Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Plasticity role in strength behavior of cement-phosphogypsum stabilized soils

Dredged soil and phosphogypsum are frequently regarded as wasted materials,which require further treatment to control their environmental impact.Hence,phosphogypsum is proposed as a binder to stabilize dredged soil,aiming at efficiently reducing and reusing these waste materials.In this study,the engineering properties of cement-phosphogypsum stabilized dredged soils were investigated through a series of unconfined compression tests,and the effects of plasticity index of original soils on the strength improvement were identified.Then,the microstructure test and mineralogical test were performed to understand the mechanism of physical role of original soils in strength improvement.The results revealed that the unconfined compressive strength significantly decreased with the increase in plasticity index at the same binder content.The essential factor for strength improvement was found to be the formation of cementitious materials identified as calcium silicate hydrate(CSH),calcium aluminate hydrate(CAH),and ettringite(Aft).The normalized integrated intensity of cementitious materials(CSH+CAH+Aft)by pore volume decreased with the increase in plasticity index.Consequently,the density of cementitious materials filling the soil pores controlled the effectiveness of strength improvement.More cementitious materials per pore volume were observed for the original soils with lower values of plasticity index.That is,the higher strength of stabilized soils with lower values of plasticity index was attributed to a packed structure forming by integrated fabric through denser cementitious components.It can be anticipated from the above findings that the effectiveness of stabilization treatment will significantly reduce with the increase in plasticity of origin soil.

Stability and reinforcement analysis of rock slope based on elasto-plastic finite element method

The rigid body limit equilibrium method(RBLEM) and finite element method(FEM) are two widely used approaches for rock slope's stability analysis currently. RBLEM introduced plethoric assumptions; while traditional FEM relied on artificial factors when determining factor of safety(FOS) and sliding surfaces. Based on the definition of structure instability that an elasto-plastic structure is not stable if it is unable to satisfy simultaneously equilibrium condition, kinematical admissibility and constitutive equations under given external loads, deformation reinforcement theory(DRT) is developed. With this theory, plastic complementary energy(PCE) can be used to evaluate the overall stability of rock slope, and the unbalanced force beyond the yield surface could be the identification of local failure. Compared with traditional slope stability analysis approaches, the PCE norm curve to strength reduced factor is introduced and the unbalanced force is applied to the determination of key sliding surfaces and required reinforcement. Typical and important issues in rock slope stability are tested in TFINE(a three-dimensional nonlinear finite element program), which is further applied to several representatives of high rock slope's stability evaluation and reinforcement engineering practice in southwest of China.

Effect of Polyethylene Terephthalate Plastic Waste on the Physico-Mechanical and Thermal Characteristics of Stabilized Laterite Bricks

The present work investigated the effect of polyethylene terephthalate (PET) plastic waste on the physico-mechanical and thermal properties of cement-stabilized laterite bricks to see the durability of the modified bricks (CSLB). Samples were formulated by mixing laterite, cement, and different percentages of PET (0%, 3%, 5%, and 7%) by volume. The bricks were produced using the M7MI Hydraform standard interlocking block and kept in the shade for a curing period of 28 days. The addition of 3% to 5% PET to the laterite stabilized with 10% cement results in a decrease in both dry and wet compressive strength, which is determined using the Controlab compression machine. However, the obtained results are in concordance with the standards. The thermal conductivity of CSLB, determined using the box method with the EI700 measurement cell, decreases as the PET content of the mixture increases. A decrease in bulk density from 1.67 to 1.58 g/cm3 was observed.

Biopolymer stabilization of clayey soil

This study investigates the efficacy of sodium alginate(SA),xanthan gum(XG),guar gum(GG)and chitosan(CS)d each applied at five different solid biopolymer-to-water mass ratios(or dosages)and cured for 7 d and 28 d d on the unconfined compressive strength(UCS)performance of a high plasticity clayey soil.Moreover,on identifying the optimum biopolymer-treatment scenarios,their performance was compared against conventional stabilization using hydrated lime.For a given curing time,the UCS for all biopolymers followed a riseefall trend with increasing biopolymer dosage,peaking at an optimum dosage and then subsequently decreasing,such that all biopolymer-stabilized samples mobilized higher UCS values compared to the unamended soil.The optimum dosage was found to be 1.5%for SA,XG and CS,while a notably lower dosage of 0.5%was deemed optimum for GG.Similarly,for a given biopolymer type and dosage,increasing the curing time from 7 d to 28 d further enhanced the UCS,with the achieved improvements being generally more pronounced for XG-and CS-treated cases.None of the investigated biopolymers was able to produce UCS improvements equivalent to those obtained by the 28-d soilelime samples;however,the optimum XG,GG and CS dosages,particularly after 28 d of curing,were easily able to replicate 7-d lime stabilization outcomes achieved with as high as twice the soil’s lime demand.Finally,the fundamental principles of clay chemistry,in conjunction with the soil mechanics framework,were employed to identify and discuss the clayebiopolymer stabilization mechanisms.

