Cavity Contraction Research Articles

Contraction and expansion of a cylindrical cavity in an elastoplastic medium: A dislocation‐based approach

AbstractThe contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post‐failure softening response of geomaterials, are observed in the form of spiral‐shaped fractures in laboratory tests. An alternative approach based on dislocation theory is introduced in this paper for modeling cavity contraction or expansion. In this model, several equally spaced spiral‐shaped shear fractures initiate and propagate away from the cavity within the linearly elastic medium. The Mohr‐Coulomb criterion and a dilatancy rule are imposed on the shear fractures to constrain the stresses and the displacement jumps. The direction of fracture propagation is determined by minimizing plastic dissipation. The displacement discontinuity method is used to discretize the shear and normal displacement jumps along the fracture and solve the problem numerically. The calculated crack path follows a logarithmic‐like spiral, similar to the slip lines predicted by plasticity theory. The relationship between the pressure and radial displacement at the cavity boundary converge towards the classical elastoplastic solution as the number of fracture branches increases.

Analytical solutions for cavity contraction in strain-softening materials with linear or exponential strength decay

This paper presents an analytical investigation into the contraction of spherical and cylindrical cavities excavated in strain-softening rock masses obeying the Mohr–Coulomb or Tresca yield criterion, with linear or exponential uniaxial compressive strength decay. The derivation of the ground response curves is based on the simplifying assumption that the strains inside the plastic zone are completely plastic. This significantly simplifies the mathematical formulation, enabling the derivation of closed-form solutions. An alternative simplifying approach which partially neglects the elastic strains inside the plastic zone and which is commonly adopted in the literature, is also examined. The accuracy of the simplified solutions is evaluated by comparing their predictions with rigorous solutions obtained by numerical finite-difference analyses. The investigation demonstrates that the proposed closed-form solutions represent a significant improvement on those based on the commonly-made simplifying assumption involving partial neglect of elastic strains.

Investigation of free surface effect on the cavity expansion and contraction in high-speed water entry

The evolution of the water-entry cavity affects the impact load and the motion of the body. This paper adopts the Eulerian finite element method for multiphase flow for simulations of the high-speed water-entry process. The accuracy and convergence of the numerical method are verified by comparing it with the experimental data and the results of the transient cavity dynamics theory. Based on the results, the representative characteristics of the cavity are discussed from the perspective of the cavity cross-section. It is found that the asymmetry of the cavity expansion and contraction durations is related to the motion of the free surface and the closure of the cavity. The uplift of the free surface suppresses cavity expansion, while the jet generated from free surface closure accelerates cavity contraction. The duration of the contraction of the cavity near the free surface is shorter than the expansion duration due to the change in the velocity distribution caused by the free surface motion. The necking phenomenon during deep closure leads to an increase in the internal pressure of the cavity, prolonging cavity contraction near the deep closure area. This work provides new insights into the cavity dynamics in high-speed water entry.

Theoretical Analysis of Drilling Unloading and Pile-Side Soil Pressure Recovery of Nonsqueezing Pipe Piles Installed in K0-Consolidated Soils

Drilling with prestressed concrete (DPC) pipe pile is a nonsqueezing pile sinking technology, employing drilling, simultaneous pile sinking, a pipe pile protection wall, and pile side grouting. The unloading induced by drilling, the pipe pile supporting effect, and the dissipation of the negative excess pore-water pressure after pile sinking, all of which have significant effects on the recovery of soil pressure on the pile side, are the main concerns of this study, which aim to establish a method to reasonably evaluate the timing selection of pile side grouting. The theoretical solutions for characterizing the unloading and dissipation of the negative excess pore-water pressure are presented based on the cylindrical cavity contraction model and the separated variable method. By inverse-analyzing the measured initial pore pressure change data from borehole unloading, initial soil pressures on the pile side of each soil layer are determined using the presented theoretical solutions. Then, the presented theoretical solutions were verified through a comparative analysis with the corresponding measured results. Moreover, by introducing time-dependent coefficients αt1 and αt2 to characterize the pore pressure dissipation and rheology effects, the effects of the negative excess pore-water pressure dissipation on the pile-side soil pressure recovery are discussed in detail.

