Plastic zone distribution laws and its types of surrounding rock in large-span roadway

In order to study the distribution laws and types of plastic zone of surrounding rock in large-span roadway, we analyzed the distribution laws with different spans and lateral pressures using FLAC3D numerical calcu- lation software. Based on the roadway support difficulty and distribution laws of the plastic zone of sur- rounding rock, we defined the large-span roadway and classified the types of large-span rectangular roadways. As a result, the distribution laws of the plastic zone on surrounding rock in a rectangular roadway with different spans and lateral pressures were obtained. The results show that the area of the plastic zone on surrounding rock increased with the increase of the spans and lateral pressures, and the plastic zone was symmetrical to the center line of roadway. At λ=0.5, 1.0, 1.5, and 2.0, the plastic zone presented ＂addle- shape＂ distribution, ＂ellipse＂ distribution, ＂thin and high＂ distribution and ＂inverse trapezium＂ distribu- tion, respectively. In addition, we classified the roadways into four types according to the different lateral pressures and spans, including small-span, moderate-span, large-span and extreme-large-span roadways.

Dilation angle variations in plastic zone around tunnels in rocks-constant or variable dilation parameter

Dilation angle is a significant parameter needed for numerical simulation of tunnels.Even though dilation parameter is physically variable and dependent on confinement and experienced shear plastic strain based on the existing dilation models,numerical simulations of tunnels and underground openings with constant dilation parameter usually lead to satisfactory results in practical use.This study aims to find out why constant dilation angle is enough under practical conditions to simulate numerically tunnels and underground excavations in spite of the fact that dilation angle is variable in laboratory and experimental scale.With this aim,this work studies how mobilized dilation angle varies in a plastic zone surrounding a tunnel.For the circular tunnel under uniform in situ stress field,the stepwise finite difference approximation analytical solution considering strain softening rock mass behavior with mobilized dilation angle was used to study how mobilized dilation angle varies in plastic zone around tunnel under very different conditions.In practical conditions determined in this study,dilative behavior of all over the plastic zone around the tunnel can be approximated to constant dilation angle in the middle region of the plastic zone.Moreover,the plastic zone displacements for mobilized and constant dilation angle models are compared with each other.Further investigation under more general non-uniform in situ stress conditions and non-circular tunnels is performed by using the commercial finite difference software to numerically simulate the Mine-by experimental tunnel of AECL(Atomic Energy of Canada Limited)and the arched tunnel.Although the Mine-by and arched tunnels were numerically simulated based on the mobilized dilation angle model,the variability associated with dilation angle around the simulated Mine-by and arched tunnels is insignificant,and dilation angle is approximately constant in the plastic zone.

Rules of distribution in a plastic zone of rocks surrounding a roadway affected by tectonic stress

In order to study the rules of distribution in a plastic zone of rocks, surrounding a roadway, affected by tectonic stress, we first analyzed the mechanics of a roadway affected by tectonic stress and derived a theoretical formula for the plastic zone of rocks surrounding a roadway. We also analyzed the distribution characteristics of the plastic zone under different levels of tectonic stress, vertical pressure, cohesion and friction angle of the surrounding rock. Secondly, we used numerical simulation to analyze the range and shape features of the plastic zone of rocks surrounding the roadway, given different tectonic stress levels. Finally we used a rock drilling detector to carry out field measurements on the broken state of rock surrounding the roadway at the –700 substation and channels in the Xinzhuang mine of the Shenhuo mining area. Given the measured ground stress, we analyzed the relationship between tectonic stress and the distribution of this plastic zone. Our results show that the range of the plastic zone at the top and bottom of the roadway increases with an increase in tectonic stress and this increase is especially obvious at the roadway corner.

Prediction of plastic zone size around circular tunnels in non-hydrostatic stress field

This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately.

Elastic-plastic analysis of antiplane crack near crack surface region

The elastic-plastic stress distribution and the elastic-plastic boundary con- figuration near a crack surface region are significant but hard to obtain by means of the conventional analysis. A crack line analysis method is developed in this paper by consid- ering the crack surface as an extension of the crack line. The stresses in the plastic zone, the length, and the unit normal vector of the elastic-plastic boundary near a crack surface region are obtained for an antiplane crack in an elastic-perfectly plastic solid. The usual small scale yielding assumptions are not needed in the analysis.

