Deformation and stress theory of surrounding rock of shallow circular tunnel based on complex variable function method

After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function. The expression of the relevant stress component is derived, and the displacement boundary conditions of the surrounding rock of shallow circular tunnel are obtained. Furthermore, the paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel. The simulation is carried out by finite element method. The establishment of complex variable function has a good application value in solving the stress of surrounding rock of shallow tunnel.

The recent stress state of Germany – results of a geomechanical–numerical 3D model

A decisive criterion for the selection and the long-term safety of a deep geological repository for high radioactive waste is the crustal stress state and its future changes. The basis of any prognosis is the recent crustal stress state, but the state of knowledge in Germany is quite low in this respect. There are stress orientation data provided by the World Stress Map (WSM, Heidbach et al., 2018) and stress magnitude data from a database (Morawietz et al., 2020) for Germany, both providing selective information on the recent stress field. However, these data are often incomplete, of low quality and spatially unevenly distributed. Therefore, a 3D continuous description is not possible with these data so far, at most for the orientation of the maximum horizontal stress (SHmax), but not for the most important magnitudes of the minimum (Shmin) and SHmax. In the course of the SpannEnD project, a geomechanical–numerical 3D model of Germany is created, with which a continuous description of the complete tensor of the recent stress field in Germany is possible. The model covers an area of 1250×1000 km2 from Poland in the east, to France in the west, from Italy in the south to Scandinavia in the north. The depth extent is 100 km. Even though the focus is primarily on Germany, the model area was chosen to be so wide to minimize boundary effects and for a simplified definition of the displacement boundary conditions, which are ideally oriented perpendicular or parallel to the orientation of SHmax. The model contains a total of 21 units: The upper part of the lithospheric mantle, the lower crust, four laterally overlapping units of the upper crust, and 14 stratigraphic units of the sedimentary cover. The stratigraphic subdivision of the sedimentary cover is only done in the core area of the model; because this area is the focus of our study, our calibration data are mainly from this region and well-resolved geometry data are available. Outside of the core area, the sediments are grouped into an undifferentiated unit. The units are parameterized with density and elastic material parameters (Poisson's ratio and Young's modulus). The model has a lateral resolution of 2.5×2.5 km2 and a vertical resolution of a maximum of 240 m; in total it includes 11.1 million hexahedral elements. The equilibrium of forces between body and surface forces is solved by finite element method. The model is calibrated with Shmin and SHmax magnitudes from the WSM and data from the stress magnitude database. First, an initial stress state is generated and in a second step displacement boundary conditions are defined at the model edges, which are adjusted until a best-fit to the calibration data is found. The results show good agreement with both the SHmax orientation data from the WSM and the magnitudes of the two principal horizontal stresses (Shmin and SHmax) from the magnitude database.

Inverse problem for cracked inhomogeneous Kirchhoff–Love plate with two hinged rigid inclusions

We consider a family of variational problems on the equilibrium of a composite Kirchhoff–Love plate containing two flat rectilinear rigid inclusions, which are connected in a hinged manner. It is assumed that both inclusions are delaminated from an elastic matrix, thus forming an interfacial crack between the inclusions and the surrounding elastic media. Displacement boundary conditions of an inequality type are set on the crack faces that ensure a mutual nonpenetration of opposite crack faces. The problems of the family depend on a parameter specifying the coordinate of a connection point of the inclusions. For the considered family of problems, we formulate a new inverse problem of finding unknown coordinates of a hinge joint point. The continuity of solutions of the problems on this parameter is proved. The solvability of this inverse problem has been established. Using a passage to the limit, a qualitative connection between the problems for plates with flat and bulk hinged inclusions is shown.

Thermomechanical training and structural tests for adaptive SMA bumps with two-way shape memory effect

In this paper, shape memory alloy (SMA) bumps with two-way shape memory effect (TWSME) are trained by simple but effective training approaches, which provides a new idea for the actuations of the shock control bump (SCB) on airfoil. Two different configurations of bump structures (2D and 3D SMA bumps) are designed and fabricated. The bumps are required to exhibit TWSME so that it can change its shape by heating and cooling between two stable states at austenitic phase and martensitic phase, respectively. To obtain the TWSME, the material is trained in the range of martensitic finish temperature and austenitic finish temperature whilst a displacement boundary condition is imposed. A set of fixtures, which can be assembled to the universal testing machine (UTM), are designed to achieve the clamped boundary condition during thermal cycles of the training process. After training, SMA bumps with the TWSME, that bulge at low-temperature and become flat at high, are obtained. Structural tests and deformation control are then carried out afterwards to show the deformation performance of the trained SMA bumps.

