Pseudo-dynamic analysis of seismic stability of reinforced slopes considering non-associated flow rule

The required reinforcement force to prevent instability and the yield acceleration of reinforced slopes are computed under seismic loading by applying the kinematic approach of limit analysis in conjunction with the pseudo-dynamic method for a wide range of soil cohesion, friction angle, dilation angle and horizontal and vertical seismic coefficients. Each parameter threatening the stability of the slope enhances the magnitude of the required reinforcement force and vice versa. Moreover, the yield acceleration increases with the increase in soil shear strength parameters but decreases with the increase in the slope angle. The comparison of the present work with some of the available solutions in the literatures shows a reasonable agreement.

Seismic failure mechanisms for loaded slopes with associated and nonassociated flow rules

Seismic failure mechanisms were investigated for soil slopes subjected to strip load with upper bound method of limit analysis and finite difference method of numerical simulation,considering the influence of associated and nonassociated flow rules.Quasi-static representation of soil inertia effects using a seismic coefficient concept was adopted for seismic failure analysis.Numerical study was conducted to investigate the influences of dilative angle and earthquake on the seismic failure mechanisms for the loaded slope,and the failure mechanisms for different dilation angles were compared.The results show that dilation angle has influences on the seismic failure surfaces,that seismic maximum displacement vector decreases as the dilation angle increases,and that seismic maximum shear strain rate decreases as the dilation angle increases.

Influences of nonassociated flow rules on seismic bearing capacity factors of strip footing on soil slope by energy dissipation method

Seismic bearing capacity factors of a strip footing placed on soil slope were determined with both associated and nonassociated flow rules. Quasi-static representation of earthquake effects using a seismic coefficient concept was adopted for seismic bearing capacity calculations. A multi-wedge translational failure mechanism was used to obtain the seismic bearing capacity factors for different seismic coefficients and various inclined angles. Employing the associated flow rule, numerical results were compared with the published solutions. For bearing capacity factors related to cohesion and equivalent surcharge load, the maximum difference approximates 0.1%. However, the difference of bearing capacity factor related to unit weight is larger. With the two flow rules, the seismic bearing capacity factors were presented in the form of design charts for practical use. The results show that seismic bearing capacity factors related to the cohesion, the equivalent surcharge load and the unit weight increase greatly as the dilatancy angle increases, and that the nonassociated flow rule has important influences on the seismic bearing capacity.

Energy analysis of rock plug thickness in karst tunnels based on non-associated flow rule and nonlinear failure criterion

The geological hazards, such as water inrush and mud outburst, are easily induced by the high water pressure caverns ahead of a karst tunnel face. Therefore, it is a pivotal issue to determine the reserved thickness of rock plug during the construction of tunnels. The limit analysis principle is employed to analyze the safe thickness from the point of energy dissipation, and the nonlinear and non-associated characteristics of geotechnical materials are both considered. On the basis of a plane failure pattern of rock plug, the expressions of detaching curve and rock plug thickness are derived. The effect of each parameter on the safe thickness of rock plug is discussed in detail, which interprets the corresponding failure scope of rock plug. The obtained results indicate that the thickness of rock plug is highly influenced by the nonlinear dilatancy coefficient and the nonlinear coefficient. The proposed method is validated by a comparison of the calculated results with those of the engineering project of the "526 karst cavern" of Yunwushan tunnel. This proposed method can provide reference basis for the design and excavation of karst tunnels in the future.

Influences of nonassociated flow rules on three-dimensional seismic stability of loaded slopes

The influences of soil dilatancy angle on three-dimensional （3D） seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-static coefficient concept. Extended Bishop method and Boussinesq theorem were employed to establish the stress distribution along the rupture surfaces that are required to obtain the rate of internal energy dissipation for the nonassociated flow rule materials in rotational collapse mechanisms. Good agreement was observed by comparing the current results with those obtained using the translational or rotational mechanisms and numerical finite difference method. The results indicate that the seismic stability of slopes reduces by decreasing the dilatancy angle for nonassociated flow rule materials. The amount of the mentioned decrease is more significant in the case of mild slopes in frictional soils. A nearly infinite slope under local loading, whether its critical failure surface is 2D or 3D, not only depends on the magnitude of the external load, but also depends on the dilataney angle of soil and the coefficient of seismic load.