PLASTIC DYNAMIC STABILITY OF A COLUMN UNDER NONCONSERVATIVE FORCES

In this paper Liapunov's second method is used to analyze the plastic dynamic stability of a column under nonconservative forces. The column is in a viscous medium, and under the action of uniformly distributed tangential follower forces. The strain-rate effect on the stress-strain relation of materials is included in the analysis. A condition of stability is derived, and the critical buckling load is obtained. The strain-rate effect on the stability of the column is discussed.

High-temperature stability of retained austenite and plastic deformation mechanism of ultra-fine bainitic steel isothermally treated below Ms

The mechanical properties of the sample and the stability of retained austenite were studied by designing two kinds of ultra-fine bainitic steel with different heat treatment methods austempering above and below Ms(martensite start tem-perature),which were subjected to tensile tests at 20 and 450℃,respectively.The results show that compared to room temperature(20℃)tensile properties,the uniform elongation of the sample at high temperature(450℃)significantly decreased.Specifically,the uniform elongation of the sample austempered above Ms decreased from 8.0%to 3.5%,and the sample austempered below Ms decreased from 10.9%to 3.1%.Additionally,the tensile strength of the sample austempered above Ms significantly decreased(from 1281 to 912 MPa),and the sample austempered below Ms slightly decreased(from 1010 to 974 MPa).This was due to the high carbon content(1.60 wt.%),high mechanical stability,low thermal stability for the retained austenite of the sample austempered below Ms.Besides,the retained austenite decomposed at high temper-atures,the carbon content and transformation driving force were significantly reduced,the transformation rate increased,and the phase transformation content reduced.

An analytical solution to wellbore stability using Mogi-Coulomb failure criterion

Deep wellbores/boreholes are generally drilled into rocks for oil and gas exploration,monitoring of tectonic stresses purposes.Wellbore and tunnel in depth are generally in true triaxial stress state,even if the ground is under axisymmetric loading condition.Stability of such wellbores is very critical and collapse of wellbore must be avoided.Mogi-Coulomb failure criterion is a better representation of rock strength under true triaxial condition.In this paper,an analytical solution is proposed using Mogi-Coulomb failure criterion.The solution is obtained for rock mass exhibiting elastic-perfectly plastic or elastic-brittle-plastic behaviour considering in-plane isotropic stresses.The proposed solution is then compared with exact analytical solution for incompressible material and experimental results of thickwall cylinder.It is shown that the results obtained by the proposed analytical solution are in good agreement with the experimental results and exact analytical solution.A reduction of about 13%e20%in plastic zone from the proposed closed-form solution is observed,as compared to the results from the finite element method(FEM)based Mohr-Coulomb criterion.Next,the influences of various parameters such as Poisson’s ratio,internal pressure(mud weight),dilation angle,and out-of-plane stress are studied in terms of stress and deformation responses of wellbore.The results of the parametric study reveal that variation in the out-of-plane stress has an inverse relation with the radius of plastic zone.Poisson’s ratio does not have an appreciable influence on the tangential stress,radial stress and radial deformation.Dilation angle has a direct relation with the deformation.Internal pressure is found to have an inverse relation with the radial deformation and the radius of plastic zone.

MECHANICAL STABILIZATION OF DEFORMED AUSTENITEDURING CONTINUOUS COOLING TRANSFORMATION IN AC-Mn-Cr-Ni-Mo PLASTIC DIE STEEL

The influence of prior austenite deformed at different temperature on the subsequent continuous cooling bainitic transformation has been investigated in an C-Ma-Cr-Ni-Mo plastic die steel. The results show that the prior deformation in low temperature region of austenite retards significantly the bainitic transformation. For the same continuous cooling schedule, as austenite deformed at lower temperature, the quantity of the classical sheaf-like bainite becomes less. The present results show that severe deformation leads to mechanical stabilization of austenite and causes the difficulty of bainitic ferrite propagation into the austenite.

