Limit Analysis Techniques Research Articles

Kinematic bearing capacity analysis of strip footings on reinforced soils using discretisation technique

The kinematic discretisation technique of upper bound limit analysis is adopted in this study to evaluate the limit load of a strip footing located on the soils reinforced with different geosynthetic layers. The reinforcement is assumed to withstand the tension but not bending moment. The failure model of the reinforced foundation soil is generated using the discretisation method, a ‘point by point’ technique. Two failure modes of the reinforcement, the tensile rupture and sliding, are considered in the analysis. This article proposed the formulas for the first time to evaluate the effect of soil friction angle φ on the ultimate bearing capacity and on the failure mechanism of foundation. The calculation results are given considering different reinforcement layers, which describe the impact of different reinforcement depth and length on the ultimate bearing capacity. The optimum positions of different reinforcement layers and the optimum reinforcement length are obtained. The bearing capacity ratios are also presented in figures combing impact of reinforcement depths, soil cohesion and friction angle. The present method was verified by the results reported in literature. The present method can provide a reference for the footing design on the reinforced soils.

Coupling FELA and computation intelligent in predicting behaviour of inclination strip anchor in anisotropic and heterogeneous clays

This study introduces new numerical investigations of the uplift capacity of inclined strip anchors buried in anisotropic and heterogeneous clays. The analyses utilize Lower Bound (LB) Finite Element Limit Analysis techniques (FELA) under plane strain conditions, employing the Anisotropic Undrained Shear (AUS) failure criterion. The undrained shear strength of the clay increases proportionally with depth, and anisotropy is introduced by adjusting the ratios between the shear strengths obtained from three different tests. Four input parameters, namely, the embedment ratio (H/B), the inclination angle (α), the ratio of increasing undrained shear strength with depth (m = ρΒ/suTC0), and the factor of anisotropic parameters (re), are considered in analyzing the uplift coefficient (Fc), and a set of design charts is proposed. The effect of dimensionless parameters on the development of failure mechanisms is also investigated. Moreover, a novel method for assessing the ultimate uplift capacity of an inclined strip anchor in natural clay is given by integrating FELA with Multivariate Adaptive Regression Splines (MARS) and Extreme Gradient Boosting (XGBoost). Based on the optimal machine-learning models, this study also calculates the contribution of each input to the value of Fc via sensitivity analysis. The engineering computations for strip anchors embedded in anisotropic and non-homogenous clays can be improved with the results of these investigations and the proposed machine-learning models.

Earth pressure in narrow cohesive-fictional soils behind retaining walls rotated about the top: An analytical approach

There is currently a lack of an available design approach to estimate the earth pressure in narrow backfills behind retaining walls rotated about the top (RT). The considerations of some significant factors, primarily load transfer mechanisms (soil arching effect and horizontal shear stress in soils), failure mechanisms (shape and number of slip surfaces) and soil cohesion are often neglected for brevity in routine design. Such simplifications may lead to significant deviations from reality. This paper first uses the finite element limit analysis (FELA) technique to identify the underlying failure mechanisms and load transfer mechanisms. The results observed in FELA models indicate that active rotation of walls about the top develops one curved slip surface, which can be approximated by the log-spiral function. Under the soil arching effect, the upper intermediate passive zone with major principal stress rotation trajectory and the lower active zone with minor one can be defined. The arched differential element method (ADEM) is then introduced to formulate the earth pressure calculation. The results from newly published tests, existing analytical approaches, and FELA are compared to validate the accuracy of the proposed approach in both purely-frictional and cohesive-frictional soils. Parametric studies are further conducted to thoroughly understand the earth pressure problems, considering the effects of sensitive design variables (e.g. aspect ratio, soil strength parameters, and wall-soil interface friction angle). The analytical approach presented here would be a great extension to the design guidelines for the retaining structures with narrow backfills.