Energy analysis of stability on shallow tunnels based on non-associated flow rule and non-linear failure criterion

On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.

The study of slip line field and upper bound method based on associated flow and non-associated flow rules

At present, associated flow rule of traditional plastic theory is adopted in the slip line field theory and upper bound method of geotechnical materials. So the stress characteristic line conforms to the velocity line. It is proved that geotechnical materials do not abide by the associated flow rule. It is impossible for the stress characteristic line to conform to the velocity line. Generalized plastic mechanics theoretically proved that plastic potential surface intersects the Mohr-Coulomb yield surface with an angle, so that the velocity line must be studied by non-associated flow rule. According to limit analysis theory, the theory of slip line field is put forward in this paper, and then the ultimate beating capacity of strip footing is obtained based on the associated flow rule and the non-associated flow nile individually. These two results are identical since the ultimate bearing capacity is independent of flow role. On the contrary, the velocity fields of associated and non-associated flow rules are different which shows the velocity field based on the associat- ed flow rule is incorrect.

Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems

The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.

Slope stability analysis considering joined influences of nonlinearity and dilation

The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule.The stability factors of slopes were calculated using vertical slice method based on limit analysis.The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique.Equating the external work rate to the internal energy dissipation,the optimum solutions to stability factors were determined by the nonlinear programming algorithm.From the numerical results,it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion,and the nonassociated flow rule reduces to the associated flow rule.The stability factors decrease by 39.7%with nonlinear parameter varying from 1.0 to 3.0.Dilation and nonlinearity have significant effects on the slope stability factors.

Failure modes of coal containing gas and mechanism of gas outbursts

In order to explain the mechanism for gas outburst, the process of evolving fractures in coal seams is described using system dynamics with variable boundaries. We discuss the failure modes of coal containing gas and then established the flow rules after failure. The condition under which states of deformation convert is presented and the manner in which these convert is proposed. In the end, the process of gas outbursts is explained in detail. It shows that a gas outburst is a process in which the boundaries of coal seams are variable because of coal failure. If the fractures are not connected or even closed owing to coal/rock stress, fractured zones will retain a certain level of carrying capacity because of the self-sealing gas pressure. When the accumulation of gas energy reaches its limit, coal seams will become unstable and gas outbursts take place.

Improved slope safety analysis by new Druker-Prager type criterion

Based on Mohr-Coulomb （M-C） criterion, the parameters of Druker-Prager （D-P） criterion for geomaterial were determined under non-associated flow rule, and thus a new D-P type criterion was presented. Two assumptions were employed during the derivation： 1） principal strains by M-C model and D-P model are equal, and 2） the material is under plane strain condition. Based on the analysis of the surface on rt plane, it is found that the proposed D-P type criterion is better than the D-P criterion with M-C circumscribed circle or M-C inscribed circle, and is applicable for stress Lode angle less than zero. By comparing the predicted results with the test data of sand under plane strain condition and other D-P criteria, the proposed criterion is verified and agrees well with the test data, which is further proved to be better than other D--P type criteria in certain range of Lode angle. The criterion was compiled into a finite difference package FLAC3D by user-subroutine, and was used to analyze the stability of a slope by strength reduction method. The predicted slope safety factor from the proposed criterion agrees well with that by Spencer method, and it is more accurate than that from classic D-P criteria.

Elastoplastic homogenization of particulate composites complying with the Mohr–Coulomb criterion and undergoing isotropic loading

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr-Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading. In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.

Critical state model for structured soil

Structure is an evident determinant for macroscopic behaviors of soils.However,this is not taken into account in most constitutive models,as structure is a rather complex issue in models.For this,it is important to develop and implement simple models that can reflect this important aspect of soil behavior.This paper tried to model structured soils based on well-established concepts,such as critical state and sub-loading.Critical state is the core of the classic Cam Clay model.The sub-loading concept implies adoption of an inner(sub-loading)yield surface,according to specific hardening rules for some internal strain-like state variables.Nakai and co-workers proposed such internal variables for controlling density(p)and structure(ω),using a modified stress space,called tij.Herein,similar variables are used in the context of the better-known invariants(p and q)of the Cam Clay model.This change requires explicit adoption of a non-associated flow rule for the sub-loading surface.This is accomplished by modifying the dilatancy ratio of the Cam Clay model,as a function of the new internal variables.These modifications are described and implemented under three-dimensional(3D)conditions.The model is then applied to simulating laboratory tests under different stress paths and the results are compared to experiments reported for different types of structured soils.The good agreements show the capacity and potential of the proposed model.

