Two-layered Clays Research Articles

Synergistic integration of isogeometric analysis and data-driven modeling for enhanced strip footing design on two-layered clays: Advancing geotechnical engineering practices

This study innovatively combines Isogeometric Analysis (IGA) with Machine Learning (ML) to assess strip footing bearing capacity on dual clayey layers. Overcoming limitations of conventional methods with small sample sizes, our research generates a dataset of 10,000 samples, allowing a thorough exploration of diverse soil profiles. Facilitated by ML, 10,000 IGA analyses using upper bound limit analysis unveil intricate patterns and relationships previously obscured. The key innovation lies in harnessing big data and employing advanced data visualization, particularly 2D and 3D Partial Dependency Plots (PDPs). These PDPs visually showcase the impact of factors such as upper layer thickness, cohesion ratios, shear strength profiles, footing depth, and foundation roughness on bearing capacity. Offering intuitive insights, these visualization tools enhance comprehension, aiding informed decision-making in design and construction. Engineers and geotechnical experts receive a precise predictive tool, optimizing strip footing performance on clayey soil layers. Moreover, this research contributes to advancing geotechnical engineering by enriching fundamental knowledge of load-bearing characteristics. In summary, the fusion of big data, advanced visualization, and upper bound limit analysis, exemplified by PDPs, signifies a substantial leap in geotechnical engineering, impacting design, construction, and infrastructure development.

Correction: 3-Dimensional Bearing Capacity of Strip and Square Footings on Two-Layered Clay

Correction: 3-Dimensional Bearing Capacity of Strip and Square Footings on Two-Layered Clay

Coupled pore pressure analysis of cone penetration test in two-layered clay

PurposeThe paper aims to clarify the distribution of excess pore pressure during cone penetration in two-layered clay and its influence on penetrometer resistance.Design/methodology/approachAn arbitrary Lagrangian–Eulerian scheme is adopted to preserve the quality of mesh throughout the numerical simulation. Simplified methods of layered penetration and coupled pore pressure analysis of cone penetration have been proposed and verified by previous studies. The investigation is then extended by the present work to study the cone penetration test in a two-layered clay profile assumed to be homogeneous with the modified Cam clay model.FindingsThe reduction of the range of pore pressure with decreasing PF will cause a decrease of the sensing distance. The PF of the underlying soil is one of the factors that determine the development distance. The interface can be obtained by taking the position of the maximum curvature of the penetrometer resistance curve in the case of stiff clay overlying soft clay. In the case of soft clay overlying stiff clay, the interface locates at the maximum curvature of the penetrometer resistance curve above about 1.6D.Research limitations/implicationsThe cone penetration analyses in this paper are conducted assuming smooth soil-cone contact.Originality/valueA simplified method based on ALE in Abaqus/Explicit is proposed for layered penetration, which solves the problem of mesh distortion at the interface between two materials. The stiffness equivalent method is also proposed to couple pore pressure during cone penetration, which achieves efficient coupling of pore water pressure in large deformations.

3-Dimensional Bearing Capacity of Strip and Square Footings on Two-Layered Clay

3-Dimensional Bearing Capacity of Strip and Square Footings on Two-Layered Clay

Structure and properties of montmorillonite containing Ca2+, Sr2+, and Ba2+ cations simultaneously

Most raw montmorillonites (MMT) used for radioactive waste disposal (HLW) contain Ca in the interlayer space. When HLW and MMT come into contact, various ions, such as Sr2+ and Ba2+, enter the mineral. Therefore, the article presents the results of modeling, based on molecular dynamics, for four different models for the replacement of part of Ca2+ with Sr2+ and Ba2+ ions in Ca-MMT.The general trend of MMT swelling does not change significantly after the introduction of Sr2+ and Ba2+ ions. The diffusion coefficient of water molecules increases with an increase in the number of H2O layers between mineral layers or the presence of a certain amount of large radius ions in the series Ca-MMT, Ca-Ba-MMT, Ca-Sr-MMT, Ca-Sr-Ba-MMT. It shown that in the state of single-layer clay hydration, all the studied cations form outer-sphere complexes. During two-layer clay hydration, Ca2+ tends to form outer-sphere complexes, while Sr2+ and Ba2+ ions predominantly form inner-sphere complexes. With a further increase in the number of water molecules, the interaction of Ca2+ with the basal surface of the MMT mineral layer increases.

