Cavity Expansion Theory Research Articles

Necking Analysis of High-speed Penetrating Projectile against Reinforced Concrete

Abstract The complexity of penetrating projectile’s structure is not adequately considered in existing research of penetration. Based on this actuality, high-speed reinforced concrete penetration experiment is conducted and necking at the front end of projectile’s shank is found to be the most significant phenomenon. Mindlin–Herrmann rod theory is adjusted with elastoplastic constitution and finite element method to be applied in penetration calculation. Cavity expansion theory is applied as the longitudinal and radial load estimation. The calculation results denote that both longitudinal and shear waves propagate along the projectile when penetration begins. The necking is achieved instantly during the first circulation of stress wave propagation and the uniaxial compression state at the shank’s front end makes this structure vulnerable of initial yielding. Mindlin–Herrmann rod theory successfully explains the origin and influence zone of necking, while the necking’s degree and radial contraction at projectile’s tail require further investigation.

Size effect analysis of projectile penetrating semi-infinite concrete target

Abstract Accurately assessing the damage effects of deep-penetrating weapons is of great significance for promoting the development of large-caliber kinetic energy penetrator warheads and the design of engineering protection. To accurately predict the penetration depth of projectiles into semi-infinite concrete targets, this paper derives through rigorous dimensional analysis and similarity theory that the maximum coarse aggregate size not scaling with the scale ratio and the strain rate effect are among the factors preventing small-scale projectile penetration tests on concrete targets from being extrapolated to full-scale tests. Based on the cavity expansion theory, the predictive model for the penetration depth of projectiles into concrete is derived. The accuracy and generality of the established model are verified through 20 groups of experimental data under different conditions, with an average prediction error of about 6.7% and a maximum error not exceeding 20%. Comparative analysis with the Wiffen’s model, Forrestal’s model, Wu’s model, Y.Peng’s model, and Feng’s model demonstrates the superiority of the model established.

Interpretation of Pressuremeter Test in Fractured and Weathered Phyllite for Back-Analysis of Pipe Jacking Forces

AbstractCharacterisation of highly fractured and weathered rock masses within the young Tuang Formation in Sarawak, Malaysia is challenging, mainly due to the difficulties in extracting intact samples for conventional rock testing. Pressuremeter test was used as a viable alternative since it is performed in-situ, hence eliminating the need for sample extraction. A methodology was developed to interpret pressuremeter test results in highly fractured and weathered phyllite using an analytical approach, from which useful strength and stiffness parameters can be obtained. The interpretation method was based on the fundamental theory of cylindrical cavity expansion, which was originally established for soils. The results of the interpretation were in terms of commonly known Mohr–Coulomb strength parameters, which were subsequently used for assessment of frictional pipe jacking forces through back-analysis method. The results of the back-analysis showed the reliability of the developed methodology in analysing pressuremeter test results within highly fractured and weathered phyllite.

Macro/micro failure mechanism of transparent armour subjected to multiple impacts of 7.62mm bullets

Transparent armor is widely used in military and civilian impact protection fields due to its excellent light transmittance and ballistic performance. This work focused on the macro/micro failure mechanisms of transparent armor for vehicles subjected to multiple impacts. Results showed that the penetration depth after the first impact by a 7.62 mm bullet is about 14 mm, regardless of the impact position. Based on the cavity expansion theory, the penetration depth under multiple projectile impacts was predicted, relating it to the distance between the impact points, the distance from the projectile hole to the edge of the target plate, and the damage radius caused by the first impact. In the thickness direction, observation of the glass layer damage modes revealed that the interlayer adhesive could hinder the propagation of vertical cracks between different glass layers, with delamination primarily caused by insufficient shear strength. In the in-plane direction, the size of the fractured glass gradually increases outward from the impact point because circumferential cracks can prevent the propagation of radial cracks. Finally, the micro failure analysis of glass fragments showed that the radial cracks are dominated by numerous irregular microcracks and river-like textures, while the circumferential cracks consist of the mirror region, mist region, hackle region, and river-like texture region.