Effects of creep characteristics of natural gas hydrate-bearing sediments on wellbore stability

Natural gas hydrate(NGH)reservoirs consist of the types of sediments with weak cementation,low strength,high plasticity,and high creep.Based on the kinetics and thermodynamic characteristics of NGH decomposition,herein a heat-fluid-solid coupling model was established for studying the wellbore stability in an NGH-bearing formation to analyze the effects of the creep characteristics of NGH-bearing sediments during long-term drilling.The results demonstrated that the creep characteristics of sediments resulted in larger plastic yield range,thus aggravating the plastic strain accumulation around the wellbore.Furthermore,the creep characteristics of NGH-bearing sediments could enhance the effects induced by the difference in horizontal in situ stress,as a result,the plastic strain in the formation around the wellbore increased nonlinearly with increasing difference in in situ stress.The lower the pore pressure,the greater the stress concentration effects and the higher the plastic strain at the wellbore.Moreover,the lower the initial NGH saturation,the greater the initial plastic strain and yield range and the higher the equivalent creep stress.The plastic strain at the wellbore increased nonlinearly with decreasing initial saturation.

Catastrophe analysis on pillar instability considered mining effect

The instability of the pillar was discussed based on the potential energy principle and the cusp catastrophe theory, and a simplified mechanical model of the pillar was established considering the mining effect. The necessary-sufficient conditions, the jump value of displacement of pillar and the released energy expressions were deduced. The results show that the instability of the pillar is related to the properties of the rock, the external force and the relative stiffness of the elastic area to the plastic area. The instability of system is like to occur with the enlarging of the softening area or the decreasing of E/λ. The calculation done shows that the estimated results correspond to practical experience.

Stability analysis of complex terrain slope based on multi-source point cloud fusion

Numerical modelling is a common routine for slope stability analysis in the complex terrain,and the accuracy of topographic survey has a great impact on the results.In this study,a combination of unmanned aerial vehicle(UAV)photogrammetry and 3D laser scanning technique was first proposed to establish a high-precision digital elevation model(DEM),which could be accurate to 0.2 m,fulfilling the engineering requirements.Then,a series of 3D/2D finite element models(FEM)were constituted on the basis of DEM to investigate the slope stability in the complex terrain.The results indicate that the deformation of complex terrain slope is chiefly triggered by compression-shear failure and the failure zones are mostly distributed on the middle-upper part and the scarp.Furthermore,the complex terrain slope is divided into concave,convex,concave-convex and convex-concave slope according to the topographical curvature,and the factor of safety(FOS)is as follows:the maximum value 1.8504 for the concave-convex slope,the minimum value 1.1129 for the convexconcave slope,and the median for either concave or convex slope.The inflection points and curvature of the slope jointly determine the shape of nonlinear slope,dominating the morphological effect on the slope stability,so the rational use of section morphological effect will be conducive to the overall stability of the slope.For four representative slopes,the plastic deformation first emerges into the middle,then progressively develops to the upper,and finally forms the connected failure zones.

Stability and reinforcement analyses of high arch dams by considering deformation effects

The strict definition and logical description of the concept of structure stability and failure are presented. The criterion of structure stability is developed based on plastic complementary energy and its variation. It is presented that the principle of minimum plastic complementary energy is the combination of structure equilibrium, coordination condition of deformation and constitutive relationship. Based on the above arguments, the deformation reinforcement theory is developed. The structure global stability can be described by the relationship between the global degree of safety of structure and the plastic complementary energy. Correspondingly, the new idea is used in the evaluations of global stability, anchorage force of dam-toe, fracture of dam-heel and treatment of faults of high arch dams in China. The results show that the deformation reinforcement theory provides a uniform and practical theoretical framework and a valuable solution for the analysis of global stability, dam-heel cracking, dam-toe anchorage and reinforcement of faults of high arch dams and their foundations.

Soil Stabilization Using Waste Plastic Materials

Expansive clay soils are the types of soils whose volume changes with the change in water content. They have a behavior of swelling and shrinking that is a serious hazard to structures built over them. Expansive soils are abundantly existing soil types in Ethiopia, particularly Addis Ababa. This paper shows the outcomes of an attempt to reinforce and stabilize expansive clay soil with plastic bottle strips. The plastic strips were prepared and added at three different mixing ratios (0.5%, 1% and 2%) by weight and in three different aspect ratios (5 mm × 7.5 mm, 10 mm × 15 mm, 15 mm × 20 mm). The experimental results showed that there was a significant improvement in shear strength parameters. The swelling and desiccation cracking behavior of the soil were also expressively reduced. There was a substantial reduction in the optimum moisture content and slight increment in maximum dry density. The optimum plastic size (aspect ratio) and plastic content that results in optimum result can be selected based on the importance of the selection parameter for a specified engineering work. Stabilizing expansive clay soils with waste plastic bottles simultaneously solves the challenges of improper plastic waste recycling that is currently a teething problem in most developing countries. The results obtained from this study favorably suggest that inclusion of this material in expansive soils would be effective for ground improvement in geotechnical engineering.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

