Expansion Of Plastic Zone Research Articles

The Influence of Rock Thermal Stress on the Morphology and Expansion Pattern of the Plastic Zone in the Surrounding Rock of a Deep-Buried Tunnel under High Geothermal Temperature Conditions

The extent of the plastic zone is critical in determining the stability and extent of damage to the surrounding rock in tunnels, crucial for designing support structures and thermal insulation layers. This study focuses on understanding how rock thermal stress affects the expansion of the plastic zone in deep-buried tunnels subjected to high geothermal temperatures, based on the derivation of the boundary line formula of the plastic zone in a high geothermal tunnel, and combined with the test results of the hydraulic fracturing method in a high geothermal tunnel of the Bulunkou Hydropower Station in Xinjiang. The findings indicate that thermal stress in the rock mass slows the growth of the plastic zone but significantly increases its extent. However, the influence of thermal stress on the shape and size of the plastic zone is less significant compared to the lateral pressure coefficient. In conditions of high geothermal temperature and geostress, rock mass thermal stress induces substantial changes in the morphology and extent of the plastic zone, which cannot be overlooked and can lead to significant errors if not properly considered. The theoretical formulas derived from engineering analysis, along with observed patterns of plastic zone expansion, demonstrate practical applicability.

Study on the dynamic response and roadways stability during mining under the disturbance of hard roof break

Under the condition that the working face was directly covered with hard roof, the abrupt breaking of hard roof release significant amount of energy, thus prone to triggering dynamic disasters such as roadway instability or rockburst. This paper based on the engineering background of the Xieqiao Coal Mine's 11,618 working face, a numerical simulation method was put forward to study the dynamic response of roadway under the disturbance of hard roof breaking and proposed an evaluation index IC for roadway stability. Research indicates that the elastic energy released during the periodic weighting of the hard roof is higher than that released during the first weighting. Under the dynamic disturbance caused by hard roof breaking, the peak stresses of the roadway was slight decreased, accompanied by a significant increase in the range of stress concentration and plastic zone expansion. Roadway deformation patterns are significantly influenced by hard roof breaking, with noticeable increases in deformation on the roof and right side. During the period of hard roof breaking, the possibility of instability of the roadway increase significantly due to the disturbance caused by the dynamic load. The research results reveal the instability mechanism of roadway under the condition of hard roof, and provide a more reliable basis for evaluating the stability of roadway.

Evolution law of coal and gas outburst hole shapes with varying underground stress conditions: Numerical analysis and on-scene evidence

A rock-coal-rock excavation model was established, and a coal and gas outburst (Abbreviated as CAGO) numerical simulation was carried out, which takes into account the dual-pore model and the desorption of gas. The plastic zone expansion was simulated under the different gas pressures and lateral pressure coefficients, and the variation in hole shape was characterized by the change in the plastic zone and compared with the actual engineering. The results indicate that: (1) There is a critical time in the CAGO process that divides the gas action into two stages: the first stage is the energy that causes the destruction of the coal body and throws out the crushed coal, the pressure difference between atmospheric and gas provides energy for this. The second stage is that the pressure difference will only provide energy for the throwing of broken coal. (2) Under the same loading conditions, gas pressure is set from 0.5 MPa to 0.9 MPa in 0.1 MPa increments, the area of the plastic zone around the exposed surface increases from 1.323 m2 to 1.3238 m2, and the peak velocity is reached faster. Meanwhile, the plastic zone increased from 1.319 m2 to 1.3238 m2 under the gas pressure of 0.9 MPa. This suggests that gas also has an effect on coal seam damage, but it is relatively weak compared to the geo-stress. (3) Pre-destruction of coal by geo-stress determines the size and shape of the hole, and the lateral pressure coefficient determines the pre-destruction situation. When the coefficient is small, the hole develops into an asymmetrical butterfly shape with a larger upper part and a smaller lower part, and when the coefficient is close to 1, the hole tends to develop into a semi-elliptical shape. Finally, the simulation result was compared with the experiment and the on-scene evidence. This study has guiding significance for the prevention and control of CAGOs at different depths.