DEM simulation of cone penetration tests in sand in a virtual calibration chamber

In this paper, cone penetration tests (CPT) in a virtual calibration chamber (VCC) were simulated using the discrete element method (DEM) to investigate the factors influencing the cone penetration tip resistance (qc) in sand. The microscopic parameters of the Fontainebleau sand were calibrated by comparing the simulated macroscopic mechanical behavior to that from experimental drained triaxial tests. The influences of VCC dimensions and prescribed boundary conditions, penetration rate, and confining stress on the qc were investigated. The results show that the qc under different boundary conditions converges as the diameter of the VCC increases. It is recommended that a ratio of chamber diameter to cone diameter larger than 20 should be used to eliminate the potential boundary effects for CPT in VCC for samples of different relative density (Dr). The comparison between the numerical simulations and cavity expansion theory predictions presents significant relationships among critical state parameters (Ψcri), peak internal friction angle (φpeak) and normalized cone tip resistance (Q).

Sand State Parameter from CPT

A cone penetration test (CPT) based procedure is proposed to determine the in-situ density and state parameter (ψ) of cohesionless soils. To date several correlations have been developed to estimate ψ from CPT results, but most correlations are based on limited calibration testing and/or require soil constitutive parameters from laboratory shear tests. The new framework is based on a limit pressure calculated using cavity expansion theory and a semi closed-form solution that is scaled to existing calibration chamber data using a chamber shape factor. This enables estimation of ψ directly from CPT results, which makes it practical and theoretically sound. This facilitates determining ψ for use in flow failure assessment procedures for dams and embankments.

Root Circumnutation Reduces Mechanical Resistance to Soil Penetration.

Root circumnutation, the helical movement of growing root tips, is a widely observed behaviour of plants. However, our mechanistic understanding of the impacts of root circumnutation on root growth and soil exploration is limited. Here, we deployed a unique combination of penetrometer measurements, X-ray computed tomography and time-lapse imaging, and cavity expansion modelling to unveil the effects of root circumnutation on the mechanical resistance to soil penetration. To simulate differences in circumnutation amplitude and frequency occurring among plant species, genotypes and environmental conditions, we inserted cone penetrometers with varying bending stiffness into soil samples that were subjected to orbital movement at different velocities. We show that greater circumnutation intensity, determined by a greater circumnutation frequency in conjunction with a larger circumnutation amplitude, decreased the mechanical resistance to soil penetration. Cavity expansion theory and X-ray computed tomography provided evidence that increased circumnutation intensity reduces friction at the cone-soil interface, indicating a link between root circumnutation and the ability of plants to overcome mechanical constraints to root growth. We conclude that circumnutation is a key component of root foraging behaviour and propose that genotypic differences in circumnutation intensity can be leveraged to adapt crops to soils with greater mechanical resistance.

Coupling algorithm of cavity expansion theory and finite element for penetrating reinforced concrete

Aiming at the dynamic problem of projectile penetrating reinforced concrete, this paper creatively proposes a coupling algorithm combining cavity expansion theory and the finite element method. This approach effectively resolves the problem of low efficiency in finite element simulations while ensuring computational accuracy. In this study, based on the cavity expansion theory, we have redeveloped the display dynamics software. Radial stress in the concrete is applied to the warhead surface in the normal direction, and the interaction between the projectile and the steel bar is simulated using the finite element contact algorithm. A coupling algorithm has been developed that can stably and quickly simulate the penetration of reinforced concrete by a projectile. The study indicates that the implementation of the coupling algorithm primarily includes four steps: model establishment and meshing, stress load program design, load application, and initial condition setting. Through verification and analysis, the coupling algorithm presented in this paper is demonstrated to effectively compute the dynamic response of a projectile during penetration. It exhibits superior computational stability and speed compared to the finite element method, and shows minimal sensitivity to grid size. When applied to numerical models with small meshes, it achieves both high precision and rapid computation. The coupling algorithm program design proposed in this paper can be implemented in any display dynamics software, offering a robust approach for engineers and researchers to predict projectile penetration effects. Furthermore, it provides a rapid assessment method for the anti-penetration performance of reinforced concrete structures.