Probabilistic bearing capacities of strip foundation on two-layered clay

The bearing capacity of a shallow foundation on two-layered soil has been widely studied using deterministic methods, without considering the spatial variation within layered soils. In this study, the bearing capacity of strip foundations on two-layered clay considering spatial variability is investigated by using the random finite element method (RFEM). The results show that the embedment ratio and the spatial variability parameters of the upper layer could significantly affect the normalized probabilistic bearing capacities. Based on the random forest algorithm, a model is established to predict probabilistic bearing capacities, which can be applied as an easy-to-use method without carrying out RFEM analysis.

Failure Envelopes for Circular Foundations on Two-Layered Clay under Combined Loading

This study numerically investigates the undrained bearing capacity of circular foundations founded on a two-layered clay under combined loading of vertical, horizontal, and moment loads using three-dimensional finite-element analysis. Each clay layer has different thicknesses and shear strengths, and two types of foundation–subsoil interface are considered: an interface with (a) zero tensile capacity or (b) nonzero tensile capacity. Analysis results are presented in the form of normalized failure envelopes for a wide range of layer thicknesses and shear strength ratios. The presented normalized failure envelopes under combined loads with or without the interface tension can be considered as graphical solutions for circular foundations on a two-layered clay in offshore marine environments. Failure mechanisms under various combined loads provide further insights into foundation-layered soil interactions.

Calculation Method for Optimizing the Bearing Capacity of Two-Layer Clay Foundation Based on Upper-Bound Limit Analysis

In this study, a foundation bearing capacity limit analysis upper-bound solution (FLU) was proposed under the theoretical framework of limit analysis. To be more specific, an optimized mathematical model based on a rigid block discrete system was first established, with the minimum bearing capacity as the objective function, block velocity as the main variable, and the satisfaction of velocity compatibility, associated flow rule, and functional equilibrium equations of adjacent blocks as main constraints. Then, using an optimization approach, the upper-bound value of the foundation’s bearing capacity was obtained. On this basis, the principle of establishing the value interval of the most dangerous slip depth of the two-layer clay foundation was developed by investigating the effects of varying depths on the bearing capacity of the two-layer clay foundation. Meanwhile, an approach for calculating the bearing capacity of the two-layer clay foundation was proposed to achieve the goal of reaching the foundation’s minimum bearing capacity. Furthermore, using a mathematical example, the proposed approach was proven to be rational.

Effect of Compressibility on Undrained Bearing Pressure of Circular Footing Resting on Two-Layered Clay

Effect of Compressibility on Undrained Bearing Pressure of Circular Footing Resting on Two-Layered Clay

Ultimate uplift resistance of circular plate anchorsin undrained two-layer clays

The vertical uplift resistance of circular plate anchors buried in undrained two-layered clays was studied by means of finite element method. Anchors with immediate breakaway (vented) and no breakaway (bonded) are taken into account. The numerical results are given in the form of the breakout factors accounting for the anchor embedment depth, top layer thickness, clay strength ratio, and clay overburden (clay self-weight), which are compared with existing empirical and analytical solutions.It is found that the breakout factors for strong-over-soft clays are greater than those for soft-over-strong clays. Also, the breakout factors of bonded anchors are identical to those of vented anchors with large overburden pressure. Failure patterns are examined for the cases of soft-over-strong clay and strong-over-soft clay, depending on anchor embedment depth and top layer thickness.