Feasibility analysis on the utilization of TWH-caverns with sediment space for gas storage: A case study of Sanshui salt mine

Underground salt cavern (USC) has emerged as an optimal location for large-scale energy storage, encompassing oil, gas, hydrogen, carbon dioxide, and compressed air energy storage (CAES), owing to its inherent advantages of substantial capacity, stability, and hermeticity. However, most salt mines in China are characterized by a relatively thin salt layer thickness, a large number of interlayers and low salt layers grade. Consequently, a substantial proportion of the cavernous space resulting from water solution mining becomes progressively covered by insoluble sediment. Herein, the feasibility of gas storage in two butted-well horizontal (TWH) caverns with sediments, located within the Sanshui salt mine in Guangdong Province, China, is comprehensively analyzed through engineering investigation, physical model experimentation, numerical simulation, and theoretical analysis. Firstly, a theoretical model was developed to calculate the volume of caverns based on salt grade (soluble content). Secondly, a joint physical model experiment and numerical simulation were conducted to obtain the most probable shape of the process for forming water-soluble caverns. Moreover, a novel technology was proposed to utilize sediment space for gas storage in TWH-caverns. Ultimately, the support pressure of surrounding rock was determined by using the passive earth pressure theory, and subsequently, an assessment of cavern stability was conducted. Here, the numerical simulation results demonstrated that in the absence of sediment space utilization, there was a limited capacity for gas storage, resulting in significant deformation of the surrounding rock and an increased level of roof instability. On the contrary, sediment can provide structural support to the surrounding rock, thus increasing its stability (the plastic zone expansion was reduced from 1600 % (0.3 σz), 1345 % (0.35 σz) and 1297 % (0.4 σz) to 109 %, 87 % and 78 %, respectively) and enhancing the capacity for gas storage. Accordingly, this study provides valuable guidance for the assessment of gas storage in low-grade salt sedimentary environments, as well as for the design of gas injection and brine discharge, and stability evaluations.

Analysis of Rock Mass Parameters and Plastic Zone of a Tunnel in Southwest Mountainous Area

The deformation damage and support difficulties caused by the formation and expansion of plastic zone of surrounding rock have always been urgent engineering problems to be solved, especially in areas with prominent non-uniform stress fields. Choosing a reasonable and practical method to determine the plastic zone is of great significance for ensuring the long-term stability and safety of tunnels. Based on a tunnel project in the southwest mountainous area, this paper conducted mechanical tests to obtain the mechanical parameters of granite. The analytical method optimized based on the principle of stress balance was applied, and the numerical simulation was carried out according to the field displacement monitoring data and experimental parameters, the plastic zone of the medium quality granite cross-section and fault fracture zone granite cross-section was analyzed comprehensively. The results shown that the analytical and numerical solutions are in good agreement with engineering practice. It proved that the theory and method in this paper are scientific and practical in engineering. The research results can provide support for the design optimization and construction safety of the tunnel, and the research ideas and methods can also provide reference for similar projects.

Indentation Size Effect in Electrodeposited Nickel with Different Grain Size and Crystal Orientation

Indentation size effect at shallow indentation depths still remains a challenge as it cannot be correctly described by the Nix–Gao model based on the concept of strain gradient plasticity and geometrically necessary dislocations. The reasons for this discrepancy may be various, and multiple microstructural factors may play a role at the nanoscale. In the present paper, the breakdown of the Nix–Gao model was explored in electrodeposited nickel with different grain size/shape and crystallographic orientation. Crystallographic orientation has no significant effect on the indentation process at shallow depths if plastic deformation has already developed. On the other hand, decreasing the grain size leads to constrained plastic deformation in the grains below the indenter and to an effective plastic zone expansion. Further grain refinement down to the nanograin material leads to a change in the plastic deformation mechanisms to grain boundary-mediated deformation and a more pronounced breakdown of the Nix–Gao model.