Incorporating inherited variability into the drainage effect analysis of piezocone tests in gold tailings

The piezocone test (CPTu) is a commonly used field investigation method for analyzing the geomechanical behavior of mine tailings. However, the effect of drainage conditions on CPTu measurements is a critical factor in assessing tailings properties, particularly as tailings are often characterized as silty materials with intermediate permeability. Previous studies of drainage conditions have been hindered by the high variability of tailings materials, leading to considerable dispersion in experimental results. To address this challenge, the present paper proposes a numerical approach to characterize and incorporate the inherent variability of tailings to identify probabilistic limits of drainage. This approach involves characterizing site statistics through piezocone tests and incorporating this variability into a set of Monte Carlo analyses using cavity expansion theory. The results indicate that the probabilistic analysis accurately represents the variability of the normalized resistance, although there is a greater discrepancy when considering pore pressure measurements. As a practical application, probabilistic values of cone resistance were used to establish profiles of fully drained and undrained tests. These corrected profiles can then be used in load capacity methods, providing rational limits of behavior.

Similarity Solutions for Spherical Cavity Expansion in Strain-Softening Soils and its Application in Cone Penetration Test

The cavity expansion theory is commonly employed to predict the grouting pressure and cone penetration resistance. However, existing theoretical solutions for cohesive-frictional soils with dilation fail to simultaneously consider both the elastic deformation in the plastic zone and strain-softening behaviour of soils. To address this limitation, a similarity solution was derived for the expansion of spherical cavities from a zero initial radius with an initial confining pressure in strain-softening Mohr–Coulomb materials. The results demonstrate good agreement with previous theories, predicting an ultimate pressure higher than that obtained by neglecting elastic deformation in the plastic zone but lower than that calculated by neglecting softening characteristics. Moreover, several influential factors affecting the radius of the plastic zone and ultimate pressure were meticulously examined. On-site cone penetration test data and the theoretical results showed notable agreement. This indicates that the proposed solution exhibits a better conformance with the field data than do the previous solutions.

Force and wear prediction model of disc cutter under compression shear failure mode based on dense core–cavity expansion theory (U-713)

Calculating disc cutter wear and predicting wear life are long-standing issues affecting the efficiency and cost of tunnel boring machines (TBMs). During the TBM excavation process, the wear of the disc cutter is a comprehensive outcome of the interaction between the tool and rock. Studying the mechanisms of tool rock breaking and wear can assist in developing a more precise model for predicting cutter wear. Therefore, based on the rock-breaking and wear mechanisms of a cutter, this study developed a model for predicting the cutter wear rate and life. The model is based on the theory of dense core–cavity expansion combined with the motion state of a cutter. First, the TBM excavation process and rock-breaking mechanism of a cutter were analyzed in detail. A cutting force model under the compression shear failure mode based on the dense core–cavity expansion theory was established. Based on the force model, a prediction model for the wear rate and life of the disc cutter was established, considering the working characteristics and wear mechanism. Furthermore, the impact of penetration on the prediction model was investigated. In addition, to demonstrate the practicality of the method, this study conducted a comprehensive examination using engineering examples. The results showed that the average difference in the cutter average wear rate using the developed model was less than 3% compared with the actual engineering result. In addition, the average difference in the wear life rate was less than 5%. Finally, the developed prediction method was compared with other models. The wear rate fitting accuracy was improved by 4.91–10.85% and the wear life fitting accuracy was improved by 5.11–12.19% by the developed method. This improvement confirms the reasonableness and reliability of the method. This method can estimate the wear rate and lifespan of a cutter more accurately and reliably than other methods, providing a practical tool to TBM engineers to make informed decisions and optimize tool replacement programs.