STABILITY ANALYSIS OF PILLARS IN CONSIDERATION OF RHEOLOGICAL BEHAVIOUR OF ROCK

The mined-out area of a gypsum mine is right un-derneath civil constructions of a township, threatening the safety of the latter. To evaluate the long-term stability of the mined-out area, a visco-elastic plastic finite element analysis is carried out,combined with in situ measurements. The visco-elastic plastic coefficients have been determined through laboratory rock creep tests. Noticing the lim-itations of conventional element failure criteria,the authors proposed a new method to evaluate the stability of the element.i. e. ,by a si-multaneous control of the energy density and strain of the element. Computation showed that at stable state,one third of the pillars are in the visco-plastic state,the rest of the pillars ,the roof and floor are still in the visco-elastic state. The stress concentration coefficient at the boundary of pillars and roof is 2. 3,and the maximum verti-cal stress on the pillars is 11. 8 MPa. Data measured on site are con-sistent with the computation results, indicating that the proposed cal-culation method is correct. Therefore, the current mined-out area is stable,and the dimension of pillars is reasonable. The next-step ex-traction work should be carried out maintaining the current parame-ters,with only a moderate increase in pillar sizes to enhance the sta-bility of the pillars.

Influence of flange location on axial deformation stability of double-hat structure

A new structural configuration with better impact stability for increasing energy absorbing efficiency is found. Based on finite element analysis, deformation modes of double-hat structure under axial impact loading are categorized to find the main reasons that affect deformation stability. It is revealed that, in a double-hat structure, the location of the flanges is highly related to the deform- ation mode and energy absorbing efficiency. Moving the flanges away from their traditional mid-loca- tion may result in more regular and stable deformation mode and achieve higher energy absorbing ef- ficiency. The flange offset value needs to be controlled within a certain range, otherwise, the doub- le-hat structure would tend to deform like a top-hat structure and the energy absorbing efficiency could be compromised. These findings and analyses lead to a new structural design configuration- asymmetric flange locations--for enhancing the deformation mode stability in double-hat structures.

Critical Slope and Plasticity

Limit analysis based on upper bound theorem into slope stability is presented. A rotational failure mechanism (log spiral) passing through the toe in an inclined slope is assumed for getting the critical height. The proposed limit analysis, although on the kinematical admissible velocity field, always satisfies the equilibrium of forces acting on sliced rigid blocks. And the most critical slip surface can be searched by random technique. A new solution scheme is also developed for rapid searching critical slip surface. It is also applicable to a variety of slope models. The method is shown having a high accuracy compared with limit solution for simple slope.

Seismic stability analysis of concrete gravity dams with penetrated cracks

The seismic stability of a cracked dam was examined in this study. Geometric nonlinearity and large deformations, as well as the contact condition at the crack site, were taken into consideration. The location of penetrated cracks was first identified using the concrete plastic-damage model based on the nonlinear finite element method （FEM）. Then, the hard contact algorithm was used to simulate the crack interaction in the normal direction, and the Coloumb friction model was used to simulate the crack interaction in the tangential direction. After verification of numerical models through a case study, the seismic stability of the Koyna Dam with two types of penetrated cracks is discussed in detail with different seismic peak accelerations, and the collapse processes of the cracked dam are also presented. The results show that the stability of the dam with two types of penetrated cracks can be ensured in an earthquake with a magnitude of the original Koyna earthquake, and the cracked dam has a large earthquake-resistant margin. The failure processes of the cracked dam in strong earthquakes can be divided into two stages： the sliding stage and the overturning stage. The sliding stage ends near the peak acceleration, and the top block slides a long distance along the crack before the collapse occurs. The maximum sliding displacement of the top block will decrease with an increasing friction coefficient at the crack site.

Axisymmetric Strain Stability in Sheet Metal Deformation

Production of axisymmetric pieces by technology of sheet metal drawing is widespread nowadays. So the calculation analysis of capacity and forces necessary for deformation is of special interest. The length of cylindrical pieces with axisymmetric deformation is limited by loss of stability and buckling due to the development of side strains. A new technological process is based on making considerable number of folds—18 -?26 with the amplitude of 0.8 -?0.9 mm— before the deformation or immediately after the partial one. That reduces the stiffness of billets and prevents from development of large size buckles. A new technological process is developed for producing a long run of high-quality products.