The effect of mechanical inhomogeneity in microzones of welded joints on CTOD fracture toughness of nuclear thick-walled steel

This study employs the microshear test method to examine the local mechanical properties of narrow-gap welded joints, revealing the mechanical inhomogeneity by evaluating the microshear strength, stress‒strain curves, and failure strain. On this basis, the influence of weld joints micromechanical inhomogeneity on the crack tip opening displacement (CTOD) fracture toughness is investigated. From the root weld layer to the cover weld layer, the fracture toughness at the center of the weld seam demonstrates an increasing trend, with the experimental and calculated CTOD values showing a good correspondence. The microproperties of the welded joints significantly impact the load-bearing capacity and fracture toughness. During the deformation process of the “low-matching” microregions, the plastic zone expansion is hindered by the surrounding microregion strength constraints, thus reducing the fracture toughness. In contrast, during the deformation of the “high-matching” microregions, the surrounding microregions absorb some of the loading energy, partially releasing the concentrated stress at the crack tip, which in turn increases the fracture toughness.

Analysis of Malignant Expansion of Plastic Zone of Surrounding Rocks in High Ground Temperature Hydraulic Tunnels and the Mechanical Characteristics of the Support Structure

To explore the development process of the plastic zone of hydraulic tunnels and the mechanical characteristics of the support structure in a high ground temperature environment during construction period, methods, including theoretical analysis, numerical calculation, field monitoring test, etc., are used to analyze the generation and formation process of the plastic zone of surrounding rocks in the hydraulic tunnel under high ground temperature environment. The evolution law of mechanical characteristics of the support structure in surrounding rocks is studied. The development process and shape of the plastic zone in the tunnel under various high ground temperatures are simulated. The results show that after the excavation of the high ground temperature hydraulic tunnel, the plastic zone first appears at the arch waist in a crescent pattern, then extends to both sides and the spandrel, and connects with the plastic zone in the arch crown, forming a pattern of circle or butterfly. A higher initial temperature of the surrounding rock indicates a larger range and plastic strain of the plastic zone in the surrounding rock. At the same time, the plastic zone is easier to appear at the spandrel and arch foot and develop to the depth of the surrounding rock. The higher is the initial temperature of the surrounding rock, the greater will be the axial force and bending moment of supported shotcrete, the more obviously the bending moment of arch abutment and arch foot will grow, the greater will be the axial force value of the bolt and the farther the neutral point will be from the tunnel wall. While strengthening the arch waist, the support of the arch shoulder and arch foot should also be strengthened at a high temperature.

Analytical approach for the fast estimation of time-dependent wellbore stability during drilling in methane hydrate-bearing sediment

Methane hydrates (MHs) have been widely considered to be clean energy resources that are stored in great quantities in the ocean. During wellbore drilling in methane hydrate-bearing sediment (MHBS), the coupling effect of the mass/heat transfer, MH dissociation and creep response of MHBS makes wellbore stability a complex time-dependent problem.Aimed at efficiently estimating the time-dependent wellbore stability when drilling in MHBS, this study provides an efficient analytical approach (solution) for quickly predicting the plastic zone and displacement around the wellbore, precisely considering the rheological properties (i.e.., viscoelastic-brittle-plastic) of the sediments, the effect of the unsteady seepage/temperature fields and the sharp deterioration of the mechanical properties of the sediments after hydrate dissociation. Because of the time-dependent hydrate dissociation caused by the unsteady seepage/temperature field, a multiregion problem with time-varying boundaries is deduced, and the Laplace transformation is employed when solving the differential equations under various working conditions. The analytical solutions agree well with the results from the numerical method under the same assumptions, and the boundary and compatibility conditions of the analytical solutions are satisfactorily verified. Furthermore, the analytical predictions of the dissociation front radius and the distribution of the pressure and effective stress near the wellbore are essentially consistent with the results from complex numerical simulations, which validates the applicability of the analytical solutions. A parametric investigation on the specific effect of the rheological properties and drilling fluid pressure on the wellbore stability during drilling in MHBS is finally performed. The results show that both the plastic radius and displacement increase sharply at the beginning of drilling. When the plastic zone is smaller than the dissociated region, the slower the creep rate of MHBS is, the slower the plastic zone expansion in the dissociated region is, and the slower the displacement increase is over time.

