precursors in geo-electricity and deformation in the case of Tangshan earthquake and Datong earthquake in North China, the same feature of geo-electricity and deformation precursors before the Zhangbei earthquake has also been found. It seems that the existence of the quadrant behavior is not accidental, which might be related to existence of the earthquake generations. It is known in terms of rock experiment and theoretical analysis that there exists actually quadrant feature in earthquake-generating process with the range of quadrant spatial distribution unfixed, showing features of (gradual increasing ? maximum ? lessening slightly(, showing that the increasing zone and the decreasing one (or compressing zone and expanding one) of the quadrant in the near-source region could be different from that in the far-source region. Based on the knowledge of quadrant characters of earthquake precursors, we analyze space distributions of different types of precursor anomalies which may be a useful reference for one to predict the location of a strong earthquake occurrence.

INTERACTION BETWEEN A SCREW DISLOCATION AND A PLASTIC ZONE OF AN ARBITRARY SHAPE

A plastic deformation zone near a screw dislocation is treated as an equivalent transformation inclusion by means of the Eshelby inclusion theory. A closed form solution for determining the interaction between a screw dislocation and a plastically deformed zone of an arbitrary shape is obtained by using the solution between a dislocation and an equivalent transformation inclusion.