Non-homogeneous Clay Research Articles

Numerical Study on the Behavior of Square Stiffened Caissons Penetrating into Normally Consolidated Clay

Significant difference between predicted and measured installation resistance of stiffened suction caissons was identified due to the existing uncertainty regarding the mobilized soil flow mechanisms. This paper describes an extensive investigation of square stiffened caisson penetration in nonhomogeneous clays undertaken through large deformation FE (LDFE) analysis to identify the soil flow mechanisms around and between lateral ring stiffeners. A detailed parametric study has been carried out, exploring a range of nondimensional parameters related to stiffened caisson geometry, caisson roughness, and soil strength. The LDFE results were compared with centrifuge test data in terms of soil flow mechanisms, with good agreement obtained. Two interesting features of soil flow inside the caisson were observed including soil backflow into the gaps between the embedded stiffeners and soil heaving at the surface. It shows that the cavity depth can reach ∼5 m. Finally, simple expressions were proposed for estimating the critical depths of soil backflow and cavity formation.

Design equation for stability of a circular tunnel in anisotropic and heterogeneous clay

The safety assessment of tunnel stability is critical to tunnel construction and requires accurate analysis to obtain a reliable prediction. Strength anisotropy is an important aspect of clay behavior, but it is mostly neglected in practical stability analyses. In this study, the effects of undrained strength anisotropy and strength nonhomogeneity on the stability of unlined circular tunnels in clays are investigated. The static approach of lower-bound (LB) analysis using finite-element and second-order cone programming is employed to examine the aforementioned effects. The anisotropic shear strength of clay is modeled by employing an elliptical yield function under plane strain conditions. A complete set of dimensionless parameters covering the cover depth ratios of tunnels, normalized overburden pressure ratios, normalized strength gradient ratios of clays, and anisotropic strength ratios, are systematically investigated. The new LB solutions indicate that the stability load factor of the problem has a nonlinear relationship with the cover depth ratio and the anisotropic strength ratio, and there exists a linear relationship with the normalized overburden pressure and the normalized strength gradient. Their influence on the predicted failure mechanism is parametrically evaluated. A statistically approximate stability equation of unlined circular tunnels in anisotropic and non-homogeneous clay is proposed for the first time, which contains four new stability factors, namely, constant undrained strength, linearly increasing strength gradient, undrained strength anisotropy, and soil unit weight, and it can serve as a fast and accurate tool for predicting the undrained stability of this problem in practice.

Stability of active trapdoors in axisymmetry

Trapdoor stability has been widely studied by many researchers in the field of tunneling engineering. A general question being frequently asked is that why most sinkholes have a near-perfect circular shape on the ground surface. This could be possibly explained by the current numerical study using finite element limit analysis under axisymmetric condition, where upper and lower bound solutions of active circular trapdoors are determined. The failure study of sinkholes and the associated failure mechanisms in this paper are for non-homogeneous clay with a linear increase of strength with depth under various cover depth ratios and dimensionless strength gradients. A design equation for predicting the stability solutions is also developed based on the novel three dimensional solutions using axisymmetry.

Undrained stability analysis of dual unlined horseshoe-shaped tunnels in non-homogeneous clays using lower bound limit analysis method

A rigorous adaptive lower bound limit analysis method with 3-noded element (LB-FELA) is adopted to discuss the tunnel stability and failure mechanism of dual unlined horseshoe-shaped tunnels in non-homogeneous clays. The clays mass has heterogeneity, where the shear strength increases linearly with depth. This problem is defined as a plane strain analysis model. The calculation results are provided using the dimensionless stability numbers, which are affected by dimensionless parameters C/D, S/D and ρD/c0.The typical failure mechanisms of the dual horseshoe-shaped tunnels are presented based on the parametric studies using the final refined meshes of the proposed method. The results show that the dimensionless parameters ρD/c0, C/D,and S/D have great influences on tunnel stability and failure mechanism of the dual horseshoe-shaped tunnels. Using the calculation results provided by this paper, the tunnel designers can directly evaluate the stability of the tunnel in non-homogeneous clays.

