Understanding of the failure mechanism and limit support pressure of a shield tunnel face under seepage condition is important in engineering design and construction. Nine physical model tests, i.e. ...three tests in dry sands, three tests in submerged sands under undrained condition, and three tests under seepage condition were carried out. A rigid plate was set in front of the tunnel face to maintain stability at the initial state. By moving the plate backward from the soil, the displacement and earth pressure curve of the tunnel face was obtained. The earth pressure dropped sharply to a constant value which corresponds to the limit support pressure required to stabilize the tunnel face. The limit pressure was found to increase with the cover-to-diameter ratio in a shallow tunnel, and it turned to be irrelevant to cover-to-diameter ratio in a deep tunnel. The ratio of limit pressure and initial earth pressure decreases with the cover-to-diameter ratio, indicating the effect of soil arching in stabilizing tunnel face stability. Under the same water level condition, the limit pressure of tunnel face with seepage is larger than the one without seepage. The limit support pressure under seepage condition is about 70% of the earth pressure at rest; it is about 50% under undrained condition and is about 15% in dry sand. The flow line around the tunnel face was traced by infused pigment, and the distribution was shown to be irrelevant with water level. The image captured by a HD camera during the test was analyzed by PIV (particle image velocimetry) analysis; the soil particle movements and the distribution of shear strain showed the failure mechanism of tunnel face. The failure mode is a combination of a wedge with slip arc and a prism. Comparing with the failure mode in dry sands and in saturated sands below water table undrained condition, the inclination angle of the wedge block under seepage condition is much smaller.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
•Shield face stability model is proposed for layered ground with seepage flow.•Collapse mechanism includes wedge with inclined angle varying between soil layers.•Limit equilibrium is established by ...method of slices and considering seepage force.•Stability model is validated by 3D stress-seepage coupled FEM.
This paper presents a limit equilibrium model for the shield face stability with special emphasis on the effects of ground heterogeneity and seepage flow. The model considers a new wedge mechanism whose inclination is capable of changing across soil layers to account for the spatial variation of soil mechanical properties. The limit equilibrium of the mechanism is established by using the method of slices, which considers horizontal arching without the need for arbitrary assumptions on soil stress distribution. The deterioration effects of groundwater flow are included by evaluating seepage force in the limit equilibrium based on an analytical hydraulic head field. To assess the proposed model, three-dimensional coupled pore fluid flow and stress finite element simulations are conducted. The above two methods are compared under different combinations of ground profiles, soil parameters, and hydrogeological conditions. These comparative analyses show the suitability of the limit equilibrium model. The influences of how horizontal arching is considered on the computed necessary face pressures under complex geological and hydrogeological conditions are explored.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
This work presents a viscoplastic localization criterion to detect quasi‐instantaneous (i.e., load‐induced) and delayed (creep‐induced) strain localization in rate‐dependent solids. The study is ...based on the theory of controllability and a viscoplastic description of the mechanical response. Analytical precursors of unstable states are defined through systems of ordinary differential equations (OEDs). The use of the proposed criteria is illustrated at the material point level through a set of strain localization analyses simulating active strain localization of a porous rock. In addition, full‐field finite element simulations of compression tests conducted under various pressures are reported to demonstrate the role of local unstable viscoplasticity in the spontaneous propagation of deformation bands under stationary boundary conditions. The study shows that the viscoplastic localization criterion maintains a negative sign as long as the behavior is unstable, that is, the rate of deformation is accelerating. The sign switch coincides with the transition to decelerating deformation. The analyses revealed that pulses of overstress always emerge in correspondence with the growth of unstable behavior, and the peak matches the transition to stable behavior. The local responses recovered from full‐field analyses were consistent with those observed in analyses at material point level and the predictions of the presented theory.
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BFBNIB, FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
In this paper we consider solutions to the reflection equation related to the higher spin stochastic six vertex model. The corresponding higher spin R-matrix is associated with the affine quantum ...algebra Uq(sl(2)ˆ). The explicit formulas for boundary K-matrices for spins s=1/2,1 are well known. We derive difference equations for the generating function of matrix elements of the K-matrix for any spin s and solve them in terms of hypergeometric functions. As a result we derive the explicit formula for matrix elements of the K-matrix for arbitrary spin. In the lower- and upper- triangular cases, the K-matrix simplifies and reduces to simple products of q-Pochhammer symbols.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•The self-consolidating CTG was prepared to fill voids of pre-placed CGs skeleton.•The relationship between the rheology of CTG and the filling ability was investigated.•The strength efficiency, ...cost, and embodied CO2 of CGFB were analyzed.