Active Earth Pressure Acting on Circular Shafts Using Numerical Approach

Retaining walls in axi-symmetric conditions and in plane strains have been widely treated in the literature using different approaches (limit equilibrium, limit analysis, slip line, and numerical techniques by finite elements or finite differences). The finite element or finite difference method provides more accurate solutions to the problem than the limit equilibrium method. In this paper, a new model of retaining wall in the axi-symmetry conditions under outward pressure is considered, this case can be widely used in the design of grain silos, buildings and road constructions. Numerical calculations using FLAC are reported to evaluate the evolution of the earth pressure distribution on a cylindrical wall filled with granular material and subjected to radial displacement. A parametric study is carried out in order to evaluate the distribution of the active earth pressure on the wall according to the radius, the angle of friction of the granular material, and the angle of friction of the interface granular material-wall. This study shows that there is an effect of the circular shape and the inclination of the wall on the active earth pressures. Doi: 10.28991/CEJ-2022-08-04-09 Full Text: PDF

Sinkhole Stability in Elliptical Cavity under Collapse and Blowout Conditions

Road subsidence and sinkhole failures due to shallow cavities formed by defective water main have increased in recent decades and become one of the important research topics in geotechnical engineering. The present paper numerically studies the stability and its associated failure mechanism of ellipse-shaped cavity above defective water mains using the finite element limit analysis technique. For a wide range of geometrical parameters, the pressure ratio method is used to formulate the stability solutions in both blowout and collapse scenarios. Even though there is no published solution for elliptical cavities under blowout failure conditions, the obtained numerical results are compared with available circular solutions. Several conclusions are drawn based on the failure mechanism study of the various ellipse shape transformations in this study, whilst design charts and equations proposed for practical uses.

Bifurcation and Calabi-Bernstein type asymptotic property of solutions for the one-dimensional Minkowski-curvature equation

In this paper, we investigate the global structure of bifurcation branches of one-sign solutions and sign-changing solutions for one-dimensional Minkowski-curvature problems with a strong singular weight. Our interest of the nonlinearity is either linear or sublinear near zero. Growth conditions near ∞ are not necessary and the proofs are mainly employed by bifurcation theories based on Whyburn's limit argument and analysis techniques. We also show Calabi-Bernstein type asymptotic property of one-sign solutions by proving that one-sign solutions on two bifurcation branches converge to two linear functions.

The study on yield acceleration and permanent displacement of broken-back gravity quay walls – a case study

In the recently developed performance-based design method, permanent displacement is a key parameter for evaluating seismic performance quay walls, which can be achieved by fully dynamic and simple pseudo-static limit equilibrium (PS-LE) based methods. PS-LE methods have some ambiguities concerning the calculation of yield acceleration (ay ); therefore, the present study shows an alternative approach to determining ay based on the recently proposed limit analysis technique: Discontinuity Layout Optimization (DLO). The seismic performance of quay walls located in the Pars Petrochemical Port is evaluated as a case study. Firstly, according to the wall’s geometry, a modified expression of ay for PS-LE methods is provided. The parametric studies illustrate that the DLO gives a higher acceleration (ay = 0.271 g) than the LE method (ay =0.196 g). Then, a simple dynamic Finite Element (FE) analysis is also conducted to assess the permanent displacement. Comparison of resulting displacements with pseudo-dynamic (PD) methods indicated that accurate acceleration could lead to good agreement between Whitman and Liao as a PD (dmax=21cm) and FE (dmax=23.46 cm) analysis. Eventually, it is demonstrated that besides retaining the features of simple analysis, the DLO technique is more adaptable to complex geometries and offers a more realistic failure mechanism than the PS-LE approach.