Basal stability analysis of braced excavations in anisotropic and non-homogeneous undrained clay using streamline velocity fields

A basal heave stability analysis in anisotropic and non-homogeneous undrained clay by using the kinematic approach of limit analysis is presented. The proposed failure mechanism consists of four translational rigid blocks and a streamline-based shear zone. The velocity field for the shear zone, formulated by a streamline solution in a polar coordinate system, is a supplement to the previous streamline solution in rectangular coordinates. The present study is first verified by comparison with other existing solutions in homogeneous and isotropic soils. It is found that the streamline solution can produce sufficiently accurate upper-bounds compared with the multi-block mechanism, the finite element limit analysis and the shear strength reduction finite element method. Subsequently, validation of the streamline solution on basal stability in anisotropic and non-homogeneous clay is carried out by discussion on a well-documented case study.

Undrained stability of plane strain active trapdoors in anisotropic and non-homogeneous clays

Despite a large number of studies on the active failure of trapdoors conducted in the literature, there are very limited studies examining the combined influences of undrained strength anisotropy and non-homogeneity of clays on the problem. This paper presents the new lower bound solutions of the active failure of plane strain trapdoors in clays with linearly increasing anisotropic strengths. To achieve this purpose, the lower bound (LB) finite element limit analysis (FELA) of an anisotropic undrained strength criterion using second-order cone programming (SOCP) is developed to investigate the undrained stability of the problem under plane strain conditions. The anisotropic strengths of clays are modelled by employing an elliptical strength envelope requiring strengths in plane strain compression, extension and direct simple shear. The LB FELA is formulated by using a discrete form of the LB theorem of classical plasticity and a resulting optimization problem of anisotropic clay is cast and solved using the framework of conic quadratic optimization. A dimensionless technique is adopted to express the undrained stability of the problem in terms of adhesion factors of trapdoor roughness, cover-depth ratios, strength gradient ratios, and anisotropic strength ratios. The effects of these parameters on the trapdoor stability factor and associated failure mechanisms of trapdoors are also examined and discussed. Employing a nonlinear regression analysis to the computed LB solutions, the new design equations for the estimation of the undrained stability of trapdoors are proposed, where the effects of strength anisotropy and non-homogeneity as well as width and depth of trapdoor and its roughness can be considered for practical stability applications.

Upper bound finite element limit analysis method with discontinuous quadratic displacement fields and remeshing in non-homogeneous clays

As is known, limit analysis is a common way to study stability and failure mechanism of geotechnical engineering. This paper presents an upper bound finite element limit analysis (UB-FELA) formulation for non-homogeneous clays using discontinuous quadratic displacement fields and second-order cone programming (SOCP). The details are provided about the application of SOCP to the UB-FELA formulation for non-homogeneous clays. To reduce the calculation error, the analytic expressions are proposed concerning the rate of external work done by body forces and power dissipation caused by the plastic deformation following discontinuous quadratic displacement fields. With SOCP solver MOSEK, large-scale optimization problems of UB-FELA can be achieved in minutes via a desktop computer. The method is then applied to analyzing the stability of an undrained square tunnel and an undrained plane strain heading. The numerical results are compared with those reported in related studies. This method helps to obtain highly precise upper bound solution and clear failure mechanism of the computational domain.

Undrained Bearing Capacity of Strip Footings Under Inclined Load on Non-homogeneous Clay Underlain by a Rough Rigid Base

This paper aims to study the undrained bearing capacity of strip footings under inclined load on clay with linear increase of cohesion with depth underlain by a rigid base. The elasto-plastic finite element analyses through PLAXIS 2D 2012 code are carried out for rough footings. The results are presented in terms of the bearing capacity factor N′c with the inclination factor ic and failure envelopes. A new prediction of the yield locus for strip footings on non-homogeneous clay underlain by a rigid base is presented in this study. The numerical results are compared with the available publications in the literature.

Effects of strain softening on the penetration resistance of offshore bucket foundation in nonhomogeneous clay

The concrete-made bucket foundations were employed as emerging solution to support the wind turbine or breakwater, where the relatively large thicknesses of skirts and the strain softening effect related to the soil sensitivity and ductility were necessary to be explicitly accounted for. However, few of current study concerned this topic. This paper therefore reported an extensive parametric investigation of penetrating behaviour for bucket foundation in nonhomogeneous clay to allow a better estimation of penetration resistance of bucket foundation. The three-dimensional (3D) large deformation finite element (LDFE) analysis model incorporating the effect of strain softening on soil strength was set up and validated by comparing to the published centrifuge data. Then the evolution of soil flow mechanism and the distribution of soil strength softening were examined with the soil plug generated inside skirt assessed. Based on the numerical results, a new analytical model was proposed to predict the penetration resistance of bucket foundation in clay accounting for a partially-remoulded condition.