Fracturing mechanisms and deformation characteristics of rock surrounding the gate during gob-side entry retention through roof pre-fracturing

To study the fracturing mechanism and deformation characteristics of the rock surrounding the gate during gob-side entry retention through roof pre-fracturing, the roof fracture laws and mechanism of the gob-side entry were analyzed. Based on the results, a 6-zone distribution law of the gob-side entry was developed through theoretical analysis. In this study, the fracturing mechanism of the gate roof in different zones and the plastic zone expansion law of the coal side were clarified through numerical simulations based on a gate in the Halagou Coal Mine. The numerical simulation results showed that the fracture mechanism of the gate roof above the coal side is closely related to the tensile strengths of the immediate roof and the main roof. The fractures above the solid coal are the main cause of the dramatic appearance of dynamic pressure in the gob-side entry. The slewing subsidence of the main roof causes the deformation of and damage to the surrounding rock to sharply increase. To ensure the stability of the gob-side entry, a support design scheme consisting of a high-pretension force, constant resistance, and the use of large deformation cables + single hydraulic props + steel beams + U section steel is proposed. The field test results showed that after the working face was mined, although the fractures in the overlying strata penetrated to the ground surface, the maximum roof and floor convergence was only 196–212 mm, which is within a reasonable range. The results of this study provide an important support design for gob-side entry retention under similar conditions.

Sliding Impact Mechanism of Square Roadway Based on Complex Function Theory

To clarify the process of stress change and plastic zone evolution of square roadways under high-stress conditions, the rotational square expansion plastic zone evolution model of square roadway was established by theoretical analysis, numerical simulation, and engineering verification. The shear slip impact stress criterion of square roadway based on complex variable function theory was studied, and the law of surrounding rock stress distribution, plastic zone expansion, elastic energy density, local energy release rate (LERR), and total energy release of square roadway were analyzed. The results show that the compressive stress is concentrated in the four corners of the roadway after the roadway excavated and transfers with the change of plastic zone. Main shear failures start from the four corners and develop in a rotating square shape, forming square failure zones I and II. The square failure zone I is connected with the roadway contour and rotated 45°. The square failure zone II is connected with the square failure zone I and rotated 45°. When the original rock stress is low, the surrounding rock tends to be stable after the square shear slip line field formed. When the original rock stress is high, the shear failure of the surrounding rock continues to occur after the square failure zone II formed, showing a spiral slip line. Corners of the square roadway and square failure zones I and II are the main energy accumulation and release areas. The maximum elastic energy density and LERR increase exponentially with the ratio of vertical stress to uniaxial compressive strength (Ic). When square corners of the roof are changed to round corners, the plastic zone of the roof expands to form an arch structure. The maximum elastic energy density decreases by 22%, which reduces the energy level and possibility of rock burst. This study enriches the failure mechanism of roadway sliding impact. It can provide a basic theoretical reference for the design of the new roadway section and support form based on the prevention of rock burst.

A new method for constructing finite difference model of soil-rock mixture slope and its stability analysis

A new method for constructing a digital model of soil-rock mixture is proposed in this paper. Using this method, rock blocks of arbitrary shapes can be considered and the construction of soil-rock mixtures with different block size distribution and rock content can be realized. First, through digital image processing, a large number of rock block contours that are analogous with reality are obtained. Then, a corresponding rock block library is established. Next, an improved intersection detection algorithm based on axis-aligned bounding box is developed to construct the digital model of the soil-rock mixture slope. Furthermore, the stabilities of soil-rock mixture slopes with different block size distribution and rock content are investigated. The results show that the soil-rock mixture slope exhibits multiple sliding zone under the combined action of various plastic zone expansion. And the influence of block size distribution and rock content on the stability of soil-rock mixture slope has a coupling effect.