Bearing capacity evaluation for shallow foundations on unsaturated soils using discretization technique

Bearing capacity evaluation for shallow foundations is conventionally completed according to the equations derived for dry or saturated soils neglecting the effect of matric suction. However, many shallow foundations are mostly constructed upon the soil layer above the groundwater table, where a large portion of soils under shallow foundations is in fact in unsaturated conditions. The failure of shallow foundations is usually related to shear failure which is one of the main engineering properties required in foundation design. The shear strength of unsaturated soils depends on the matric suction which usually changes with depth. Since the discretization technique of limit analysis is particularly suitable for considering the variation of soil parameters, the bearing capacity for shallow foundations considering the shear strength of unsaturated soils is therefore evaluated by this technique. The results obtained by the present technique are compared with the ones obtained from different authors, and good agreement is observed. Then a parametric analysis is performed using the present technique, and the bearing capacity for shallow foundations are given considering different soil types, foundation widths, effective internal friction angle φ′, air-entry pressure 1/α with various n values, different water table depth with surface flux boundary conditions, different unit weight of soil γ, and surcharge load q0. Some useful conclusions are given and a useful method is therefore provided for the bearing capacity evaluation of shallow foundations on unsaturated soils.

Pipeline burst-related ground stability in blowout condition

Sinkhole incidents have increased rapidly in recent decades due to water main breaks. Although numerous researchers have recently conducted investigations in sinkhole phenomenon, most of the studies are related to natural sinkhole formation, underground cavity detection, and collapse analysis. Very few studies can be found in relation to the blowout stability of soils due to defective pipeline under high water main pressures, in spite the frequent media news about the water main bursts which enlighten the relevance of the problem. The present paper aims to study the soil's blowout stability above a damaged water main pipeline in three idealized stages of internal soil erosion, i.e. horizontal, semi-circular, and circular cavities using the latest finite element limit analysis technique. Dimensionless design parameters are used throughout the paper to present rigorous bounding solutions that can be used directly by designers to evaluate blowout stability of soils above defective pipelines. Design charts and tables are presented to cover a wide range of design parameters, and a practical example is introduced to illustrate their use in practice.

Productivity Improvement of BOB T-shirt through Line Balancing Using Control Limit analysis and discrete event simulation (Case study: - MAA Garment and Textile Factory)

This study deals with line balancing of BOB T-shirt model with the help of control limit analysis and discrete event simulation of the assembly lines. In this study control limit analysis is used to measure the performance of the assembly line and used to show the bottleneck operations of the assembly line and line balancing technique improves the productivity of the sewing line of the model. BOB T-shirt model has 16 main operations and each operation’s time is analyzed as standard minute value (SMV). The main bottleneck operations are analyzed using the control limit analysis and simulation modeling. Based on the SMV of each operation, those operations which are out of lower control limit and upper control limit is called us bottlenecks of the sewing lines of the garment section and the 1st bottleneck operation is tread trimming operation. When we apply control limit analysis and discrete event simulation technique for the line balancing; the daily output has been increased from 1032 pieces to 1289 pieces. And labor productivity and machine productivity are increased from 46.9 and 54.32 to 58.59 and 71.61 respectively. And then finally, the profit that the line generated also increased from 22704 to 28358birr.

Effect of inclined and eccentric loading on the bearing capacity of strip footing placed on the reinforced slope

The present study considers the influence of inclined and eccentric loading on the bearing capacity of a strip footing placed on the reinforced cohesionless soil slope by using lower bound finite element limit analysis technique. The effects of other parameters such as soil friction angle, embedment depth of reinforcement layer below the footing, interface friction angle between soil and reinforcement, and vertical spacing between two reinforcement layers are also investigated. Results are presented as the variation between reinforcing efficiency and various combinations of above-mentioned parameters. The bearing capacity of strip footing reduces under combined effects of inclined and eccentric loading. However, with the inclusion of reinforcement layers at the optimum depth, the bearing capacity enhances significantly. The reinforcing efficacy increases with the increasing value of load inclination. The reinforcing efficiency reduces with the consideration of partial roughness between soil and reinforcement layer. Stress contours are also plotted in the two-dimensional object space to understand the failure mechanism of slopes.

