Strain Path Method Research Articles

Heave Analysis of Unreinforced Inclusion Column in Low Sensitivity Soft Clay

The ground improvement technique with inclusions, is now widely available and used in Indonesia. Typically, it uses unreinforced concrete/mortar columns, commonly referred as rigid inclusions, for enhancing the composite ground engineering properties. Using this approach, the applied load will be distributed to both the rigid inclusions and in-situ soft soil. On the surface, this technique is analogue to compression-only cast-in-situ deep foundation element (i.e., bored pile), but with different design concept. Nonetheless, when these inclusions are installed in clay soil, either with displacement or semi-displacement method, the installed inclusions may experience heave (similar like driven pile), which is caused by ground deformation in the vicinity of installed inclusions. As these inclusions are not reinforced, mobilizing upward skin friction from excessive heave may develop into an integrity issue, specifically, when the mobilized upward force is larger than the inclusion tensile capacity. This study shows an observed heave on unreinforced inclusion columns. Retrospective soil heave prediction using shallow strain path method (SSPM), is presented. Proposed recommendations for avoiding such issue are discussed.

Research on the penetration characteristics of elliptical cross-section projectile into semi-infinite metal targets

To better understand the penetration characteristics of the elliptical cross-section projectile (ECSP) into metal targets, a series penetration experiments of projectiles with different shape cross-section to semi-infinite aluminum target were carried out. The shape ratios of typical ECSPs were 1.25 and 1.56, respectively, and another was circular cross-section projectile (CCSP) which has the same cross-section area in accordance with ECSP. In the penetration experiments, the projectiles were launched with striking velocities ranged from 400 m/s to 1000 m/s, and strain sensors were arranged on the impact surface of the aluminum target to catch the dynamic response during the penetration process. Then, characteristics of cracks on the impact surface of targets, penetration depths and penetration trajectory were measured after the penetration experiments. The results indicated that the dynamic response and damage behavior of targets showed obvious asymmetry under the penetration of ECSPs. Strain data had a decreasing trend from the major axis to the minor axis of the ellipse, and the length and number of cracks of the ECSP were larger than that of the CCSP. Besides, a theoretical model was developed to explain the asymmetric deformation and failure behavior of targets based on the conformal mapping theory and the strain path method. Calculation results showed that the asymmetric deformation of targets was directly caused by the displacement boundary conditions of the ellipse.

Soil flow mechanisms around cone penetrometer in layered clays

The cone penetrometer test is widely used for in situ site investigations and for establishing direct penetrometer-to-foundation or -anchor design correlations. This paper focuses on soil flow mechanisms during the continuous penetration of a cone penetrometer in layered clays. A series of centrifuge tests was conducted with the cone penetrating through soft–stiff, stiff–soft, soft–stiff–soft and stiff–soft–stiff clay profiles. Particle image velocimetry allowed accurate resolution of the soil flow mechanism around the cone where a half-cone model was penetrated into layered clays against a transparent window. The observed soil movement was compared both with previous observations for piles/cones and with movement from the shallow strain path method (SSPM). A comparison with SSPM results showed that the SSPM can provide reasonable evaluations on maximum lateral and vertical displacements even though the upheave movement can be overestimated. The effect of soil layering on the failure mechanisms was studied extensively by exploring soil flow mechanisms and soil displacement paths at various distances from the advancing cone centreline and soil layer interface. The reported characteristics of cone penetration in layered soils provided in-depth understanding of cone penetration responses that will lead to the development of mechanism-based theoretical models for cone penetration in layered fine-grained soils.

A semi‐analytical solution for displacement‐controlled elliptical cavity expansion in undrained MCC soil

AbstractConventional cavity expansion theory is a one‐dimensional problem and is not applicable for the two‐dimensional cavity expansion issue, which is also required for geotechnical problems. This paper proposes a novel semi‐analytical solution for displacement‐controlled elliptical cavity expansion (DC‐ECE) in undrained soil. The displacement and strain fields for DC‐ECE are obtained from the strain path method (SPM) with the aid of conformal mapping theory. The effective stress can be subsequently obtained by the incremental stress‐strain calculation using a suitable constitutive model such as the MCC model. Then, the computed effective stress results are substituted into the stress equilibrium equation to give the pore pressure solution. The new semi‐analytical solution reveals the non‐axisymmetric characteristics of DC‐ECE and allows the elastic‐plastic (EP) boundary, excess pore pressure, stress, and displacement to be calculated. The proposed method provides a solution to non‐axisymmetric cavity expansion issues and it can be applied to geotechnical engineering problems, including vertical drain installation, flat dilatometer tests and noncylindrical pile penetration in clay.