General forms of elastic-plastic matching equations for mode-Ⅲ cracks near crack line

Crack line analysis is an effective way to solve elastic-plastic crack problems. Application of the method does not need the traditional small-scale yielding conditions and can obtain sufficiently accurate solutions near the crack line. To address mode- Ⅲ crack problems under the perfect elastic-plastic condition, matching procedures of the crack line analysis method axe summarized and refined to give general forms and formulation steps of plastic field, elastic-plastic boundary, and elastic-plastic matching equations near the crack line. The research unifies mode-III crack problems under different conditions into a problem of determining four integral constants with four matching equations. An example is given to verify correctness, conciseness, and generality of the procedure.

EXACT SOLUTIONS OF NEAR CRACK LINE FIELDS FOR MODE I CRACK UNDER PLANE STRESS CONDITION IN AN ELASTIC－PERFECTLY PLASTIC SOLID

The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσy, and σsy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σs is different.

PLASTIC ZONE OF SEMI-INFINITE CRACK IN PLANAR KAGOME AND TRIANGULAR LATTICES

The fracture investigations of the planar lattices made of ductile cell walls are currently limited to bending-dominated hexagonal honeycomb. In this paper, the plastic zones of stretching-dominated lattices, including Kagome and triangular lattices, are estimated by analyzing their effective yield loci. The normalized in-plane yield loci of these two lattices are almost identical convex curves enclosed by 4 straight lines, which is almost independent of the relative density but is highly sensitive to the principal stress directions. Therefore, the plastic zones around the crack tip of Kagome and triangular are estimated to be quite different to those of the continuum solid and also hexagonal lattice. The plastic zones predictions by convex yield surfaces of both lattices are validated by FE calculations, although the shear lag region caused by non-local bending effect in the Kagome lattice enlarges the plastic zone in cases of small ratio of rp/l.

Elastoplastical analysis on cylinder of different moduli in tension and compression

The constitutive equation was deduced. The results were obtained from theelastic and elastoplastical analysis of the cylinder sample applied with different ratios ofload on both the inner and outer sides and different moduli ratio. The factors affecting thedevelopment of the plastic field of the cylinder with finite radius were shown. The resultsshow that the different moduli ratio is the most important factor in the development of theplastic zone. The slight fluctuation of the ratio will bring multiplied increment of the displacement, which may result in the final destruction of the engineering material.

A SUPPLEMENTARY STUDY OF ANISOTROPIC PLASTIC FIELDS AT A RAPIDLY PROPAGATING PLANE－STRESS CRACK－TIP（I）

The results in Ref. [1] are not suitable for the cases of β≥2. For this reason, byusing the methods in Ref [1] and Ref [2], we derive the general expressions ofamsotropic plastic fields at a rapidly propagating plane-stress crack-tip for both thecases of β=2 and β>2 .

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.

Modified Model of Crack Tip Stress Field Considering Dislocation Slip Accumulation and Crack Tip Blunting

This study uses the digital image correlation technique to measure the crack tip displacement field at various crack lengths in U71MnG rail steel,and the interpolated continuous displacement field was obtained by fitting with a back propagation(BP)neural network.The slip and stacking of dislocations affect crack initiation and growth,leading to changes in the crack tip field and the fatigue characteristics of crack growth.The Christopher-James-Patterson(CJP)model describes the elastic stress field around a growing fatigue crack that experiences plasticity-induced shielding.In the present work,this model is modified by including the effect of the dislocation field on the plastic zone of the crack tip and hence on the elastic field by introducing a plastic flow factorρ,which represents the amount of blunting of the crack tip.The Levenberg-Marquardt(L-M)nonlinear least squares method was used to solve for the stress intensity factors.To verify the accuracy of this modified CJP model,the theoretical and experimental plastic zone errors before and after modification were compared,and the variation trends of the stress intensity factors and the plastic flow factorρwere analysed.The results show that the CJP model,with the introduction ofρ,exhibits a good blunting trend.In the low plasticity state,the modified model can accurately describe the experimental plastic zone,and the modified stress intensity factors are more accurate,which proves the effectiveness of dislocation correction.This plastic flow correction provides a more accurate crack tip field model and improves the CJP crack growth relationship.