Modelling T-bar penetration in soft clay using large-displacement sequential limit analysis

T-bar penetrometers are commonly used for the measurements of undrained strength profiles for clay (e.g. intact shear strength, sensitivity, ductility). The adoption of a constant resistance factor in the absence of a full-flow failure mechanism, coupled with the strain-softening effect, usually leads to considerable underestimation of soil strength within the depth of up to several T-bar diameters. This paper presents a numerical investigation into the vertical penetration behaviour of a T-bar using a sequential limit analysis (SLA) technique. The T-bar is penetrated from the mudline to a maximum of eight diameters to capture the behaviours related to differing failure mechanisms. The robustness of the SLA is demonstrated through comparisons between lower- and upper-bound solutions and between the SLA and the coupled Eulerian–Lagrangian results, in terms of penetration resistance and failure mechanism. The influences of unit weight, strain softening and strain rate are then examined, based on which an analytical model is developed for more accurate quantification of soil strength back-calculated from T-bar penetration resistance.

Three-Dimensional Heading Stability of Twin Circular Tunnels

This paper investigates the three-dimensional (3D) heading stability of twin circular tunnels horizontally aligned in cohesive undrained clayey soil. The stability is described by Broms and Bennermarks’ undrained stability number, which combine all stresses into a single dimensionless number. A recently developed 3D finite element limit analysis technique is used to obtain rigorous upper bound and lower bound critical stability numbers at collapse and blowout. The interaction effects of the distance between the tunnels on the stability are determined for a series of tunnel cover-to diameter ratios. As an additional verification of the rigorous bounding solutions, the obtained stability results are compared with other published solutions available in the literature. Results from this study are summarized in stability charts and tables for use by designers and practising engineers.

Probabilistic bearing capacity of strip footing on reinforced anisotropic soil slope

The probabilistic bearing capacity of a strip footing placed on the edge of a purely cohesive reinforced soil slope is computed by combining lower bound finite element limit analysis technique with random field method and Monte Carlo simulation technique. To simulate actual field condition, anisotropic random field model of undrained soil shear strength is generated by using the Cholesky-Decomposition method. With the inclusion of a single layer of reinforcement, dimensionless bearing capacity factor, N always increases in both deterministic and probabilistic analysis. As the coefficient of variation of the undrained soil shear strength increases, the mean N value in both unreinforced and reinforced slopes reduces for particular values of correlation length in horizontal and vertical directions. For smaller correlation lengths, the mean N value of unreinforced and reinforced slopes is always lower than the deterministic solutions. However, with the increment in the correlation lengths, this difference reduces and at a higher correlation length, both the deterministic and probabilistic mean values become almost equal. Providing reinforcement under footing subjected to eccentric load is found to be an efficient solution. However, both the deterministic and probabilistic bearing capacity for unreinforced and reinforced slopes reduces with the consideration of loading eccentricity.

Determination of critical tunnel heading pressures using stability factors

This paper investigates the three-dimensional (3D) stability of a circular tunnel in drained cohesive-frictional soil. Numerical simulations are performed to study the face stability of a circular tunnel for various soil properties and tunnel diameter-to-depth ratios. The finite element limit analysis (FELA) is employed to determine rigorous upper and lower bounds solutions of tunnel stability factors (Fc, Fs and Fγ), which are functions of the depth ratio and soil internal friction angle. These stability factors are used to estimate the critical heading pressures at collapse. The obtained results are compared with existing published solutions in the literature. The study aims to improve the available solutions by using the latest 3D finite element limit analysis technique. A number of examples are provided, which demonstrate the practical use of the three stability factors in estimating tunnel heading pressures.