Development of a biomechanical model for dynamic occlusal stress analysis

The use of traditional finite element method (FEM) in occlusal stress analysis is limited due to the complexity of musculature simulation. The present purpose was to develop a displacement boundary condition (DBC)-FEM, which evaded the muscle factor, to predict the dynamic occlusal stress. The geometry of the DBC-FEM was developed based on the scanned plastic casts obtained from a volunteer. The electrognathographic and video recorded jaw positional messages were adopted to analyze the dynamic occlusal stress. The volunteer exhibited asymmetrical lateral movements, so that the occlusal stress was further analyzed by using the parameters obtained from the right-side eccentric movement, which was 6.9 mm long, in the stress task of the left-side eccentric movement, which was 4.1 mm long. Further, virtual occlusion modification was performed by using the carving tool software aiming to improve the occlusal morphology at the loading sites. T-Scan Occlusal System was used as a control of the in vivo detection for the location and strength of the occlusal contacts. Data obtained from the calculation using the present developed DBC-FEM indicated that the stress distribution on the dental surface changed dynamically with the occlusal contacts. Consistent with the T-Scan recordings, the right-side molars always showed contacts and higher levels of stress. Replacing the left-side eccentric movement trace by the right-side one enhanced the simulated stress on the right-side molars while modification of the right-side molars reduced the simulated stress. The present DBC-FEM offers a creative approach for pragmatic occlusion stress prediction.

Compressive strain measurements in porous materials using micro-FE and digital volume correlation

A local Digital Volume Correlation (DVC) based measurement of displacements and strains of synthetic bone samples under an ex-situ compression using the time-lapsed imaging procedure was performed in the present study. Micro Finite Element (µFE) model was used to simulate the compression of synthetic bone samples with experimental-based ( ExBC), and DVC interpolated displacement boundary conditions ( IPBC). The obtained µFE nodal displacement data compared with DVC. A good match of displacement patterns and correlation values of R2 = 0.85–0.99 and RMSE ≤ 12 µm was observed for the IPBC predicted displacements against DVC displacements. However, the ExBC provided a good correlation of transverse displacements only (U: R2 = 0.85–0.99 and V: R2 = 0.77–0.99). The average axial displacement of ExBC matched well with DVC, and a qualitative and quantitative understanding of the axial displacement was possible with ExBC. A moderate agreement of axial strain patterns was observed between DVC and IPBC, even though a good agreement on displacement was observed. The ExBC showed a higher axial strain compared to DVC in all samples. The transverse strains varied between the same extreme values for both boundary conditions and within the DVC range.

The Mechanics of Initiation and Development of Thrust Ramps

We examine the mechanics of thrust fault initiation and development in sedimentary rocks which accounts for vertical variation in mechanical strength of the rocks. We use numerical mechanical models of mechanically layered rocks to examine thrust ramp nucleation in competent units, and fault propagation upward and downward into weaker units forming folds at both fault tips. We investigate the effects of mechanical stratigraphy on stress heterogeneity, rupture direction, fold formation, and fault geometry motivated by the geometry of the Ketobe Knob thrust fault in central Utah. The study incorporates finite element models to examine how mechanical stratigraphy, loading conditions, and fault configurations determine temporal and spatial variation in stress and strain. We model the predicted deformation and stress distributions in four model domains: (1) an intact, mechanically stratified rock sequence, (2) a mechanically stratified section with a range of interlayer frictional strengths, and two faulted models, (3) one with a stress boundary condition, and (4) one with a displacement boundary condition. The models show that a dramatic increase in stress develops in the competent rock layers whereas the stresses are lower in the weaker rocks. The frictional models reveal that the heterogeneous stress variations increase contact frictional strength. Faulted models contain a 20° dipping fault in the most competent unit. The models show an increase in stress in areas above and below fault tips, with extremely high stresses predicted in a ‘back thrust’ location at the lower fault tip. These findings support the hypothesis that thrust faults and associated folds at the Ketobe Knob developed in accordance with the ramp-first kinematic model and development of structures was significantly influenced by the nature of the mechanical stratigraphy.

3D In Situ Stress Estimation by Inverse Analysis of Tectonic Strains

The determination of a 3D engineering-scale in situ stress field is essential in underground rock mechanics and engineering. The inverse analysis method is a useful technique to determine the in situ stress around the zone of interest. This paper presents a new approach with tectonic strains based on traditional stress-based or displacement-based inverse analysis. In this approach, there are only six tectonic strain variables at the boundary to be optimized, which does not need to select the stress or displacement boundary conditions as the traditional inverse analysis. Therefore, the proposed approach has a better clarity. The proposed approach is applied to the determination of the engineering-scale in situ stress of the underground powerhouses of the Three Gorges Project, and the results are compared with those obtained by traditional approaches. The comparison further shows that the proposed method has better accuracy than traditional methods.

Study on the Generalized Displacement Boundary and Its Analytical Prediction for Ground Movements Induced by Shield Tunneling

The process of shield tunnel excavation would inevitably cause surrounding ground movement, and excessive displacement in the soil could lead to large deformation and even collapse of the tunnel. The methods estimating convergence deformation around tunnel opening is summarized. Then, a universal pattern of displacement boundary condition around the tunnel cavity is originally introduced, which is solved as the combination of three fundamental deformation modes, namely, uniform convergence, vertical translation, and ovalization. The expression for the above-mentioned displacement boundary condition is derived, by imposing which the analytical solution for ground movements, based on the stress function method, is proposed. The reliability and applicability of this proposed solution are verified by comparing the observed data in terms of surface settlement, underground settlement, and horizontal displacement. Further parametric analyses indicate the following: (1) the maximum settlement increases linearly with the gap parameter and the tunnel radius, while it is negatively related to the tunnel depth; (2) the trough width parameter is independent of the gap parameter and the radius, while it is proportional to the tunnel depth. This study provides a new simple and reliable method for predicting ground movements induced by shield tunneling.