Effect of Principal Stress Field on the Development of Plastic Zone ahead of the Gateroad

The distribution of a plastic zone ahead of a gateroad plays a significant role in maintaining the long-term stability of mining spaces. For a long time, the principal stress field such as the values, the direction, etc. have been observed to have impacts on plastic zone development, but has not been looked into deeply and systematically. To this end, the influence of principal stress field including the maximum principal stress (P1), the angle between the P1 direction and the Z-axis (α), the minimum principal stress (P3), and the ratio of maximum principal stress to minimum principal stress (P1/P3) on the expansion of the plastic zone ahead of the gateroad is investigated by the (Fast Lagrangian Analysis of Continua) FLAC3D models. The results show that: (1) The plastic zone volume increases first and then decreases with the increase of α, and the direction of butterfly-shaped plastic zone ahead of gateroad is rotating with the evolution of α. (2) The plastic zone volume ahead of excavation face increases gradually with the increase of P1/P3. Mutagenicity of butterfly-shaped plastic zone occurs ahead of the gateroad under a certain value of P1/P3. (3) With the increase of P1 and decrease of P3, the plastic zone volume is of exponential growth. The plastic zone volume approaches infinity when the critical value of maximum principal stress ([P1]) and the minimum principal stress ([P1]) is obtained. (4) The study of the effect of principal stress field on the expansion of plastic zone ahead of the gateroad is helpful for revealing the mechanisms of coal and gas outbursts. The critical stress state of butterfly-shaped plastic zone mutagenicity ahead of the gateroad can be used as an important indicator for assessing the risk of coal and gas outburst. The research can also guide the prevention of coal and gas outburst ahead of the gateroad.

Anisotropic continuum damage analysis of thin-walled pressure vessels under cyclic thermo-mechanical loading

The present study intends to analyze damage in thin-walled steel cylinders undergoing constant internal pressure and thermal cycles through use of anisotropic continuum damage mechanics (CDM) model coupled with nonlinear kinematic hardening rule of Chaboche. Materials damage in each direction was defined based on plastic strain and its direction. Stress and strain distribution over wall-thickness was described based on the CDM model and the return mapping algorithm was employed based on the consistency condition. Plastic zone expansion across the wall thickness of cylinders was noticeably affected with change in internal pressure and temperature gradients. Expansion of plastic zone over wall-thickness at inner and outer surfaces and their boundaries demarking elastic and plastic regions was attributed to the magnitude of damage induced over thermo-mechanical cycles on the thin-walled samples tested at various pressure stresses.

Study on the Aging Deterioration Curve of Tunnel Lining in Water Rich Area

In this paper, the main influencing factors of tunnel lining deterioration are summarized, and the stability of surrounding rock, structural safety and the law of annual change of crack width under combined deterioration factors are analysed by numerical analysis method. The results show that the change of groundwater level has the most significant influence on the stability of surrounding rock. The rise of groundwater level makes tunnel appear obvious phenomenon of vault sinking and invert floating. When the water level has passed the vault, the lining structure has a significant reduction of safety factor and an increase of crack width. The deteriorated surrounding rock is prone to damage under the influence of groundwater, which directly shows an obvious expansion of plastic zone. The deterioration of lining material will not have a significant impact on the stability of surrounding rock and the structural safety factor. Among various deterioration factors, the position of wall feet on both sides and the invert are the most disadvantageous position in the tunnel. They are under high risk of cracks and seepage, which should be paid attention during the tunnel construction, operation and maintenance.

Evaluation of the Mechanical Instability of Mining Roadway Overburden: Research and Applications

Under the superposed action of the primary rock stress and the mining stress, the compound roof of a roadway will have irregular plastic failure zone with greater depth, resulting in a wide range of non-uniform deformations and roof failures. Mastering the deformation and failure characteristics of this roof is essentially to recognize the development of the plastic zone of a compound roof. In this paper, the on-site roof detection method is mainly adopted to arrange a large number of boreholes for visualization and the deep displacement monitoring with the high-density points. Combined with numerical simulations, the rupture development characteristics and deformation mechanisms of the compound roof are revealed. The results show that the magnitude and direction of the principal stress of surrounding rock in a mining roadway are constantly changing, and the penetrating phenomenon will occur during the plastic zone expansion process. The order of the compound roof rupture as follows: shallow strata plastic failure, deep strata penetrating plastic failure and middle strata rupture. Severe roof deformation is mainly caused by plastic failure, and the strong deformation pressure caused by deep strata penetration plastic failure can easily lead to tensile failure and rupture in the middle strata. According to the plastic zone penetration development of the compound roof, the hierarchical support design led by the long-extension bolt is carried out on the test roadway. The monitoring results show that the roof is controlled well. The research results can provide a reference for the control of compound roofs in mining roadways.