Analysis of hole wall stability in saturated clay using undrained solution for cylindrical cavity contraction

To investigate the stress state of soil during the instability of the hole wall (hole shrinkage) in saturated clay, the theory of cylindrical cavity contraction in an infinite medium is applied, utilizing the modified Cam-Clay (MCC) model. By employing intermediate variables, the issue of cylindrical cavity contraction is reformulated into a first-order ordinary differential equation in Lagrangian form, with three effective stress components and pore pressure as the unknowns. In MATLAB, the stress conditions at the elastoplastic boundary serve as the initial values for solving the initial value problem of the differential equation system. After determining the correlation between the stress distribution around the cavity and the diameter reduction ratio, the analysis proceeds to evaluate the internal support pressure required for stabilizing the hole wall according to various stability criteria. This pressure is then integrated into the hole wall stability coefficient formula within the soil pressure model, facilitating the evaluation of hole wall stability. The effectiveness and accuracy of the proposed semi-analytical elastic–plastic solutions were subsequently confirmed through comparison with finite element analysis results, underscoring its relevance for addressing hole wall stability challenges.

Elastoplastic solution for cylindrical cavity contraction in unsaturated soils

This paper develops an elastoplastic solution for cylindrical cavity contraction in unsaturated soils under constant suction conditions. The elastoplastic cavity contraction problem is formulated into a set of first-order ordinary differential equations by introducing a new auxiliary variable, which is solved as an initial value problem. The new solution is validated by comparison with numerical simulation results. Finally, parametric studies show that, as soil suction increases, the internal support pressure decreases faster with cavity contraction, the unloading-induced plastic zone becomes narrower, and the changes in effective stresses are smaller for a given tunnel convergence.

Analysis of the Subsidence Evolution Characteristics of Existing Railway Lines Due to Surface Subsidence from Salt Cavern Gas Storage Facilities

The railway subgrade is a crucial component of the railway transportation system and serves as the foundation for the normal operation of the railway. Uneven subsidence of the railway subgrade is an important factor affecting the safety of train operations. In areas surrounding salt cavern gas storage facilities, subsidence caused by underground engineering can pose a threat to the safe operation of nearby railways. Through finite element numerical simulations, this study reveals the dynamic characteristics of cavity contraction and surface subsidence in salt cavern gas storage facilities under long-term operational conditions. These conclusions emphasize the complexity and long-term impacts of surface subsidence during the operation of salt cavern gas storage, providing important references for the safe operation of these facilities.

Stability analysis of energy dissipation mechanisms in rocks surrounding circular opening

This study analyzes the stability of surrounding rock for a circular opening based on the energy and cavity expansion theory, and regards the surrounding rock failure of circular opening as an unstable state driven by energy. Firstly, based on the large-strain cylindrical cavity contraction and energy dissipation method, the deformation caused by the excavation of surrounding rock is regarded as the cylindrical cavity contraction process. By introducing the energy dissipation mechanism, the energy dissipation solution of cylindrical cavity contraction is obtained. The energy dissipation process of surrounding rock is characterized by the strain energy changes in the elastic and elasto-plastic regions of this cavity contraction analysis. Secondly, the deformation control effect of support and surrounding rock parameters on the energy dissipation of surrounding rock is studied based on the energy dissipation solution of surrounding rock under support conditions. Finally, the effectiveness and reliability of the analytical approach was demonstrated by comparing the support design results with those in the literature. The research results indicate that the three-dimensional mechanical properties and dilatancy angle of rock and soil mass have a significant impact on the energy support design of surrounding rock. This study provides a general analysis method for the stability analysis of surrounding rock of deep buried tunnels and roadway.

Numerical Study of High-Speed Vertical Water Entry of Hollow Projectiles with Different Aperture Sizes and Velocities

The hollow projectile is a new type of projectile that has complex water entry hydrodynamics characteristics and has attracted significant attention in recent years. As such, it is important to investigate the effects of different entry velocities and aperture diameters on the cavity morphology, cavitation, dynamics, and motion characteristics of hollow projectiles when entering water at high speeds. In this study, four stages of an open cavity, cavity stretching, cavity closure, and cavity contraction in the water entry processes of a hollow projectile at 50–200 m/s and four aperture diameter projectiles at 100 m/s were studied using the volume of fluid (VOF), realizable k-ε turbulence, and Schnerr-Sauer cavitation model. With an increase in the speed, the depth of the cavity closure increases, thereby advancing the closure time. The timing of the surface closure at 50 m/s is clearly different from that at 100–200 m/s. Cavitation is not obvious and is near the cavity wall at 50 m/s, although the entire cavity is almost filled with vapor at 100–200 m/s. The friction resistance has two step points when impacting the water surface and entering the water completely. As the velocity increases or the aperture ratio reduces, the splash is higher, the cavity volume is larger, the cavitation phenomenon is more obvious, the cavity closure time is delayed, and the frictional resistance of the projectile is greater. The results of this study can guide the production and application of hollow projectiles in the future.