Undrained stability of unsupported rectangular excavations in non-homogeneous clays

Solutions for the undrained stability of unsupported excavations are important in practice as they can be used for assessing the safety of temporary excavations associated with various civil works. Even though the previous stability solutions of unsupported excavations namely infinitely long trenches and circular excavations are available in the literature, there is a lack of the stability solution of unsupported rectangular ones. In this paper, the lower bound solutions for the undrained stability of unsupported rectangular excavations in non-homogeneous clays are presented for the first time. A three-dimensional lower bound finite element limit analysis is developed in order to investigate the stability of this problem. The undrained shear strength of non-homogeneous clays are considered as a linearly increasing one with depth. The effects of aspect ratios of rectangular excavations, excavated depth ratios, and normalized strength gradients on the stability number of the problem and its associated failure mechanisms are examined parametrically. A new design equation of the problem is also firstly presented for practical use by practising engineers.

Undrained Stability of Unlined Square Tunnels in Clays with Linearly Increasing Anisotropic Shear Strength

In general, the undrained strength anisotropy of clays is found in nature. Its effect on a stability problem during undrained loading should be considered in order to get a more accurate and realistic safety assessment. In this paper, the undrained stability of unlined square tunnels in anisotropic and non-homogeneous clays is investigated by the lower bound finite element limit analysis using second-order cone programming. The anisotropic undrained strength of clays is modelled by using an elliptical strength envelope under plane strain conditions. The stability analyses of the problem are performed by the comprehensive investigations of the effects of the cover-depth ratio, the normalized overburden pressure, the normalized strength gradient, and the anisotropic strength ratio on the stability load factor and associated failure mechanisms. The computed lower bound solutions are validated with the existing results of square tunnels in isotropic clays. The new approximate equations of the stability load factor and factor of safety for square tunnels in anisotropic and non-homogeneous clays are first time presented by using a nonlinear regression, hence providing a reliable, accurate and convenient tool for stability analyses of the problem in practice. The numerical results reveal that the strength anisotropy has a significant impact on the stability load factor, especially when anisotropic clays have much difference in undrained strengths between compression and extension.

Undrained basal stability of braced circular excavations in non-homogeneous clays with linear increase of strength with depth

Braced circular excavations are commonly used as one of effective retaining structures in practice. Despite a number of studies in the past on the stability of this problem, its stability solution under the framework of lower bound limit analysis is very rare in the literature. The present study focuses on the stability analysis of braced circular excavations in non-homogeneous clays using the lower bound finite element limit analysis under axisymmetric conditions. The stability number of the problem is comprehensively investigated, and is affected by depth-radius aspect ratios of excavation, depth ratios of rigid base, and strength gradient factors. The influence of these dimensionless parameters on the predicted failure mechanisms are discussed and compared. The presented new lower bound solutions of braced circular excavations in non-homogeneous clays are useful for an accurate, convenient and reliable stability assessment of the problem in practice.

Lower bound solutions for undrained face stability of plane strain tunnel headings in anisotropic and non-homogeneous clays

In this paper, the face stability of plane strain tunnel heading in anisotropic and non-homogeneous clays is investigated by the lower bound (LB) finite element limit analysis (FELA) with second-order cone programming (SOCP). New LB solutions of the problem are numerically derived and described by the set of the dimensionless parameters consisting of the stability load factor, the cover-depth ratio, the normalized overburden pressure, normalized strength gradient, and anisotropic strength ratio while failure mechanisms associated with these parameters are also discussed and compared. The computed LB solutions are validated with the existing results of isotropic strengths confirming the accuracy and correctness of the solutions. Based on a nonlinear regression, the new design equations for the stability load factor and factor of safety for plane strain headings in anisotropic and non-homogeneous clays are first time proposed for assessing the undrained stability of relatively long-wall tunnels particularly considering the effects of strength anisotropy and non-homogeneity.