The Catastrophe Criterion for Instability of Deep Roadway based on Malignant Expansion of Plastic Zone

In order to solve the problem of discriminant criterion for deep roadway instability, the core of surrounding rock failure in deep roadway and its two types of instability mechanisms were analysed. Based on the cusp catastrophe model and taking the plastic radius function as the potential function of the roadway system, the instability discriminant of surrounding rock was derived and the catastrophic criterion for instability of deep roadway under the influence of disturbance was established. Aiming at the engineering application of this criterion, the implementation method and detailed procedure of stability discrimination for the deep roadway were proposed. The numerical results show that the malignant expansion of plastic zone often occurs in surrounding rock causing large deformation or transient instability in the ultra-high deviatoric stress environment. Under the influence of external disturbance, the plastic radius experienced two stages including slow increase and nonlinear acceleration. The discriminant conclusion of the deep roadway instability according to the calculation results of the catastrophic eigenvalues is consistent with the extension of the plastic zone during the instability process of surrounding rocks, which verifies that the established instability criterion is feasible and applicable.

Numerical investigation into effect of rear barrier pillar on stress distribution around a longwall face

Numerical investigation was performed to examine the effect of rear barrier pillar on stress distribution around a longwall face. Salamon theoretical formula was used to calculate the parameters of the caving zone, which was later assigned to double yield constitutive model in FLAC3D. Numerical results demonstrate that high stress concentration zone exists above the region where the second open-off cut intersects with the rear barrier pillar due to stress transfer and plastic zone expansion. It is also found that the maximum vertical stresses with varied distance to the seam floor are all within the projective plane of the rear barrier pillar and their positions concentrate on the barrier pillar adjacent to the connection corner of the second open-off cut. In addition, position of the maximum vertical stresses abruptly transfer from the connection corner adjacent to former panel to that adjacent to current panel along the panel direction.

Plastic zone analysis and support optimization of shallow roadway with weakly cemented soft strata

Based on a shallow roadway with weakly cemented soft strata in western China, this paper studies the range and degree of plastic zones in soft strata roadways with weak cementation. Geological radars were used to monitor the loose range and level of surrounding rocks. A mechanical model of weakly cemented roadway was established, including granular material based on the measured results. The model was then used to determine the plastic zone radium. The predicted results agree well with measured results which provide valuable theoretical references for the analysis of surrounding rock stability and support reinforcing design of weakly cemented roadways. Finally, a combined supporting scheme of whole section bolting and grouting was proposed based on the original supporting scheme. It is proved that this support plan can effectively control the deformation and plastic zone expansion of the roadway surrounding rock and thus ensure the long-term stable and safe mining.

The Effect of Friction at the Strip Footings’ Underside on the Expansion of Plastic Zones in Subgrade

There exists horizontal friction besides vertically pressure at the foundations' underside. Considering the effect of friction on the expansion of plastic zones in subgrade is needed to accurately evaluate subgrade’s safety. A strip footing is chose as the research object. Assuming the distribution of friction at the strip footing’s underside is two symmetrical triangles. With the help of Flamant formula and via definite integration, the formulas of stress in subgrade induced by the friction are got. Setting the Coulomb-Mohr strength theory as the yielding criterion for the subgrade soil, through the comparison among the different friction angles in expansion characteristics of plastic zones, the research object is achieved. Two major conclusions as following: (1) the friction makes the plastic zones appear in advance, the initial critical load get smaller with the friction get bigger; (2) the plastic zones get broader in horizontal direction under the action of the friction, this makes the plastic zones in two sides beneath the footing run-through later and so enhances the subgrade’s ultimate bearing capacity.