Computational mechanobiology model evaluating healing of postoperative cavities following breast-conserving surgery

Breast cancer is the most commonly diagnosed cancer type worldwide. Given high survivorship, increased focus has been placed on long-term treatment outcomes and patient quality of life. While breast-conserving surgery (BCS) is the preferred treatment strategy for early-stage breast cancer, anticipated healing and breast deformation (cosmetic) outcomes weigh heavily on surgeon and patient selection between BCS and more aggressive mastectomy procedures. Unfortunately, surgical outcomes following BCS are difficult to predict, owing to the complexity of the tissue repair process and significant patient-to-patient variability. To overcome this challenge, we developed a predictive computational mechanobiological model that simulates breast healing and deformation following BCS. The coupled biochemical-biomechanical model incorporates multi-scale cell and tissue mechanics, including collagen deposition and remodeling, collagen-dependent cell migration and contractility, and tissue plastic deformation. Available human clinical data evaluating cavity contraction and histopathological data from an experimental porcine lumpectomy study were used for model calibration. The computational model was successfully fit to data by optimizing biochemical and mechanobiological parameters through Gaussian process surrogates. The calibrated model was then applied to define key mechanobiological parameters and relationships influencing healing and breast deformation outcomes. Variability in patient characteristics including cavity-to-breast volume percentage and breast composition were further evaluated to determine effects on cavity contraction and breast cosmetic outcomes, with simulation outcomes aligning well with previously reported human studies. The proposed model has the potential to assist surgeons and their patients in developing and discussing individualized treatment plans that lead to more satisfying post-surgical outcomes and improved quality of life.

Numerical study on the cavity dynamics for vertical water entries of twin spheres

In this study, a three dimensional (3D) numerical model of six-degrees-of-freedom (6DOF) is applied to simulate the water entries of twin spheres side-by-side at different lateral distances and time intervals. The turbulence structure is described using the shear-stress transport k-ω (SST k-ω) model, and the volume of fluid (VOF) method is used to track the complex air-liquid interface. The motion of spheres during water entry is simulated using an independent overset grid. The numerical model is verified by comparing the cavity evolution results from simulations and experiments. Numerical results reveal that the time interval between the twin water entries evidently affects cavity expansion and contraction behaviors in the radial direction. However, this influence is significantly weakened by increasing the lateral distance between the two spheres. In synchronous water entries, pressure is reduced on the midline of two cavities during surface closure, which is directly related to the cavity volume. The evolution of vortexes inside the two cavities is analyzed using a velocity vector field, which is affected by the lateral distance and time interval of water entries.

Large‐strain analysis for cylindrical cavity contraction in strain‐softening geomaterials

AbstractThis study presents a large‐strain analysis for cylindrical cavity unloading–contraction problem in strain‐softening geomaterials. Based on the unified strength theory (UST) and non‐associated flow rule, the process of cavity contraction in cohesive‐frictional geomaterials is regarded as a large‐strain problem by introducing the UST parameters and the volumetric force of seepage into the conventional cylindrical cavity contraction analysis, the effects of strain‐softening characteristic, intermediate principal stress, large‐strain, and seepage are considered. Finally, according to the comparison of the results of the radius ratio with those in the published literature, the correctness and reliability of the theoretical method are proved. The results show that it is necessary to consider the effect of volume force of seepage in the stability of excavation problem in geomaterial, the larger the volume force of seepage, the smaller the plastic radius. The traditional two‐dimensional cavity contraction solution overestimates the plastic radius. The results provide a theoretical basis for the elasto‐plastic analysis of excavation in rich water geomaterial and have a certain reference value for engineering design.

