Solution For Cavity Expansion Research Articles

An extended graphical solution for undrained cylindrical cavity expansion in K0‐consolidated Mohr–Coulomb soil

AbstractThis paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with . It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between and or on the specific line of . The salient advantage/feature of the present general graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr–Coulomb plastic regions. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils.

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.

Cavity expansion-based interpretation of piezocone penetration test (CPTu) data in clays

A cavity expansion-based method is proposed in this paper to correlate the relevant findings with the piezocone penetration test (CPTu) data in clays. The rigorous and explicit solution for both spherical and cylindrical undrained cavity expansion is adopted based on a unified critical state constitutive model for clays and sands. The analogous model developed is comprehensively validated against two series of advanced numerical simulations and calibration chamber tests of the CPTu in fine-grained soils, along with bias analyses. The effects of the overconsolidation ratio and initial state parameter are extensively investigated for various clay types. Both theoretical and empirical correlations are then proposed for back-calculations of cone factor, undrained shear strength, overconsolidation ratio and initial state parameter of clays. Two case studies of CPTu tests are conducted in addition to examine correlations and contours of the in situ state parameter, demonstrating the applicability of the proposed theoretical approach for interpretation of the CPTu data.

Elastoplastic Solution of Cylindrical Cavity Expansion in Unsaturated Offshore Island Soil Considering Anisotropy

An elastoplastic analysis scheme for the cylindrical cavity expansion in offshore islands unsaturated soils considering anisotropy is established. The hydraulic properties and anisotropy caused by stress of unsaturated soils are coupled in an elastoplastic constitutive matrix for unsaturated soil to obtain the governing equations for the cylindrical cavity expansion problem, with an analytical solution that utilizes the original hydro-mechanical state of the soil as the initial conditions. Through a comparative analysis with other analytical solutions, the effectiveness of the new solution is verified. Moreover, the swelling response of the cylindrical cavity expansion in unsaturated soils is examined by systematically analyzing different parameters of the surrounding soil. The findings reveal that the development and rate of anisotropy in normal consolidated soil and over-consolidated soil exert a significant impact on the soil’s mechanical characteristics. Nevertheless, the alteration in the model constant h has little effect on the soil’s mechanical characteristics. The analytical solution introduces anisotropy and broadens the expansion theory of unsaturated soils to yield a more comprehensive theoretical framework for the comprehensive analysis of offshore islands’ unsaturated soils.

CEM–DSR-based explicit solution of limit expansion pressure in unsaturated soils and its application

In this study, an explicit solution for the limit expansion pressure of cavity expansion in unsaturated soil, which follows a hydraulic coupling constitutive model, was proposed based on the cavity expansion method (CEM) and deep symbolic regression (DSR). In detail, a semi-analytical elastic–plastic solution for cavity expansion in unsaturated soils was obtained based on the unsaturated critical state model; hence, a database was created. To obtain an explicit solution for the limit expansion pressure, DSR, which is a gradient-based approach to symbolic regression based on reinforcement learning, was applied. Subsequently, 13- and 4-parameter regression analyses were conducted, with satisfactory results being obtained. Finally, based on the proposed explicit expression, a theoretical calculation model for the jacked-pile penetration resistance in unsaturated soils was established. The study presented in this paper opens up possibilities for obtaining theoretical solutions to issues such as predicting pile driving performance in unsaturated soils.

Undrained expansion analyses of a cylindrical cavity in anisotropic sands incorporating the SANISAND model

AbstractSoils are known to be inherently anisotropic, resulting in complex responses to loading. This paper aims to develop an elastoplastic solution for the undrained expansion of a cylindrical cavity in sands adopting a non‐associated and anisotropic model, SANISAND. The rigorous derivation of the stress‐strain state of the soil element is provided following a standardized solving procedure. The dilatancy and crushing of the soil are invoked in the three‐dimensional cavity expansion solution by adopting the critical state soil mechanics and limiting compression curve, respectively. By combining this with a governing equation that considers the undrained condition, the stress‐strain state of the surrounding soil around the cavity can be determined. A subroutine is then implemented into the ABAQUS FEM simulation to verify the solution. The solutions are also validated against those based on an isotropic model, and anisotropic sand is used to investigate the effects of the initial effective mean stress, at‐rest coefficient of earth pressure, and overconsolidation ratio on the stress distribution, stress path, and boundary surfaces.