Large-strain analysis of undrained smooth tube sampling

Borehole tube sampling is a key process of geotechnical engineering. The paper presents numerical analyses of smooth tube sampling in clay using the particle finite-element method. The soil is described by a conventional elasto-plastic constitutive model (Tresca plasticity and a quasi-incompressible elastic law). The sampler is advanced by several diameters into the soil until a steady state is observed. The elasto-plastic numerical solution for a round-tipped sampler clearly identifies a localised shear failure mechanism at the entrance of the tube. Relevant strain path method (SPM) solutions are numerically evaluated to facilitate full field comparison. For a given thickness ratio elasto-plastic simulation predicts far less compression but much larger extensions at the centreline than SPM. The results also show how including a bevelled sampler tip or a stationary piston changes the failure mechanism and significantly reduces induced peak extension strains. The results agree with available experimental data and well-established empirical observations. The methodology presented may open the way to a soil mechanics-based rational approach to soil sampling simulation.

Geotechnical properties of 3D-printed transparent granular soil

This paper proposes a 3D-printed transparent granular soil technique based on the contour rotation interpolation method, 3D printing and transparent soil technologies. Laboratory tests, including one-dimensional compression, direct shear and triaxial compression tests, are assessed for mechanical properties of 3D-printed transparent granular soil. The results show that 3D-printed transparent granular soil can be used to consider the effect of shape on macromechanical soil properties, which is an advantage that cannot be achieved by the previously presented transparent soil techniques. Subsequently, a simple model test of rigid flat plate penetration into transparent granular soil is performed. The obtained soil displacements using the PIV technique are compared with the classical shallow strain path method solution. This comparison indicates that the proposed 3D-printed transparent granular soil can capture the soil deformation pattern, although the accuracy needs to be further improved. The proposed 3D-printed transparent granular soil technique could be used for model test that needs to consider the shape of sand particle.

Displacement analysis of open pipe piles sinking based on strain path method

The displacement field in the process of opening pipe piles sink has always been a hot issue in the study, especially in the area of pile, the soil body has produced a large strain, regardless of the large deformation effect of the soil, there will be a large calculation error. The strain path method can obtain the flow velocity of the soil because it does not rely on the constitutive relationship of the soil, which is a favorable theory for solving large strain problems. In this paper, the modified strain path method is used as the theoretical basis. The open pipe pile is equivalent to a closed pipe pile through the soil plug effect, and the sunk pile displacement of the open pipe pile is calculated to further reveal the soil plug effect and the soil squeeze effect of the open pipe pile mutual restraint and mutual influence, thus providing a theoretical basis for the pile displacement of open pipe piles.

Soil compacting displacements for two jacked piles considering shielding effects

Shielding effects have a significant influence on the estimation of soil displacements for jacked piles, which have received minimal attention in previous studies. To include the shielding effects, a novel model was established for the soil compacting displacements of two jacked piles based on the strain path method and the source–sink method. The corresponding closed-form analytical expressions were also derived. Soil compacting displacements were calculated using the proposed method and the previous method, which disregard the shielding effects. The results showed that the soil displacements obtained based on the shielding effects are larger than those obtained when the effects are disregarded in the frontal direction, whereas the opposite results are obtained in the dorsal direction. The shielding effects have significant influence on the soil displacements in the frontal direction and those in the dorsal direction. Consequently, shielding effects should be included in the calculations of soil compacting displacements in the frontal and dorsal directions. An in situ test was also performed to investigate the reasonability of the proposed approach. Computed displacements were compared with the measured data. The results showed that the proposed model effectively predicts practical displacements, which demonstrates the validity of the proposed model. Further research is needed to verify the practicality of the described method.