Seismic Bearing Capacity of a Strip Footing Over an Embankment of Anisotropic Clay

The present study adopts lower bound finite element limit analysis technique in association with non-linear optimization to compute the seismic bearing capacity of a strip footing placed over an embankment of anisotropic clay. The influence of seismic loading is incorporated in terms of a horizontal seismic acceleration coefficient. The bearing capacity factor Nc of the strip footing is obtained for various combinations of (i) slope angle, (ii) footing setback distance, (iii) horizontal seismic acceleration coefficient, and (iv) anisotropic strength ratio of clay. The bearing capacity factor of the strip footing increases with the increasing setback distances. However, beyond a certain setback distance, hardly any influence is found. For a particular footing position and constant value of horizontal seismic acceleration coefficient, the magnitude of bearing capacity factor increases with the increase in anisotropic strength ratio. However, the percentage increment in the bearing capacity reduces when the value of anisotropic strength ratio becomes greater than one. In addition, the bearing capacity reduces with the increasing slope angle and horizontal seismic acceleration coefficient. Failure patterns are obtained to understand the failure mechanism.

Stability of an Unsupported Vertical Trench in Sloping Ground

The lower bound limit analysis technique in combination with the finite elements is implemented to generate the stability numbers for an unsupported vertical long trench in a sloping ground, associated with the critical state of shear failure in a cohesive-frictional soil medium. The computational results are derived for various combinations of normalized excavation depth, friction angle of soil and slope angle. From the results of the analysis, it can be noted that with the increase in the slope angle the stability of the unsupported trench reduces drastically. With an enhancement in the magnitude of slope angle, the plastic zone in the vicinity of the trench becomes increasingly asymmetric. The results provided in this paper are expected to be beneficial from the point of view of designing vertical trench in sloping ground.

Theoretical Bending Collapse of Hat-Section Tubes

This paper presents an attempt to modify an existing theoretical model to predict the bending collapse response of hat-section tubular structures. The analytical collapse model was based on Kim and Reid. Additional hinge lines created during deformation of the tube were examined and integrated with existing model to forming a modified analytical solution. Variation of the hinge moments were solved using limit analysis technique. Procedure for developing the finite element (FE) models of tube specimens was also presented. Moment-rotation characteristics from pure bending simulation were compared with analytical model and good agreement was achieved. The average of differences between simulation and calculation were found to be <5% within plastic region. In conclusion, the modified analytical solution has adequate capability to predict the moment-rotation relationship of hat-section tubes subject to pure bending..

Use of a non-associated flow rule for determining the stability of a vertical circular excavation

An axisymmetric lower bound limit analysis technique in combination with the finite elements has been used to investigate the effect of considering a non-associated flow rule on the stability number (γH/c) for a vertical circular unsupported excavation in a general cohesive–frictional soil medium, where (1) H is the excavation height, (2) γ defines the unit weight of the soil mass, and (3) c indicates the cohesion of the soil mass. The results are derived for different magnitudes of dilative coefficient (η), friction angle (ϕ), and normalized excavation height (H/b), where b = the radius of the excavation. The results clearly indicate the increase in γH/c with an increase in η value. It is expected that the charts provided in this note will be quite helpful for the practicing engineers.

Sequential limit analysis of pipe–soil interaction during large-amplitude cyclic lateral displacements

A newly developed sequential limit analysis (SLA) technique is used to perform large-displacement numerical simulations relevant to thermally induced lateral buckling of untrenched subsea pipelines. A rigid plane-strain pipe segment, partially embedded in undrained clay, is subjected to cyclic lateral displacements with amplitudes of up to eight pipe diameters. A constant vertical dead load is applied to the pipe during each lateral sweep, but in some analyses this load is varied from one sweep to the next. The SLA method directly models the evolution of the soil surface profile, including active and dormant berms, and incorporates strain softening behaviour caused by soil remoulding. Comparisons of the numerical results with published centrifuge model test data, for a range of loading cases, are provided in terms of the pipe invert trajectory and lateral soil resistance. There is good overall agreement between the numerical and experimental results, demonstrating the suitability of SLA for solving such problems. Detailed aspects of the cyclic loading behaviour are discussed with reference to soil failure mechanisms and bearing capacity failure envelopes for combined vertical and horizontal loading. Finally, two brief parametric studies are used to explore the effects of the initial pipe embedment and vertical loading history on the subsequent lateral loading behaviour.