A graphical solution for undrained cylindrical cavity expansion in strain-hardening frictional soil

A graphical solution for undrained cylindrical cavity expansion in strain-hardening frictional soil

Interpretation of piezocone tests in normally- and over-consolidated clay using a spherical cavity expansion solution

This paper presents the derivation of closed-form expressions for the interpretation of piezocone tests in clay on the basis of an undrained cavity expansion solution. The cavity expansion solution employs the modified Unified Hardening model to describe the undrained behaviour of normally- and over-consolidated clays upon shearing. The derived expressions correlate the measured tip resistance and pore pressure with the undrained shear strength and the over-consolidation ratio, using a cone factor that, unlike empirical formulas, is calculated directly from the constitutive model parameters and the cone geometry. The cavity expansion solution is validated via comparison of its results against published studies, and accordingly the accuracy of the proposed expressions is benchmarked against field data. We show that, despite the simplifications introduced in the derivation, the calibrated expressions are capable of reproducing the field data with reasonable accuracy.

Undrained semi-analytical solution for cylindrical cavity expansion in anisotropic soils under biaxial stress conditions

This paper presents an undrained semi-analytical elastoplastic solution for cylindrical cavity expansion in anisotropic soil under the biaxial stress conditions. The advanced simplified SANICLAY model is used to simulate the elastoplastic behavior of soil. The cavity expansion is treated as an initial value problem and solved as a system of eight first-order ordinary differential equations including four stress components and four anisotropic parameters. The results are validated by comparing the new solutions with existing ones. The distributions of stress components and anisotropic parameters around the cavity wall, the expansion process, the stress yield trajectory of a soil element and the shape and size of elastoplastic boundary are further investigated to explore the cavity expansion response of soils under biaxial in situ stresses. The results of extensive parameters analysis demonstrate that the circumferential position of the soil element and the anisotropy of the soils have noticeable impacts on the expansion response under biaxial in situ stresses. Since the present solution not only considers the anisotropy and anisotropy evolution of natural soil, but also eliminates the conventional assumption of uniform radial pressure, the solution is better than other theoretical solutions to explain the pressure test and pile installation effect of shallow saturated soil.

Drained expansion analyses of a cylindrical cavity in sands incorporating the SANISAND model with fabric change effect

Sandy soil exhibits inherently anisotropy due to its microstructure, also known as ‘fabric’. However, the drastic change in fabric observed during the dilatant phase is often overlooked in current cavity expansion research. This paper presents a drained expansion solution of a cylindrical cavity with fabric change effect in the sand using a simple non-associated and anisotropic model, SANISAND. The problem is formulated as a set of first-order differential equations with the unknown variables as functions of an auxiliary coordinate, which can be solved as an initial value problem. A subroutine is implemented into the FEM simulation to verify the proposed method. Additionally, cavity expansion solutions in sand are compared with those based on state-dependent dilatancy. The anisotropic fabric of the sand is studied to investigate the impact of the initial void ratio, initial mean stress, and at-rest coefficient on the void ratio path, stress distributions and paths, and bounding surfaces. The proposed solution provides a framework for the potential use of cavity expansion in sand, considering the fabric change effect, and a benchmark for further developments and numerical calculations by using the SANISAND model.