Review of Proposed Stress-dilatancy Relationships and Plastic Potential Functions for Uncemented and Cemented Sands

Stress-dilatancy relationship or plastic potential function are crucial components of every elastoplastic constitutive model developed for sand or cemented sand.This is because the associated flow rule usually does not produce acceptable outcomes for sand or cemented sand.Many formulas have been introduced based on the experimental observations in conventional and advanced plasticity models in order to capture ratio of plastic volumetric strain increment to plastic deviatoric strain increment(i.e.dilatancy rate).Lack of an article that gathers these formulas is clear in the literature.Thus,this paper is an attempt to summarize plastic potentials and specially stress-dilatancy relations so far proposed for constitutive modelling of cohesionless and cemented sands.Stress-dilatancy relation is usually not the same under compression and extension conditions.Furthermore,it may also be different under loading and unloading conditions.Therefore,the focus in this paper mainly places on the proposed stress-dilatancy relations for compressive monotonic loading.Moreover because plastic potential function can be calculated by integration of stress-dilatancy relationship,more weight is allocated to stress-dilatancy relationship in this research.

Characterization of the asymmetric evolving yield and flow of 6016-T4 aluminum alloy and DP490 steel

6016-T4 aluminum alloy and DP490 steel were systematically tested under 24 proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive and simple shear tests with a 45°increment,and biaxial tensile tests using cruciform specimens.Cruciform specimens in the rolling/transverse and 45°/135°sampling directions were tested with seven and four different stress ra-tios,respectively.The normal and diagonal planes plastic work contours and the yield stresses under uniaxial tension and compression were measured to investigate the anisotropic yield.Meanwhile,the normal and diagonal planes directions of plastic strain rate and the rα-values under uniaxial tension and compression were characterized to confirm the plastic flow.Several existing asymmetric yield crite-ria under the associated and non-associated flow rules were comprehensively evaluated to describe the asymmetric plastic anisotropy of 6016-T4 aluminum alloy and DP490 steel.The results suggest that in the investigated yield criteria,the non-associated models can predict the tension and compression asym-metry of materials more accurately than the associated models,and the function of stress triaxiality can more effectively describe the asymmetric yield behavior than the first stress invariant.In addition,the pure shear stress states are helpful in assessing the validity and applicability of advanced asymmetric yield stress functions,and the inspection of diagonal plane plastic work contours containing more pure shear stress states should prioritized over that of normal plane plastic work contours.The evaluation of plastic potential functions should not only consider the prediction accuracy of the normal plane di-rections of plastic strain rate,but also further check the diagonal plane directions of plastic strain rate.Expressing mechanical properties as a function of equivalent plastic strain to calibrate parameters of the yield criterion allows the continuous capture of anisotropic evolution of the asymmetric yield surface and the changes in the asymmetric plastic potential surface.

A lightweight DDoS detection scheme under SDN context

Software-defined networking(SDN),a novel network paradigm,separates the control plane and data plane into dif-ferent network equipment to realize the flexible control of network traffic.Its excellent programmability and global view present many new opportunities.DDoS detection under the SDN context is an important and challenging research field.Some previous works attempted to collect and analyze statistics related to flows,usually recorded in switches,to address DDoS threats.In contrast,other works applied machine learning-based solutions to identify DDos and achieved promising results.Generally,most previous works need to periodically request flow rules or packets to obtain flow statistics or features to detect stealthy exceptions.Nevertheless,the request for flow rules is very time-consuming and CPU-consuming;moreover may congest the communication channel between the controller and the switches.Therefore,we present FORT,a lightweight DDoS detection scheme,which spreads the rule-based detection algorithm at edge switches and determines whether to start it by periodically retrieving the ports state.A time-series algorithm,ARIMA,is utilized to determine the port statistics adaptively,and an SVM algorithm is applied to detect whether a DDoS attack does occur.Representative experiments demonstrate that FORT can significantly reduce the controller load and provide a reliable detection accuracy.Referring to the false alarm rate of 1.24%in the comparison scheme,the false alarm rate of this scheme is only 0.039%,which significantly reduces the probability of false alarm.Besides,by introducing the alarm mechanism,this scheme can reduce the load of the southbound chan-nel by more than 60%in the normal state.