Spudcan Penetration Simulation Using the Coupled Eulerian-Lagrangian Method with Thermo-Mechanical Coupled Analysis

A novel modeling technique based on the coupled Eulerian-Lagrangian (CEL) method is provided to solve the geotechnical problems with large deformations. The technique is intended to solve the update problem of soil mechanical properties during spudcan penetration in normally consolidated clay soil. In the CEL model, the normal method of assigning an increasing shear strength profile with depth (NA) is defective due to its Eulerian framework. In this paper, a new technique is proposed to update soil material properties by introducing thermo-mechanical coupled analysis (TMCA) to the CEL models. During establishment of the CEL models, the optimal penetration velocity and minimum mesh size are determined through parametric studies. Reasonability and accuracy are then verified through comparison of the preliminary results with the soil flow configuration and penetration resistance (Fv) of a centrifuge test, and the results of the proposed method are compared with those of the remeshing and interpolation technique with small strain (RITSS) method. To achieve a CEL model with satisfactory accuracy, the NA and TMCA methods implemented in the CEL models and the RITSS method are first adopted in weightless soil. Comparison of the findings with those obtained in previous studies shows that the TMCA method can update material properties and predict Fv. The TMCA method is then applied to soils with self-weight and different shear strength profiles. Results show that the proposed method is capable of accurately modeling the large deformation problem of spudcan penetration in non-homogeneous clay.

Simple Equations for Considering Spatial Variability on the Bearing Capacity of Clay

In the present paper, the effect of spatial variability of undrained shear strength on the bearing capacity of shallow strip footing on clay was investigated and two new and simple equations were introduced for incorporating the effect of soil variability parameters on the undrained bearing capacity of strip footing on clay. For investigating the spatial variability of clay, undrained shear strength was assumed as a spatial variable parameter with the use of random field theory. The Monte Carlo simulation technique was used to obtain the probability distribution of the bearing capacity of footing on nonhomogeneous clay. The spatial variability of the undrained shear strength was investigated using three controlling parameters: coefficient of variation (COV) of the undrained shear strength as well as the scales of fluctuation of the shear strength in horizontal and vertical directions. The Mohr-Coulomb failure criterion and finite difference method were used to model the plastic behaviour of soil and calculate the bearing capacity of the footing. The results show that by increasing the COV of the undrained shear strength, the average bearing capacity decreases while the COV of the bearing capacity increases. Moreover, the average bearing capacity of footing has an approximate increasing trend with increasing the scales of fluctuation.

Evaluation of Undrained Bearing Capacities of Wide‐Shallow Bucket Foundation with Honeycomb Bulkheads in Clay

As a new type of offshore wind foundation, the wide‐shallow bucket foundation with honeycomb bulkheads mainly bears vertical, horizontal, and moment loads. As yet, no systematic study has been conducted regarding the effects of honeycomb bulkheads on the undrained bearing capacities of the wide‐shallow bucket foundation. In this study, a large number of three‐dimensional (3D) finite element (FE) analyses were performed to investigate the undrained bearing capacities of the wide‐shallow bucket foundations with and without honeycomb bulkheads, thereby evaluating the influence of honeycomb bulkheads on the bearing capacities under different conditions. The results show that under uniaxial loading, the uniaxial bearing capacities of the wide‐shallow bucket foundation are basically unaffected by the honeycomb bulkheads in homogeneous clay. For nonhomogeneous clay, the moment bearing capacity will be considerably enhanced with the increase in soil shear strength heterogeneity. Under combined loading, the honeycomb bulkheads will enhance the combined bearing capacities only in nonhomogeneous clay. The enhancement effects will increase with the increase in soil shear strength heterogeneity but decrease with the increase in vertical load. Besides, the simplified equations for calculating the uniaxial bearing capacities of the wide‐shallow bucket foundation with honeycomb bulkheads are also proposed considering the influence of embedment ratio and soil shear strength heterogeneity. At last, the parameters of an approximating expression are fitted to predict the failure envelopes of this foundation under combined loading.