Analytical model for evaluating XCC pile shaft capacity in soft soil by incorporating penetration effects

The derivation of a new analytical model for predicting the soil displacement of X-section cast-in-place concrete (XCC) piles installed vertically into soft clay as well as for predicting limit shaft resistance during loading phases is presented in this paper. The analytical model is formulated by assuming that the XCC pile penetration process is an X-shaped cylindrical cavity expansion process. Based on the theoretical framework of the Strain Path Method (SPM), the strain, displacement and stress induced by X-shaped cavity expansion can be obtained. The proposed analytical model is validated by comparing the degenerate solution of this study with that of conventional circular (cylindrical) cavity expansion theory. Analytical model-based design methods are then proposed for evaluating soil displacement and XCC pile shaft capacity. Theoretical predictions are compared with field test measurements to verify the suitability of the proposed design method. The proposed new analytical model reveals the fundamental penetration mechanics of XCC piles and gives improved design methods for determining XCC pile shaft capacities.

A novel analytical approach for predicting the noncylindrical pile penetration‐induced soil displacement in undrained soil by combining use of cavity expansion and strain path methods

SummarySince development of cavity expansion theory and strain path method, almost all the conventional analyses of pile penetration problem have been based on circular cross section penetrometer. However, noncylindrical pile (with noncircular cross section) is also required in geotechnical engineering such as rectangular cross‐sectional pile, X‐sectional cast‐in‐place concrete pile, H‐shaped steel pile, prefabricated vertical drains, and flat dilatometer. This paper presents a novel and general analytical approach for capturing the soil deformation mechanism around the pile with arbitrary cross section. The penetration problem is simulated by a new 2‐dimensional (radial and circumferential) cavity expansion model. Based on the theoretical framework of strain path method, the kinematics (velocity field) of the noncylindrical cavity expansion is reduced to solve the Laplace equation with arbitrary velocity boundary conditions by using the conformal mapping technique. Then, solutions for the strain and displacement, which could consider the large deformation effect, are obtained by the integration of the strain rate and velocity along the streamline. The analytical solution is validated by comparing the degenerate solution of this study with conventional circular (cylindrical) cavity expansion theory. Subsequently, typical numerical examples for the deformation mechanism of elliptical and rectangular cavity expansion are presented to prove the advantage of the proposed new solution particularly in capturing the noncylindrical symmetric displacement field. A brief application of the proposed new analytical solution to the interpretation of the smear effect of prefabricated vertical drain installation confirms its useful in geotechnical engineering.

Transparent Sand Experimental Method for Geotechnical Physical Modeling Using Digital Imaging of Particle Image Velocimetry

By means of the technology of particle image velocimetry (PIV), the physical modelings, using transparent sand and natural sand, were set up to simulate the shallow foundation, respectively. The transparent soil is composed of fused quartz and correspondingly refractive index-matched flammable liquid. The flammable liquid is blended by two white mineral oils, Krystol40 and Puretol7. Transparent sand model was projected by a laser light sheet; meanwhile, the digital images of soil deformations caused by shallow foundation were captured. The PIV was employed to obtain the generated displacement fields from the digital images. The experimental results indicate that the deformation trends in transparent sand model are consistent with that in natural Ottawa sand model; however, the influential region is expanded by about 1.5 times, and the zone and magnitude of down-drag subsidence are extremely enlarged in transparent soil model, compared with those in Ottawa sand model. The verification of test results shows that the shallow strain path method is not suitable for the small-scale transparent sand and natural sand models.

Numerical simulations of deep penetration problems using the material point method

Penetration problems in geomechanics are common. Usually the soil is heavily disturbed around the penetrating bodies and large deformations and distortions can occur. The simulation of the installation of displacement piles is a good example of the interest of these types of problems for geomechanics. In this paper the Material Point Method is used to overcome the difficulties associated with the simulations of problems involving large deformation and full displacement type penetration. Recent modifications of the Material Point Method known as Generalized Interpolation Material Point and the Convected Particle Domain Interpolation are also used and evaluated in some of the examples. Herein a footing submitted to large settlements is presented and simulated, together with the processes associated to a driven pile under undrained conditions. The displacements of the soil surrounding the pile are compared with those obtained by the Small Strain Path Method. In addition, the Modified Cam Clay model is implemented in a code of MPM and used to simulate the process of driving a pile in dry sand. Good and rather encouraging agreement is found between compared data.