Research On Soil Displacement Prediction Method Caused By High-pressure Jet Grouting Pile Group Construction Under Adjacent Pile Response

This paper analyzes the soil displacement effect during high-pressure jet grouting pile construction by simplifying the construction process as a series of pressure-controlled spherical cavity expansions in a semi-infinite soil medium. Based on the elastic-plastic solution of pressure-controlled spherical cavity expansion theory, a calculation method is proposed to estimate the soil displacement caused by high-pressure jet grouting pile construction. Non-linear contact theory between the pile and soil is introduced, and the finite difference method is employed to determine the internal forces and deformations of the pile. The proposed method is applied to field construction cases, and its validity is verified by comparing the results with on-site monitoring data. The research findings reveal that the soil displacement effect decreases with depth and primarily occurs in shallow soil layers during the construction of individual high-pressure jet grouting piles. The lateral displacement at the ground surface increases first and then decreases with the increase in horizontal distance, while the ground uplift exhibits an exponential decay trend.

Oblique penetration of tungsten spheres against steel targets based on compressible and incompressible cavity expansion theory

In penetration problems, empirical formulas from different sources may easily lead to calculation conflicts. In the present work, based on the spherical cavity expansion theory of compressible and incompressible models, the resistance decay model and the kinematics analysis of projectiles, a 3-Danalytical model for the oblique penetration of tungsten spheres against low-carbon steel targets was built. The modeling method was described in detail. Subsequently, calculation results were compared with experimental data of tungsten spheres penetrating 100 mm thick Q235 steel targets and 8 mm thick Q345 steel targets to check computational performance of the established model. It is proved that resistance models can be used to calculate penetration problems after considering the resistance correction coefficient. The 3-D model is suitable for penetration problems of plastic cratering of targets.

Analytical analysis of spherical cavity expansion considering particle breakage effect of sand and its application for CPT tests

Particle breakage in sand significantly influences the stress and deformation predictions of the spherical cavity expansion theories. However, existing theories often overlook or lack a quantitative description of particle breakage, leading to significant errors in the actual results. Based on the Simple Critical State Sand (SIMSAND) model, considering the particle breakage effect, the traditional Euler’s problem of the drainage spherical cavity expansion is converted into a set of first-order ordinary differential equations described by Lagrangian. Fontainebleau sand is taken as an example, and the influence of the initial stress of the sand on the stress state and void ratio is studied. An analysis of the relative breakage surrounding the cavity reveals that the primary impact zone extends to a distance thrice the expansion radius. An axisymmetric model of the cone penetration test is established, the analytical and numerical solutions of expansion stress and cone tip resistance are analysed and the correctness of the spherical cavity expansion theory is verified. Furthermore, the cone tip resistance results, derived from the theory of spherical cavity expansion, are consistent with the results of numerical calculations. Notably, when the particle breakage effect is not considered, the calculated results of cone tip resistance significantly increase.

From macro-morphology to micro-mechanics: a deep dive into hydraulic fracturing of compacted bentonite

A series of injection tests with compacted Gaomiaozi bentonite of varying dry density were performed using an innovative testing apparatus for hydraulic fracturing visualization, with emphases placed on fracturing macro-morphological dynamics and micro-mechanical mechanisms. Results showed that fracturing dynamics mainly consisted of three stages, namely the hydrating stage, the cracking stage, and the fracturing stage. As dry density increased, the circular hydration zone expanded, the cracking network became more intricate, and the fracturing pattern transitioned from long and clear to short and fuzzy. Breakthrough time and breakthrough pressure increased exponentially with increasing dry density, while injection rate decreased exponentially and breakthrough water volume increased linearly. The fracturing mechanism in compacted bentonite was turning from tensile to shear mode with increasing dry density. By comparing the shear strength with the sum of swelling pressure and tensile strength, a simple criterion for determining the limit state between tensile and shear modes was established, which can be popularized in other soils without swelling potential but under different confining pressures. Finally, a novel calculation method for breakthrough pressure was proposed based on cavity expansion theory, taking into account swelling effects and fracturing failure modes.