Coefficient of consolidation measured by cone penetration tests in overconsolidated cohesive soils

In offshore investigations, the dissipation test following penetration of a piezocone is extensively used in cohesive soils to obtain the consolidation behavior. Compared with that in normally consolidated soil, the dissipation response in overconsolidated silty clay or silt is more complicated, since the distribution of initial excess pore pressures and the subsequent dissipation depend on the overconsolidation ratio and partially drained conditions simultaneously. Large deformation finite element analyses within the formula of effective stress are carried out, where the large-amplitude displacement of piezocone under different drainage conditions and the dissipation are simulated. The large deformation approach is validated against centrifuge tests and cavity expansion solutions. A unique curve is established to estimate the nominal initial pore pressure at the shoulder of piezocone in overconsolidated soil, against a new normalized penetration rate. The curve is applicable to piezocone penetrations under different drainage conditions. The previous definition of operative coefficient of consolidation can be used to interpret the dissipation curves in overconsolidated soils as well. A unique backbone curve is proposed for overconsolidated soils to quantify the relationship between the operative and conventional coefficients of consolidation. A procedure is thus developed to determine in-situ conventional coefficient of consolidation of overconsolidated silty soils.

Analytical Solution of Cylindrical Cavity Expansion in the Construction Process of Pipe Pile

Analytical Solution of Cylindrical Cavity Expansion in the Construction Process of Pipe Pile

Undrained Solution for Cylindrical Cavity Expansion in Structured Clays Using a Hypoplastic Model

Undrained Solution for Cylindrical Cavity Expansion in Structured Clays Using a Hypoplastic Model

A graphical method for undrained analysis of cavity expansion in Mohr–Coulomb soil

A rigorous analytical solution is developed for undrained cavity expansion problems in non-associated Mohr–Coulomb soil, based on a novel graphical analysis approach and on the Lagrangian description through tracking only the responses of a soil particle at the cavity surface. The mathematical difficulties involved with the flow rate calculation when the stress state lies on the corner/edge of two adjacent (Mohr–Coulomb) yield surfaces, for both cylindrical and spherical cases, are tackled by using the generalised Koiter theory for non-associated plasticity. In particular, through the unique geometrical formulation, the effective stress path pertaining to the cylindrical cavity problem can be very conveniently directly determined, and is found to consist of simple, piecewise straight lines in the deviatoric stress plane with the orientations dependent of the relative magnitude of Poisson's ratio and the friction angle. This thus renders possible the removal of the stringent intermediacy assumption for the vertical stress that is commonly adopted in previous formulations, and hence the development of a complete cylindrical cavity expansion solution in Mohr–Coulomb soil under undrained loading conditions. The stress and deformation responses of the cavity, including the typical pressure–expansion curves and limiting cavity pressure, are finally analytically obtained along with the Lagrangian form of the radial equilibrium equation in completely explicit forms. The closed-form solution provided in this paper is the first rigorous one of its kind, thus completing the analytical analysis of the cavity expansion problem with the classical Mohr–Coulomb model; this is deemed to be essential for the interpretation of in situ test results pertaining to cohesive-frictional soils.

A numerical investigation on undrained expansion of a cylindrical cavity under biaxial in situ stresses using anisotropic S‐CLAY1 model

AbstractCavity expansion under biaxial in situ stresses is commonly encountered in geotechnical engineering, which, however, has not been well‐investigated at present. This paper numerically investigates the undrained expansion responses of a cylindrical cavity in S‐CLAY1 soil under biaxial in situ stresses. The advanced anisotropic S‐CLAY1 model is integrated by the semi‐implicit scheme and implemented as a user‐defined subroutine (UMAT) in the finite element model (FEM) to represent the elastoplastic behavior of the soil around the cavity during expansion. To validate and calibrate the FEM, a benchmark solution for cavity expansion under uniform in situ stress is specifically developed and compared with the FEM. Parametric studies are performed based on the FEM to numerically investigate the salient expansion responses under biaxial in situ stresses. The results reveal that the expansion responses, including the expansion pressures, the excess pore water pressures at the cavity wall, the distributions of the stress components around the cavity, are not only remarkably different with those under uniform in situ stress, but also different with the findings from the approximate analytical solutions. What is particularly surprising is that the positions of the maximum and minimum expansion pressures reverse with expansion of the cavity. The outcomes of present study reveal the significant mechanisms of undrained expansion of a cylindrical cavity under biaxial in situ stresses.