Failure characteristics of three-body model composed of rock and coal with different strength and stiffness

Four different types of three-body model composed of rock and coal with different strength and stiffness were established in order to study the failure characteristics of compound model such as roof-coal-floor. Through stress analysis of the element with variable strength and stiffness extracted from the strong-weak interface, the tri-axial compressive strength of the weak body and strong body near the interface as well as the areas away from the contact surface was found. Then, on the basis of three-dimensional fast Lagrangian method of continua and strain softening constitutive model composed of Coulomb-Mohr shear failure with tensile cut-off, stress and strain relationship of the four three-body combined models were analyzed under different confining pressures by numerical simulation. Finally, the different features of local shear zones and plastic failure areas of the four different models and their development trend with increasing confining pressure were discussed. The results show that additional stresses are derived due to the lateral deformation constraints near the strong-weak interface area, which results in the strength increasing in weak body and strength decreasing in strong body. The weakly consolidated soft rock and coal cementation exhibit significant strain softening behavior and bear compound tension-shear failure under uni-axial compression. With the increase of confining pressure, the tensile failure disappears from the model, and the failure type of composed model changes to local shear failure with different number of shearing bands and plastic failure zones. This work shows important guiding significance for the mechanism study of seismic, rock burst, and coal bump.

Residual Strength of Stiffened LY12CZ Aluminum Alloy Panels with Widespread Fatigue Damage

Experimental and analytical investigations on the residual strength of the stiffened LY12CZ aluminum alloy panels with widespread fatigue damage （WFD） are conducted. Nine stiffened LY12CZ aluminum alloy panels with three different types of damage are tested for residual strength. Each specimen is pre-cracked at rivet holes by saw cuts and subjected to a monotonically increasing tensile load until failure is occurred and the failure load is recorded. The stress intensity factors at the tips of the lead crack and the adjacent WFD cracks of the stiffened aluminum alloy panels are calculated by compounding approach and finite element method （FEM） respectively. The residual strength of the stiffened panels with WFD is evaluated by the engineering method with plastic zone linkup criterion and the FEM with apparent fracture toughness criterion respectively. The predicted residual strength agrees well with the experiment results. It indicates that in engineering practice these methods can be used for residual strength evaluation with the acceptable accuracy. It can be seen from this research that WFD can significantly reduce the residual strength and the critical crack length of the stiffened panels with WFD. The effect of WFD crack length on residual strength is also studied.

Effect of indentation size and grain/sub-grain size on microhardness of high purity tungsten

Hardness of materials depends significantly on the indentation size and grain/sub-grain size via microindentation and nanoindentation tests of high-purity tungsten with different structures.The grain boundary effect and indentation size effect were explored.The indentation hardness was fitted using the Nix-Gao model by considering the scaling factor.The results show that the scaling factor is barely correlated with the grain/sub-grain size.The interaction between the plastically deformed zone（PDZ） boundary and the grain/sub-grain boundary is believed to be the reason that leads to an increase of the measured hardness at the specific depths.Results also indicate that the area of the PDZ is barely correlated with the grain/sub-grain size,and the indentation hardness starts to stabilize once the PDZ expands to the dimension of an individual grain/sub-grain.

Rockburst mechanism in soft coal seam within deep coal mines

A number of rockburst accidents occurring in soft coal seams have shown that the rockburst mechanism involved in soft coal seams is significantly different from that involved in hard coal seams. Therefore, the method used to evaluate rockburst in hard coal seams is not applicable to soft coal seams. This paper established an energy integral model for the rockburst-inducing area and a friction work calculation model for the plastic area. If the remaining energy after the coal seam is broken in the rockburstinducing area is greater than the friction work required for the coal to burst out, then a rockburst accident will occur. Mechanisms of ‘‘quaking without bursting" and ‘‘quaking and bursting" are clarified for soft coal seams and corresponding control measures are proposed as the optimization of roadway layouts and use of ‘‘three strong systems"(strong de-stressing, strong supporting, and strong monitoring).