Discrete element modelling and cavity expansion analysis of cone penetration testing

This paper uses the discrete element method (DEM) in three dimensions to simulate cone penetration testing (CPT) of granular materials in a calibration chamber. Several researchers have used different numerical techniques such as strain path methods and finite element methods to study CPT problems. The DEM is a useful alternative tool for studying cone penetration problems because of its ability to provide micro mechanical insight into the behaviour of granular materials and cone penetration resistance. A 30° chamber segment and a particle refinement method were used for the simulations. Giving constant mass to each particle in the sample was found to reduce computational time significantly, without significantly affecting tip resistance. The effects of initial sample conditions and particle friction coefficient on tip resistance are investigated and found to have an important effect on the tip resistance. Biaxial test simulations using DEM are conducted to obtain the basic granular material properties for obtaining CPT analytical solutions based on continuum mechanics. Macro properties of the samples for different input micro parameters are presented and used to obtain the analytical CPT results. Comparison between the numerical simulations and analytical solutions show good agreement.

XCC pile installation effect in soft soil ground: A simplified analytical model

This paper presents a simplified analytical model: the X-shaped cylindrical cavity expansion method (XCEM), which can be used to interpret and predict the displacement, stress, and excess pore pressure caused by the X-section cast in place concrete (XCC) pile installation in soft soil. Analytical solutions for the displacement and strain field are obtained with a streamlined solution, base on the strain path method (SPM). The stress and excess pore pressure can then be subsequently determined with the assumption of the elastic-perfectly plastic soil behavior. A positive agreement was found when the theoretical prediction of the displacement, stress, and excess pores pressure was compared against the field measurements. The proposed XCEM improves the conventional cavity expansion method (CEM) and offers a framework for understanding the non-circular cross-section penetrator problem, which is different from the conventional circular penetrator problem.

Interpretation of Cone Factor in Undrained Soils via Full-Penetration Finite-Element Analysis

AbstractThe cone penetration test is widely used to interpret the undrained shear strength of soil. The interpretation methods are commonly based on bearing capacity, cavity expansion, or strain-path methods. In this paper, the cone penetration test is analyzed using the large deformation FEM and contact mechanics. The full penetration process from the ground surface is modeled. The three-parameter Tresca model is used to represent the undrained soil behavior in a total stress analysis, to derive a cone factor equation for interpretation of the undrained shear strength. This equation is then compared with existing solutions in the literature as well as experimental data. The complexities that arise in more sophisticated soil models are elaborated in an effective stress analysis using the Modified Cam Clay model.

Study on Different Methods of Computing Consolidation Coefficient by Excess Pore Pressure Dissipation Datum on CPTU

Based on the different methods of computing the soil consolidation coefficient by excess pore pressure dissipation datum on CPTU, through computing the soil consolidation coefficient by different methods on the datum of CPTU model test and CPTU application research on Pearl River Delta, the applicability on different methods of computing consolidation coefficient by CPTU has been studied. The results show that on the computing value of consolidation coefficient, TB10041-2003 is more conservative; because of poor applicability on Strain Path Method and difficulty for obtaining t100 on Zhu-Xiaolin Method and α on Empirical Coefficient Method, some results can not be solved, so Strain Path Method and Zhu-Xiaolin Method and Empirical Coefficient Method are poor in engineering application; the computing way and the computing result on Zhang-Chenghou Method are similar with Torstensson Method with 50% consolidation degree. The achieved result can provide a foundation for further study for CPTU application research.