Cavity expansion solutions applied to help assess the partial drainage behavior characterization of the piezocone test

The present paper presents cavity expansion applications to help assess the drainage behavior characterization during piezocone tests. The solution considered a semi-analytical model and finite element approach with Drucker Prager plasticity models. The semi-analytical model initially presented by Dienstmann et al. (2017) is briefly presented to focus on a revision of the initial state of excess pore pressure, which adds more consistency to the previous work. We compared the numerical results and performed a complementary and broader sensitivity analysis based on this modification. Sequentially the solutions were applied in a set of parameters representative of piezocone tests performed at different rates on silty materials (gold tailings) and clay mixtures (kaolin and clayey sand). The results proved useful in identifying the transitional rates of behavior, especially from undrained to partially drained behavior.

Energy dissipation analysis for large-strain cylindrical cavity expansion problem in cohesive-frictional soils

This work presents an energy dissipation analysis for large-strain cylindrical cavity expansion problem in cohesive-frictional soils. Based on the unified strength criterion and the non-associated flow rule, the process of cavity expansion in cohesive-frictional soils is regarded as an energy conversion problem. The energy dissipation solution for large-strain cylindrical cavity expansion is obtained by introducing the energy dissipation mechanism into the conventional cylindrical cavity expansion analysis. Subsequently, the effects of the intermediate principal stress, elastic deformation and large-strain in the plastic region are considered in proposed solution. Finally, according to the comparisons of the results of the stress distributions and non-dimensional expansion pressure with those in the published literature, the validity and reliability of the theoretical method are proved. The results show that the non-dimensional expansion pressure increases with the increase of the coefficient of intermediate principal stress, the stiffness of the response increases with the increase of the dilation angle, and most of the work done by the external force is transformed into the energy in the plastic region.

Semi-analytical solution for undrained cylindrical cavity expansion in variably saturated soils

The effect of different initial degrees of saturation on the behaviour of variably saturated soils around an expanding cavity has not been adequately studied thus far. Therefore, this study aimed to fill this gap. Moreover, it sought to theoretically explain the cylindrical cavity expansion response in unsaturated three-phase media, particularly focusing on its effect on the cavity wall during the transition from an unsaturated to a saturated state. To this end, a semi-analytical solution based on a hydro-mechanically coupled Sheng–Fredlund–Gens model was proposed for the undrained cavity expansion problem in variably saturated soils in which unsaturated and fully saturated regions coexisted around the cavity. The cylindrical cavity expansion and expansion pressure response in initially unsaturated soils (considering different initial degrees of saturation) and initially fully saturated soils were explored. The proposed solution further extends the cavity expansion theory to unsaturated soils. Furthermore, this work could serve as a theoretical framework for modelling of the cavity expansion problem in the variably saturated soils considering the effect of hydraulic state transition.

A semi-analytical undrained solution for cylindrical cavity expansion in K 0-consolidated anisotropic soils under plane stress condition

To remove the limitation that the plane stress problem cannot be considered using cylindrical cavity expansion and to explore surface response of cylinder expansion in shallow soil, a semi-analytical undrained solution is developed for cylindrical cavity expansion in anisotropic modified Cam-clay model soils under the plane stress condition. The constitutive relationship is described by the K 0-consolidated anisotropic modified Cam-clay (K 0-AMCC) model, which can properly simulate the mechanical behaviour of the K 0-consolidated natural clays. The problem is equivalent to solving ordinary differential equations to determine the effective stresses, vertical strain, and excess pore water pressure (EPWP). Parametric analyses are conducted to investigate the effective stresses, vertical strain, and EPWPs around the expanded cavity under plane stress condition. The results show a clear influence of over-consolidation ratio on the stresses, vertical strain, EPWP around the cavity, and effective stress paths for a soil particle at the cavity wall. Axial expansion or uplift of soil and negative pore water pressure are observed during cavity expansion under the plane stress condition. There are obvious differences in effective stress components around the cavity under two plane conditions. The effective axial stress around the cavity wall is generally smaller than that under the plane strain condition.

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.