Optimization analysis of state equation and failure criterion for concrete slab subjected to impact loading

Concrete slabs are typically subjected to impact loading, and the selection of the equations of state and failure criteria has significant effects on the dynamic mechanical behavior of concrete. One of the most commonly adopted impact loading is projectile impact. In this study, the optimization analysis of the equation of state and failure criterion for rigid projectile penetration, which are often available for theoretical models, were analyzed using regression evaluation methods. Subsequently, based on the analysis results, a multi-phase model for the penetration of rigid projectiles into concrete was established which combined with the dynamic cavity expansion theory. Finally, the prediction results of the proposed model were compared with existing experimental data and prediction results of existing penetration models. The results showed that the prediction model has a wide range of applicability and high accuracy.

A cavity expansion theory-based hyperbolic model for the pull-out force of a compaction-grouted soil nail

Compared with conventional soil nails, the soil nail with grout bulbs (compaction-grouted soil nail) exhibits better performance in soil. In this study, a hyperbolic relationship was used to describe the relationship between pull-out stress (pull-out force divided by the cross-sectional area of a grout bulb) and displacement, in which the initial compressive modulus and ultimate compressive strength are the key factors that need to be determined in advance. In this case, the stress-strain behaviour of the soil around the grout bulb was investigated based on cavity expansion theory during compaction grouting and pull-out processes, and the initial compressive modulus with a compaction effect and the ultimate compressive strength were then quantified. Therefore, a cavity expansion theory-based hyperbolic model for the pull-out force of a compaction-grouted soil nail was proposed, in which the contribution of compaction grouting to the pull-out force was theoretically quantified. The proposed pull-out force model that combines the hyperbolic relationship and cavity expansion theory is simple and has high accuracy and will be useful for the design of the new soil nail with grout bulbs.

Analytical analysis of cylindrical cavity expansion considering particle breakage effect of sand and its application for cone penetration tests

AbstractThe particle breakage effect in sand exerts a significant influence on the design of underground space structure. However, the existing theories seldom consider the breakage effect and often lack accurate descriptions of void ratio changes, leading to substantial errors in the numerical calculations compared to the actual scenario. This study employs the simple critical state sand model (SIMSAND) to account for the particle breakage effect and transforms the drained cylindrical cavity expansion problem into a set of first‐order ordinary differential equations described by the Lagrangian method. The analytical solution of the cylindrical cavity expansion problem is calculated using Matlab programming codes. Firstly, Fontainebleau sand is investigated to analyse the influence of initial stress, void ratio and specific volume around the cavity. The combined effects of initial stress and particle breakage on the soil around the cavities result in dilatancy characteristics and a reduction in void ratio. The stress path analysis reveals that the soil around the cavities only reaches a critical state under high initial stresses. Secondly, a plane strain numerical model is established for twice expansion to verify the calculation outcomes from the cylindrical cavity expansion theory. Finally, an axisymmetric cone penetration test (CPT) model is developed to analyse the theoretical and numerical solutions for expansion stress and sleeve friction. The research results indicate that the CPT in sand need to consider the particle breakage effect, especially under high stress conditions. Without considering particle breakage, the sleeve friction is overestimated. These research findings can offer guidance for geotechnical engineering applications, such as CPT, pressuremeter tests and predictions of bearing capacity for pile foundations in sand.

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.

Predicting monotonic lateral load-displacement behavior of offshore flexible piles in saturated MCC soils: An application of the cavity expansion theory

This paper proposes an application of the cavity expansion theory to predict the load-displacement response of monotonically laterally loaded piles and the effective stress distribution of saturated modified Cam-clay (MCC) soil surrounding the pile. This approach incorporates geometric relationship, equilibrium equation, and boundary conditions to derive governing equations. These equations are subsequently solved to obtain monotonic p-y curves, which encompass the elastic, elastoplastic, and critical processes. To determine the load-displacement behavior and effective stress distribution of the soil, the proposed approach combines the deflection equilibrium differential equation with the finite-difference method. The accuracy and effectiveness of the approach are validated through a comparison with a Finite Element Method (FEM) simulation. Parametric studies are also presented to investigate the effects of overconsolidation ratio, in-situ coefficient, and mean effective stress. The validity and capacity of the proposed model are further demonstrated using model pile tests. The results affirm that this approach can well predict the monotonic load-displacement response of the pile and effectively captures important phenomena observed in pile tests.