Aiming at the utilization of regional mining wastes including iron tailings sand and coal gangue (CG), a novel coal gangue-filled backfill (CGFB) is proposed in this paper, which is achieved by casting the self-consolidating cement-tailings grout (CTG) into pre-placed CGs skeleton. The mixture proportions of self-consolidating CTGs were first designed based on the rheological properties by adding viscosity enhancing agents (i.e. hydroxypropyl methylcellulose and polyacrylamide) and polycarboxylate superplasticizer (PCE). As a consequence, the static stabilities and filling abilities of fresh CTGs were also strengthened. The filling ability of fresh CTGs is a flowability-related parameter and can be reflected by the surface bugholes of hardened CGFBs. The results indicate that the use of CTG with flow diameter > 25 cm and flow time < 15 s is suitable for filling voids in pre-placed CGs skeleton. With the use of optimized self-consolidating CTGs with high W/C ratios (i.e. 1.0 and 1.2) and mass fraction of 70%, CGFBs show advantages in strengths and strength efficiencies over the conventional cemented tailings backfills. Moreover, owing to the utilization of high-volume solid waste, CGFBs bring benefits of low costs and low environmental impacts.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Face stability model is formed for shield tunnel in ground with confined aquifers.•Tunneling-induced seepage flow shows distinct pattern from that under phreatic water.•Analytical seepage flow model ...is combined with a multilayer wedge mechanism.
Confined aquifers with high fluid pressures pose severe risks for the stability of the face of earth-pressure-balanced shields. This study presents a method to compute the limit face pressures in the layered ground with confined aquifers. Seepage analyses based on the finite element method (FEM) are conducted to investigate the underground water flow patterns in the above ground due to shield tunneling. These analyses show: (1) the presence of confined aquifers enhances the hydraulic gradient around the tunnel face; (2) the hydraulic heads display distinct distribution patterns in the confined aquifers and adjacent aquitards; (3) the hydraulic gradients exhibit abrupt jumps at the aquifer-aquitard interface. These characteristics are in strong contrast to the distribution functions assumed in existing studies. Therefore, a new analytical flow model is proposed based on the hydraulic fields obtained from the seepage analyses. An approach to evaluate necessary face pressures is constructed by combining the flow model and a limit equilibrium model (LEM). By comparing against the results from drained FEM analyses under seepage flow, this paper shows that the proposed LEM can reasonably represent the influences of confined aquifers on the critical face pressures and the collapse mechanism of soils in front of the tunnel face.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Nonlocal implicit gradient enhancements are widely used to suppress mesh dependency in simulations involving strain localization. For example, nonlocality is often introduced through internal ...variables that account for possible material softening. This work, however, shows that this approach may become ineffective if the solid displays plastic non-normality (i.e., non-associated plastic flow). For this purpose, we consider an over-nonlocal formulation and mathematically inspect the conditions at which regularization is lost in the presence of plastic non-normality. Specifically, such loss of regularization is linked to the loss of uniqueness and/or existence of the incremental plastic response that is kinematically compatible with the development of a deformation band. By doing so, we find a lower limit for the admissibility of the parameters controlling the effectiveness of nonlocal implicit gradient regularization. Furthermore, we show that such a lower limit is regulated by a plastic modulus reflecting the loss of controllability of the constitutive response, and, hence, depends on the degree of plastic non-normality. We also derive a closed-form expression relating the thickness of the deformation band to both the controllability modulus and gradient regularization constants, which suggests that the thickness of the process zone may change in response to the prevailing plastic flow characteristics and evolve during active plastic deformation. The proposed nonlocal enhancement is applied to a non-associated elasto-plastic model for porous sedimentary rocks, which is capable of displaying both shear-dominated and compaction-dominated bands. Numerical simulations reveal that effective regularization can be enforced only when the over-nonlocal weighting coefficient is larger than the above-mentioned lower limit.
•Plastic non-normality is shown to inhibit nonlocal implicit gradient regularization.•Considering the effects of plastic non-normality allows for full regularization.•A closed-form solution of band thickness involving non-normality effects is derived.•A constitutive law for porous rocks is enhanced with implicit gradient method.•Mixed compaction/shear bands in porous rocks are numerically simulated.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In the construction of roadbeds in mountainous areas, crushed rock slag (CRS) generated by tunnel blasting is usually reused as road construction material to reduce environmental pollution and ...construction costs. A series of large-scale drained triaxial tests were conducted to investigate the mechanical behavior of CRS subjected to static and traffic loading. The static triaxial tests determined the maximum stress level that can be applied to the cyclic test. The cyclic triaxial test analyses the influence of cyclic stress amplitude and confining pressure on the cumulative strain of CRS material. The particle breakage of the sample under various conditions after cyclic loading was discussed, and the relationship between the relative breakage index and the final accumulated strain was analyzed. Test results indicated that with the increase in confining pressure, the peak strength of the material exhibits a continual enhancement, while the expansion behavior experiences a gradual attenuation. In the range of static failure strength, the increase of cyclic stress level will significantly increase the accumulated axial strain rate. After the cyclic loading, the particle breakage patterns are similar under different confining pressures. A good power function relationship exists between the relative breakage index and final axial strain, and further derivation of the functional expression of the relative breakage index and both cyclic stress ratio and confining pressure.
•It is confirmed that the tunnel slag material is a strain softening type material, and the degree of softening decreases as the confining pressure increases.•Under cyclic loading, the accumulated strain of CRS material is influenced by cyclic stress and confining pressure, and the final strain shows exponential growth with the both factors.•Under cyclic loading, the main forms of breakage of CRS are grinding and surface crushing. The degree of breakage increases with the increase of confining pressure and cyclic stress ratio.•The relative breakage index shows a good linear relationship with the cyclic stress ratio. A model was established to represent the relative breakage index using confining pressure and cyclic stress ratio.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
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