Undrained vertical pullout capacity of strip plate anchors in two-layered clay

Undrained vertical pullout capacity of strip plate anchors in two-layered clay

Bearing Capacity Factor of Circular Footings on Two-layered Clay Soils

Geotechnical engineers often deal with layered foundation soils. In this case, the soil bearing capacity assessment using the conventional bearing capacity theory based on the upper layer properties introduces significant inaccuracies if the top layer thickness is comparable to the rigid footing width placed on the soil surface. Under undrained conditions the cohesion increases almost linearly with depth. A few theoretical studies have been proposed in the literature in order to incorporate the cohesion variation with depth in the computation of the ultimate bearing capacity of the strip and circular footings. Rigorous solutions to the problem of circular footings resting on layered clays with linear increase of cohesion do not appear to exist. In this paper, numerical computations using FLAC code are carried out to assess the vertical bearing capacity beneath rough rigid circular footing resting on two-layered clays of both homogeneous and linearly increasing shear strength profiles. The bearing capacity calculation results which depend on the top layer thickness, the two-layered clays strength ratio and the cohesion increase rates with depth are presented in both tables and graphs, and compared with previously published results available in the literature. The critical depth for circular footing is found significantly less than for strip footing. Doi: 10.28991/cej-2021-03091689 Full Text: PDF

Three-dimensional trench stability in non-uniform undrained clay with discretization-based kinematic analysis

This paper presents a three-dimensional trench stability analysis in non-uniform undrained clay adopting the kinematic approach of limit analysis. Rather than assuming a classic curved cylinder (“torus”) shape, the failure surface of the proposed rotational mechanism is formulated by a spatial discretization technique in order to accommodate the non-uniformity profile of soil’s undrained shear strength in a multi-layered ground as well as better adaptation to typical trench geometries in practice. The present study agrees well with the traditional torus rotational mechanism in terms of the normalized trench stability number in uniform clay when trench length to depth ratio is greater than 0.6, while significant improvement to the previous solution is achieved for shorter trench panels. A linear variation pattern between trench stability number and soil shear strength gradient is found for non-uniform soil profiles, in particular for shorter trenches. A simplified method is thereafter introduced for preliminary trench stability evaluation in non-uniform clay profiles. For trenches in two-layered clay, a more notable change in trench safety factor with layer thickness ratio is observed when the top layer is weaker than the bottom layer.

Undrained stability of unsupported conical slopes in two-layered clays

A conical slope is widely used in many constructions of in situ piles, piers, footings, mat foundations, raft foundations, energy storages, or water tanks since this unsupported excavation is much cheaper than an excavation with supports. This paper presents new plasticity solutions for undrained stability of unsupported conical slopes in two-layered clays by using axisymmetric finite element limit analysis. Four parametric studies were performed on the slope height ratio, the slope inclination angle, the thickness ratio of two-layered clay, and the strength ratio of two-layered clay, where the stability factor of this problem is investigated. In all the cases, the exact stability factors are accurately bracketed by lower and upper bound solutions within 1%. The design charts for estimating the stability of conical slopes in two-layered clays are proposed. Three failure mechanisms, i.e., toe, based, and face failures are observed and discussed in the paper. The predicted failure mechanisms of the unsupported conical slopes in two-layered clays are presented in order to portray the impact of all considered dimensionless parameters.

Undrained stability of active trapdoors in two-layered clays

Several environmental changes can induce an underground hole, leading to failures of non-ground infrastructure, such as pavements. Under a continued overload of traffic action on the pavement, the hole can potentially collapse, leading to creation of potholes. This phenomenon is commonly known as a trapdoor problem. Even though there are several previous works considering this problem, the stability solutions of trapdoors in two-layered soils have not yet been studied. To estimate the undrained stability of active trapdoors in two-layered clays under plane strain conditions, numerical solutions based on the finite element method have been developed. The influence parameters include the coverage depth of the trapdoor, and the thickness and undrained shear strength of the clay layers. The effects of these parameters on the stability of active trapdoors as well as their associated failure mechanisms are examined and discussed in this paper. The solutions are presented in the form of dimensionless charts that can be used for the design of trapdoor systems in two-layered clays with different thicknesses and undrained shear strengths.