An elastic-plastic solution for the optimal thickness of a frozen soil wall considering an interaction with the surrounding rock

The technology of artificial ground freezing has been widely applied in geotechnical engineering to support underground spaces, whereas the effects of excavation-induced large deformation and frictional and dilatant behavior of geomaterials are neglected in the current design. In this paper, a rigorous elastic-plastic solution of cavity contraction is proposed using a non-associated Mohr-Coulomb failure criterion to provide the optimal thickness of the frozen soil wall for excavation using artificial ground freezing technology, considering an interaction between the frozen soil wall and the surrounding soil/rock. After validation of a case study on a deep mine shaft against a numerical simulation, a thorough parametric study investigates the variation in the optimal thickness with the soil properties and initial stress conditions, as well as the effects of interaction and the critical condition. Compared to the existing solution, the proposed optimal thickness of the frozen soil wall is shown to contribute to both the design and cost-effectiveness in practical engineering, including tunneling and mine shaft construction.

Computation of pull-out resistance of pressure-grouted soil nails in sand using cavity expansion and contraction solutions

ABSTRACT Pressure-grouted soil nailing has been extensively used as a soil stabilization technique in transportation infrastructure projects, wherein resistance against pull-out failure is offered by shear resistance mobilized along the nail–soil interface. However, the different stages of soil nail installation significantly alter the soil properties and residual normal stress at the grout-soil interface and thereby the maximum pull-out shear stress. This article presents a computational procedure to predict the maximum pull-out shear stress of pressure-grouted soil nails in sand, incorporating the variation in soil properties and stresses throughout the installation processes and loading. The procedure is formulated within the framework of cavity expansion-contraction solutions as the entire installation and testing phases resemble either expansion or contraction of a cylindrical cavity. The proposed approach was validated using grouting and pull-out test data of soil nails in sand. The influence of various parameters on pull-out shear stress has also been examined.

Analysis of undrained cylindrical cavity contraction in anisotropic soils under constant total vertical stress condition

A semi-analytical solution to cylindrical cavity contraction in anisotropic soils under constant total vertical stress and undrained condition is presented in this paper. The elastoplastic constitutive relationship for the problem considered is obtained via Hooke’s law in the elastic stage and the anisotropic modified Cam-Clay model in the plastic stage. By employing an auxiliary parameter to transform the equilibrium equation from Eulerian scheme into Lagrangian scheme, the problem reduces to an initial value problem with the vertical strain and the effective radial, circumferential, vertical stresses as four basic unknowns. The governing equations of this problem in the plastic region are solved as an initial value problem with the mechanical states of soil at the elastic-plastic boundary as the initial values. Parametric analyses show that, owing to the large deformation in the vertical direction, the material particle at cavity surface reaches the critical state much more quickly under constant total vertical stress condition than that under plane strain condition. The distribution of stress components does not manifest a critical-state region as a traditional plane strain solution does. Also, the overconsolidation ratio has an obvious influence on contraction responses. The proposed solution is expected to provide a more accurate prediction of stress and displacement around a drilled wellbore and to other similar geotechnical problems.

Computational implementation of bounding surface model and its verification through cavity benchmark problems

AbstractThis paper develops an implicit integration algorithm for a general form of the bounding surface model, using the return mapping approach (elastic predictor‐plastic corrector), to obtain the updated stresses for given strain increments. The formulation of the constitutive integration requires the derivation of a supplementary differential equation to describe the evolution of a key variable, that is, the ratio between the image stress and the current stress quantities. The integration algorithm for the bounding surface model is implemented into the finite element analysis commercial program, ABAQUS, through the material interface of UMAT (user defined material subroutine), and then used for the analysis of cavity contraction (wellbore drilling/tunnel excavation) boundary value problems. The predictions from the ABAQUS simulations are found to be in excellent agreement with the analytical solutions, thus demonstrating the validity and accuracy of the proposed integration scheme.

Plasticity solutions for ground deformation prediction of shallow tunnels in undrained clay

Elastic-plastic contraction solutions of a cavity within an infinite soil mass are widely used to estimate ground response curves of deep tunnels. The pressure-convergence response of soil around shallow tunnels, however, tends to vary with tunnel embedment ratio. To account for the embedment ratio effect, this paper presents a general solution procedure for undrained contraction analysis of a thick-wall cylinder or spherical shell of isotropically hardening soils, by which a set of analytical and semi-analytical large strain solutions for several Cam-Clay soil models is derived. Results obtained with the new solutions show that the cavity contraction response highly depends on the soil stress history (overconsolidation ratio) and the radial thickness of the surrounding soil. A limit ratio of the outer to the inner radii exists, beyond which the thickness ratio effect becomes negligible. The limit ratio for a spherical shell is smaller than that for a hollow cylinder, and it decreases with the overconsolidation ratio of soil. Based on the analogy between cavity contraction and tunnel convergence, theoretical methods for predicting ground response curves of shallow plane-strain tunnels in clays are proposed and validated by comparing with relevant experimental and numerical simulation results. The solutions can also provide valuable benchmark methods for verifying various numerical programmes.