Numerical investigation of novel dynamic installed fish anchors in clay and calcareous silt

This paper reports the results from three-dimensional dynamic finite element analysis undertaken to provide insight into the behaviour of a novel dynamically installed anchor (DIA), termed as fish DIA, during dynamic installation and monotonic pullout in non-homogeneous clay and calcareous silt. The fish DIA has an elliptic-shaped shaft, which reduces hydrodynamic drag resistance. The shaft is shaped to be thicker near the head to lower the mass centroid, and increase its diving potential with a specialised padeye position. A series of large deformation finite element analyses have been carried out considering the relevant range of parameters in terms of soil undrained shear strength; impact velocity, padeye offset ratio and pullout angle. Considering the difference in soil undrained shear strength, and DIA dimensions and mass; overall anchor tip embedment depths of the fish DIA lied in the range of that of the OMNI-Max DIA. The tracked anchor trajectory confirmed that, compared to the OMNI-Max DIA, the fish DIA dove deeper and earlier for a wide range of padeye offset ratio. These are more critical and beneficial for calcareous silt where the achieved embedment depths are generally lower compared to those in clay.

Basal stability analysis of braced excavations with embedded walls in undrained clay using the upper bound theorem

The embedded wall has beneficial effects on the basal stability of braced excavation in clay. Conventional basal stability analysis methods cannot evaluate the lateral resistance afforded by the wall reasonably. This paper presents a new failure mechanism to evaluate the basal stability of excavations with embedded walls in undrained clay based the upper bound theorem. The proposed mechanism consists of a rigid block and three shear zones, and the horizontal reinforcing effects of wall penetration blow the excavation base are considered. The embedded wall is regarded as an elastic beam and deforms consistently with the velocities of adjacent soil in the shear zone. The elastic strain energy stored in the wall is incorporated in the upper bound calculation to increase the stability of excavation. The proposed mechanism has also been extended to the basal stability of excavations in anisotropic and non-homogeneous clay. The applicability of the proposed mechanism was validated by comparison with the results of numerical limit analysis and FEM, as well as five field cases near or at failure. Two failure field cases in anisotropic clay were also studied using the proposed mechanism. The results showed that the proposed method is capable to yield reasonable estimation by using both isotropic and anisotropic shear strength.

Behavior of soil heave inside stiffened caissons being installed in clay

The length of suction caisson anchors has been increasing to support increasing dimensions and weight of floating facilities, which necessitates employing horizontal ring stiffeners at intervals along the inner wall of the thin skirt of caissons to ensure structural integrity. The addition of these stiffeners has created significant uncertainties regarding soil flow mechanisms, in particular soil heave inside the caisson, which may reduce the caisson final penetration depth and influence the process of installation due to the need to avoid inside soil suction in the pumping equipment. This paper reports results of large-deformation finite element (LDFE) analyses investigating soil heave inside stiffened caissons during installation in nonhomogeneous clay deposits, with the corresponding evolution of soil flow mechanisms and penetration resistance profiles reported by Zhou et al. in 2016. The LDFE analyses have simulated continuous penetration of stiffened caissons from the seabed surface. A detailed parametric study has been undertaken, exploring the relevant range of soil strength nonhomogeneity and normalized strength, stiffened caisson geometry, soil effective unit weight, and caisson roughness. Of particular interest is the influence of stiffeners on soil heave and potential penetration refusal. The results have been validated against previously published centrifuge test data in terms of soil heave and penetration resistance profile, with good agreement obtained. It is shown that the soil normalized strength at the mudline and its nonhomogeneity, caisson diameter relative to the sum of skirt thickness and stiffener width, and caisson penetration depth have significant influence on the inner soil heave and its profile across the caisson radius. An expression, based on the LDFE results is proposed to predict the maximum inner soil heave during installation of stiffened caissons in the field.

Effect of Load Eccentricity on the Bearing Capacity of Strip Footings on Non-homogenous Clay Overlying Bedrock

In underwater infrastructure design, foundations are embedded in soft clay seabeds that exhibited non-homogeneity of cohesion, and subjected to combined actions of vertical, inclined or eccentric loads due to the environmental conditions such as self-weight, wind and wave forces acting on substructure. This paper investigates the undrained bearing capacity for surface and embedded strip footings on non-homogenous clay overlying bedrock. Elasto-plastic finite element analyses are carried out for perfectly rough strip footings on Tresca soil under vertical eccentric loads. Meyerhof’s effective width rule is examined for the cases of surface and embedded footings in non-homogeneous clay. The effect of load eccentricity on the distribution of the normal stresses under strip footings is also investigated in this study. It is found that the effective width rule provides a conservative estimate of the bearing capacity. The elasto-plastic calculations predict that tensile stresses occur for surface footings because of the full bonding at the soil-footing interfaces, while for embedded footings, there is no tensile stresses.