Shape Effects on Bearing Capacity of Footings on Two-Layered Clay

The undrained vertical bearing capacity on a two-layered clay of centrally loaded rigid strip, rectangular and ring footings is studied parametrically with 2D, 3D and axisymmetric finite-element analyses. The shear strength ratio of the two layers and the relative thickness of the uppermost layer with respect to pertinent foundation dimension are the key parameters investigated. In addition, for rectangles and rings the length-to-width (“aspect”) ratio and the ring width to external radius ratio are reported. The results are portrayed in diagrams of bearing capacity and shape modification factors, in the familiar soil mechanics form, along with fitted algebraic expressions to facilitate their numerical use. The failure mechanisms are presented for a number of characteristic cases and are being contrasted with the classical Prandtl failure mechanism, giving additional insight into the mechanics of the problem. The results of the paper can be directly used in practical applications.

Effect of Fuzzy Boundaries on the Bearing Capacity of Footings on Two-Layered Clay

In this study, fuzzy logic was implemented to formulate the fuzziness of layer boundaries for a two-layered clay soil. A field of two-layered clay with fuzzy boundaries between layers was generated, and then the bearing capacity of strip footing on this field was calculated by the assumption of plane-strain conditions. The Mohr-Coulomb failure criterion was used and bearing capacity calculations were based on finite difference method. The effect of fuzziness in layer boundaries was investigated for the case of strong-over-weak clay. It is concluded that the analyses by applying fuzzy boundaries yielded more conservative results than classical two-layered bearing capacity calculations when the ratio of thickness of upper layer to the width of footing exceeds 1. When the ratio of thickness of upper layer to the width of footing is lower than 1, the bearing capacity of footing on two-layered clay is higher by considering fuzzy boundaries.

Eccentricity Effects on Bearing Capacity of Strip and Square Footings on Two-Layered Clay

The undrained ultimate capacity to combined (M, V) loading of strip and square foundations on a two-layered clay deposit is investigated. Extensive two and threedimensional parametric finite element analyses are carried out in terms of the ratio of the undrained shear strength of two layers, the normalized thickness of the top layer and the normalized load eccentricity. Two basic cases are separately investigated, referring to strength ratios higher or lower than unity. The assumption of effective width of the foundations, to account for eccentricity, generally adopted for homogeneous soil, is extended for two layers. The results are mainly presented in terms of modified bearing capacity factors for strip or square footings for a wide range of dimensionless problem parameters. However, for a better visual understanding of how the bending moment affects the ultimate vertical load failure loci diagrams (“yield surfaces”) in M, V space are also presented. Emphasis is given to developing insight into the particular failure mechanisms of most examined cases.

Undrained stability of strip footing above voids in two-layered clays by finite element limit analysis

Finite element limit analysis (FELA) is used to study the undrained bearing capacity of strip footing above voids in two-layered clays. Based on the FELA results, design charts and equations are provided to calculate the undrained bearing capacity factor Ns. The impact of parameters on Ns also has been investigated, including undrained shear stress ratio of the soil, thickness of the top layer, location, size, width, height and spacing of the voids. The failure mechanisms for a single void maybe classified into three categories: roof failure, combined roof and wall failure, bearing failure without void failure.

Dynamic installation of a torpedo anchor in two-layered clays

The behaviour of a torpedo anchor during dynamic installation in two-layered nonhomogeneous clay sediments was investigated through large-deformation finite-element (LDFE) analyses. Parametric analyses were undertaken varying the top layer thickness and strength ratio between two layers. Results show that the location of the demarcation point between the acceleration and deceleration phases of the anchor in the soil relative to the layer interface is the key factor directing the anchor behaviour in layered soils including the final embedment depth. Broadly speaking, the anchor behaviour in soft-over-stiff clay deposits is somewhat similar to that in single layer clay with strength increasing with depth. In stiff-over-soft clay deposits, the anchor penetrates deeper where the anchor deceleration phase (or the demarcation point) falls within the soft layer. Where the demarcation point lies within the top stiff layer, the anchor penetration depth decreases with increasing strength ratio, and the anchor penetration is terminated between the two layers for strength ratios ≥15. For assessing the anchor embedment depth in two-layered fine-grained ocean sediments in the field, an extended total energy–based method, along with a design expression, is proposed.