Experimental insights on the water entry of hydrophobic sphere

This article reports experimental insights into the physics of water entry of hydrophobic spheres. In the set of experiments, parameters such as sphere density, diameter, and impact velocity are varied. The trajectory of the sphere after impact, the dynamics of trapped air-cavity, including the cavity formation, and the retraction analysis are given. Furthermore, analysis of the Worthington-jet, the cavity ripple, and early bubble shedding after the air-cavity detachment is carried out. At the location of cavity closure, radial expansion and contraction behavior are reported for the case of the shallow seal (near the air–water interface), while for the deep seal, only one such behavior is observed. Further, five cavity shapes are recorded based on the cavity retraction behavior (i.e., shallow, deep seal), namely, conical shape, slender-cone shape, telescopic shape, spearhead shape, and the thick spearhead shape. The radial dynamics and radial surface energy analysis are reported at various locations on these cavity shapes to find that the thick spearhead cavities hold the most cross-sectional surface energy. The slender-cone shaped cavity generates the fastest Worthington-jet, followed by the telescopic shaped cavities. The thick spearhead shaped cavities are reported to have the longest intact Worthington-jets, followed by the spearhead shaped cavities. Finally, a new regime map is presented for single ripple and multiple ripple behaviors at the time of retraction in the wake of descending spheres. A bubble shedding behavior has also been characterized as the most frequent bubble shedding for shallow seal and associated longer bubble length compared to the other cases.

Borehole contraction and depth analysis based on Extended SMP criterion

The excavation of vertical boreholes is involved in several geotechnical engineering constructions. Earth pressure in the soil is released during the drilling process, resulting in soil stress redistribution and borehole contraction along the excavation surface. The stress and displacement responses tend to increase with soil depth, which may degrade the quality of hole formation and cause collapse. Therefore, the concerns of three-dimensional (3-D) stress and displacement states of the soil around the borehole should be addressed during the design and construction of associated engineering. This study proposes exact and simplified analytical solutions based on the Extended Spatially Mobilized Plane criterion to obtain a more accurate borehole contraction law and depth in drained soil. The 3-D stress and displacement values along the borehole depth are obtained by combining the derived plane solution of cylindrical cavity contraction with the classical earth pressure formula. The proposed solution can reasonably consider the influence of the intermediate principal stress and explicitly state its value. The contraction degree of the proposed solution is 7.76% less than the Mohr–Coulomb solution at a depth of 80 m with the specified soil parameters. A parametric analysis shows that the contraction will be reduced by 21.4% and 36.8% if the unloading ratio increases from 0.4 to 0.5 and 0.6, respectively. The borehole can be supported by a high unit weight of slurry in an elastic state. A decrease in soil shear strength impairs borehole stress state and hole formation quality, and internal friction angle affects more than cohesion in deep soil. The effect of dilatancy on borehole contraction is insignificant. Further, the proposed approximate solution, which ignores the elastic strain in the plastic zone, has a slight error in borehole displacement but is convenient for engineering calculation.

Undrained Stability Analysis of Shallow Tunnel and Sinkhole in Soft Clay: The Cavity Contraction Method

This paper presents theoretical methods for the undrained stability analysis of shallow tunnels/sinkholes in clay based on the cavity contraction theory, with some assumptions and simplifications. To examine the accuracy and reliability of the new methods, a database was assembled, which consists of stability numbers of tunnel/sinkholes in clays from 22 centrifuge model tests, 10 field tests, and 62 FELA results. It is shown that the proposed methods give an average of 2.5% overestimation for the stability numbers from model tests and is in a good agreement with the FELA results. The cavity contraction theory-based methods are then discussed, which could provide useful guidance for designers to roughly assess shallow tunnel/sinkhole stability in clays.