Microstructure-fracture toughness relationships and toughening mechanism of TC21 titanium alloy with lamellar microstructure

The independent influence of microstructural features on fracture toughness of TC21alloy with lamellar microstructure was investigated.Triple heat treatments were designed to obtain lamellar microstructures with different parameters,which were characterized by OM and SEM.The size and content ofαplates were mainly determined by cooling rate from singleβphase field and solution temperature in two-phase field;while the precipitation behavior of secondaryαplatelets was dominantly controlled by aging temperature in two-phase field.The content and thickness ofαplates and the thickness of secondaryαplatelets were important microstructural features influencing the fracture toughness.Both increasing the content ofαplates and thickeningαplates(or secondaryαplatelets)could enhance the fracture toughness of TC21alloy.Based on energy consumption by the plastic zone of crack tip inαplates,a toughening mechanism for titanium alloys was proposed.

Stability analysis of complex terrain slope based on multi-source point cloud fusion

Numerical modelling is a common routine for slope stability analysis in the complex terrain,and the accuracy of topographic survey has a great impact on the results.In this study,a combination of unmanned aerial vehicle(UAV)photogrammetry and 3D laser scanning technique was first proposed to establish a high-precision digital elevation model(DEM),which could be accurate to 0.2 m,fulfilling the engineering requirements.Then,a series of 3D/2D finite element models(FEM)were constituted on the basis of DEM to investigate the slope stability in the complex terrain.The results indicate that the deformation of complex terrain slope is chiefly triggered by compression-shear failure and the failure zones are mostly distributed on the middle-upper part and the scarp.Furthermore,the complex terrain slope is divided into concave,convex,concave-convex and convex-concave slope according to the topographical curvature,and the factor of safety(FOS)is as follows:the maximum value 1.8504 for the concave-convex slope,the minimum value 1.1129 for the convexconcave slope,and the median for either concave or convex slope.The inflection points and curvature of the slope jointly determine the shape of nonlinear slope,dominating the morphological effect on the slope stability,so the rational use of section morphological effect will be conducive to the overall stability of the slope.For four representative slopes,the plastic deformation first emerges into the middle,then progressively develops to the upper,and finally forms the connected failure zones.

Optimisation Method for Determination of Crack Tip Position Based on Gauss-Newton Iterative Technique

In the digital image correlation research of fatigue crack growth rate,the accuracy of the crack tip position determines the accuracy of the calculation of the stress intensity factor,thereby affecting the life prediction.This paper proposes a Gauss-Newton iteration method for solving the crack tip position.The conventional linear fitting method provides an iterative initial solution for this method,and the preconditioned conjugate gradient method is used to solve the ill-conditioned matrix.A noise-added artificial displacement field is used to verify the feasibility of the method,which shows that all parameters can be solved with satisfactory results.The actual stress intensity factor solution case shows that the stress intensity factor value obtained by the method in this paper is very close to the finite element result,and the relative error between the two is only−0.621%;The Williams coefficient obtained by this method can also better define the contour of the plastic zone at the crack tip,and the maximum relative error with the test plastic zone area is−11.29%.The relative error between the contour of the plastic zone defined by the conventional method and the area of the experimental plastic zone reached a maximum of 26.05%.The crack tip coordinates,stress intensity factors,and plastic zone contour changes in the loading and unloading phases are explored.The results show that the crack tip change during the loading process is faster than the change during the unloading process;the stress intensity factor during the unloading process under the same load condition is larger than that during the loading process;under the same load,the theoretical plastic zone during the unloading process is higher than that during the loading process.

Numerical Analysis of Cylindrical Cavity Expansion in Sand Considering Particle Crushing and Intermediate Principal Stress

Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critical state line are selected in the analysis of cylindrical cavity expansion.Meanwhile, combining Rowe s flow rule and Bolton s simplification to stress-dilatancy relationship to reflect soil shear dilatancy and softening behavior, this paper analyzes the problem of cylindrical cavity expansion i...