A thermoviscoelastic finite deformation constitutive model based on dual relaxation mechanisms for amorphous shape memory polymers

This paper proposes a new thermoviscoelastic finite deformation model incorporating dual relaxation mechanisms to predict the complete thermo-mechanical response of amorphous shape memory polymers.The model is underpinned by the detailed microscopic molecular mechanism and effectively reflects the current understanding of the glass transition phenomenon.Novel evolution rules are obtained from the model to characterize the viscous flow,and a new theory named an internal stress model is introduced and combined with the dual relaxation mechanisms to capture the stress recovery.The rationality of the constitutive model is verified as the theoretical results agree well with the experimental data.Moreover,the constitutive model is further simplified to facilitate engineering applications,and it can roughly capture the characteristics of shape memory polymers.

Non‑associated and Non‑quadratic Characteristics in Plastic Anisotropy of Automotive Lightweight Sheet Metals

Lightweight sheet metals are highly desirable for automotive applications due to their exceptional strength-to-density ratio.An accurate description of the pronounced plastic anisotropy exhibited by these materials in finite element analysis requires advanced plasticity models.In recent years,significant efforts have been devoted to developing plasticity models and numeri-cal analysis methods based on the non-associated flow rule(non-AFR).In this work,a newly proposed coupled quadratic and non-quadratic model under non-AFR is utilized to comprehensively investigate the non-associated and non-quadratic characteristics during the yielding of three lightweight sheet metals,i.e.,dual-phase steel DP980,TRIP-assisted steel QP980,and aluminum alloy AA5754-O.These materials are subjected to various proportional loading paths,including uniaxial tensile tests with a 15°increment,uniaxial compressive tests with a 45°increment,in-plane torsion tests,and biaxial tensile tests using laser-deposited arm-strengthened cruciform specimens.Results show that the non-AFR approach provides an effective means for accurately modeling the yield behavior,including yield stresses and the direction of plastic strain rates,simultaneously,utilizing two separate functions and a simple calibration procedure.The introduction of the non-quadratic plastic potential reduces the average errors in angle when predicting plastic strain directions by the quadratic plastic potential function.Specifically,for DP980,the average error is reduced from 3.1°to 0.9°,for QP980 it is reduced from 6.1°to 3.9°,and for AA5754-O it is reduced from 7.0°to 0.2°.This highlights the importance of considering the non-quadratic characteristic in plasticity modeling,especially for aluminum alloys such as AA5754-O.

FRACTIONAL ORDER MODELLING OF THE CUMULATIVE DEFORMATION OF GRANULAR SOILS UNDER CYCLIC LOADING

To model the cumulative deformation of granular soils under cyclic loading, a mathematical model was proposed. The power law connection between the shear strain and loading cycle was represented by using fractional derivative approach. The volumetric strain was characterized by a modified cyclic flow rule which considered the effect of particle breakage. All model parameters were obtained by the cyclic and static triaxial tests. Predictions of the test results were provided to validate the proposed model. Comparison with an existing cumulative model was also made to show the advantage of the proposed model.

Influence of Nonassociativity on the Bearing Capacity Factors of a Circular Footing

Numerical computations using the finite difference code FLAC (fast Lagrangian analysis of continua) are presented to evaluate the soil bearing capacity factors Nc,Nq and Nγ for circular smooth and rough footings. The influence of nonassociative flow rule on the ultimate bearing capacity of a circular footing is investigated. The footing rests on the surface of a homogeneous soil mass and a Mohr-Coulomb yield criterion have been assumed for the soil behavior. The values of ultimate bearing capacity factors Nc,Nq and Nγ are obtained for a wide range of values of the friction angle for five different values of the dilation angle. The values from the numerical simulation are found to decrease significantly with the increase of nonassociativity of the soil. The results are compared with those derived from existing classical solutions.