Undrained shear strengths of clay around an advancing cone

Strength anisotropy of clay is significantly associated with the orientation of principal strain. Mobilized undrained shear strength will vary with the orientation of the principal stresses because cone penetration imposes large rotations of the principal stresses in the surrounding soil. The objective of this paper is to investigate the undrained failure modes around an advancing cone. In this study, strain softening behavior is not considered. The strain field of the soil obtained using the strain path method shows that the principal strain conditions of the soil around an advancing cone can be simplified into the following zones: spherical expansion strain zone, plane strain shearing zone, cylindrical expansion shearing zone, cylindrical expansion zone, and transition zone. The mobilized undrained shear strength of clay in various strain states can be determined by employing the anisotropic strength criterion and the associated flow rule. The result shows that the ratio of the equivalent undrained strength mobilized in the vicinity of the cone tip over the undrained shear strength obtained from a Ko-consolidated undrained compression triaxial test is found to range from 0.88 to 1.07 when the strength anisotropy ratio ranges from 0.4 to 0.9.

Physical modelling of pile penetration in clay using transparent soil and particle image velocimetry

A small-scale physical modelling method was developed to study the movement of clay during pile installation. The clay was simulated using a mixture of amorphous silica and mineral oil, which becomes almost transparent when the refractive indices of the oil and the silica are well matched. After adding reflective particles and consolidating the mixture in a transparent container, cylindrical model piles were driven vertically at the centre. A vertical section aligned with the pile centreline was illuminated by a laser light sheet, and a sequence of digital images was recorded. These were analysed using particle image velocimetry, and the complete displacement distribution during the pile installation was obtained. Notwithstanding some discrepancies at shallow depths, the observed displacements generally showed fairly good agreement with the theoretical predictions of the shallow strain path method (SSPM) once the effect of some soil trapped beneath the flat pile tip was taken into account. Normalisation of the horizontal and vertical components of movement employing both the pile length and radius, based on SSPM theory, was shown to be valid. The normalised vertical displacement contours were similar to those published by previous researchers. The results of this study could be used to assess the impact of disturbance due to pile installation on, for example, buried services or archaeology.

Steady‐state solution for cylindrical penetrometers

AbstractThis paper suggests a new method for obtaining steady‐state solutions for ‘full‐flow’ penetrometers. The method is based on the numerical solution of the small strain plastic‐flow problem (i.e. rigid plastic material) with an inhomogeneous strength field, which is determined by converting changes of material properties over time in a stationary frame of reference into spatial distribution of strength in a moving frame of reference. Rather than building streamlines from back integration of soil element distortion, as previous methods have suggested, the method treats the domain as continuous with the associated field equations. The method employs an upstream weighting technique for the determination of information flow within the domain. The execution order for the calculation is based on topological ordering. This results in the calculation having a complexity of O(N), as compared with O(N1.5) for the strain path or streamline methods (N is the number of discretized points), which significantly reduces the calculation time. The formulation is presented for the cylindrical (T‐bar) penetrometer, and includes aspects of soil strength degradation, strain rate effects, strength anisotropy, and interface strength law. Comparison to previously published values, based on large displacement finite element simulations with remeshing, showed good agreement, indicating on the correctness of the suggested approach. Investigation into the soil rigid‐body rotation and the remolding effect on anisotropy characteristics showed an interesting behavior, where the decrease of strength anisotropy due to remolding has a greater influence when the soil strength is higher in the vertical direction. Copyright © 2009 John Wiley & Sons, Ltd.

Arbitrary Lagrangian Eulerian based finite element analysis of cone penetration in soft clay

This paper presents a numerical model for the analysis of cone penetration in soft clay based on the finite element method. The constitutive behaviour of the soil is modelled by modifying an elastic, perfectly-plastic soil model obeying Von-Mises yield criterion to take into account the strain-softening, rate dependent behaviour of soft clay. Since this is a problem involving large soil deformations, the analysis is carried out using an Arbitrary Lagrangian Eulerian method where the quality of the mesh is preserved during penetration. The variation of cone resistance is examined with various parameters such as rigidity index of the soil, in situ stress anisotropy and roughness at the cone–soil interface, which influence the penetration resistance of the cone. A theoretical correlation has been developed incorporating these parameters and the results have been compared with previous correlations based on the cavity expansion theory, finite element method and strain path method. With the increase in strain-softening, relative brittleness of the soil increases and the penetration resistance is significantly reduced. With the rising strain-rate dependency, penetration resistance increases but this increase is independent of the degree of brittleness of the soil.