Nonlinear Criterion Research Articles

Application of new twin-shear unified strength criterion to frozen soil

A new twin-shear unified strength criterion is proposed in this study. This criterion reveals the relationship among single-shear, twin-shear, and triple-shear strength criteria. All known linear and nonlinear strength criteria—such as Huber–von Mises, Drucker–Prager, Mohr–Coulomb, Tresca, and twin-shear series—are special cases of the new twin-shear unified strength criterion. The proposed unified strength criterion was employed to study the strength characteristics in the compressed meridional plane (where the stress Lode angle,θσ = − 30°) of frozen soil, based on the soil's nonlinear and asymmetric properties. In the criterion, β and C, which denote the relationship between the shear stress τ and normal stress σ on the twin-shear stress acting plane, are deemed variable; they vary with the change in normal stress σ or mean stress p. Through a comparison of results, we found that the results obtained with the proposed strength criterion were in good agreement with the results of tests on frozen soil. On this basis, expressions for the cohesive force and the internal friction angle of frozen soil were derived and discussed.

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain: A finite element method based approach

Abstract Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams, tunnels, bridges and widening roads. National Highway-58 connects Delhi to Badrinath in India, which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures. In the present investigation, a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas. Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator. Nonlinear generalized Hoek-Brown (GHB) criterion was adopted for stability analyses. Out of 20 slopes, five slopes (S6, S7, S18, S19 and S20) are unstable with factor of safety (FoS) less than or equal to 1, and thus needs immediate attention. The FoS values of four slopes (S2, S9, S13 and S17) lie between 1 and 1.3, i.e. marginally stable, and slopes S1, S3, S4, S5, S8, S10, S11, S12, S14, S15 and S16 are stable. Mohr-Coulomb (MC) criterion was also adopted to compare the slope stability analysis with GHB criterion. The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values, the difference is marked. For the jointed rock in the Himalayan region, the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions. Accordingly, some suggestions are proposed to strengthen the stability of cut slopes.

Geotechnical risk assessment of rock slope stability using non-linear strength criterion

Geotechnical risk assessment of rock slope stability using non-linear strength criterion

Optimal Baseline Design for Multibaseline InSAR Phase Unwrapping

Multibaseline (MB) synthetic aperture radar interferometry (InSAR) has the potential to improve the traditional single-baseline InSAR from the ill-posed problem to the well-posed problem. It is because MB InSAR phase unwrapping (PU) can take advantage of the baseline diversity to significantly increase the ambiguity intervals of interferometric phases, so it completely overcomes the limitation of the phase continuity assumption. However, due to the mathematical foundation of most of the MB PU methods, i.e., the Chinese remainder theorem (CRT), has poor measurement bias robustness (measurement bias could be caused by surface deformation, atmospheric artifact, and phase noise), CRT is sensitive to the normal baseline length. In other words, even if we choose the same CRT-based MB PU method, different system baseline lengths could result in different PU performances. Therefore, how to choose the baseline lengths to optimize CRT performance is crucial to all the CRT-based MB PU methods. In this paper, a nonlinear mixed-integer programming-based baseline design criterion (referred to NIP criterion) is proposed to maximize the measurement bias tolerance of the CRT-based MB PU. The optimality condition of the NIP criterion quantitatively provides important instructions for the CRT-based MB PU applications and offers significant guidance in the development of the practical MB InSAR system. The experiment results are shown to verify the effectiveness of the NIP criterion by using three representative CRT-based MB PU methods.

Three-Dimensional Propagation Simulation and Parameter Analysis of Rock Joint with Displacement Discontinuity Method

Displacement discontinuities method (DDM) is convenient for and efficient at dealing with discontinuity problems such as fracture and fault. However, the known method of ease iteration is not available for nonlinear joint surface problems. This paper introduces Barton-Bandis nonlinear joint deformation failure criterion, figures out the propagation model of joint through the maximum energy release rate theory of rock fracture mechanics, and establishes three-dimensional nonlinear displacement discontinuity model for rock joint. This paper gives results of the joint propagation pattern and its distribution law under tension and compression with different parameters and side pressure coefficients via compiled program.

Determination of bearing capacity factor Nc for circular piles in clays by using lower bound finite element analysis

ABSTRACT The aim of this present paper is to provide lower bound bearing capacity factor Nc for axially loaded circular piles in clays by using two-dimensional finite elements and the three-dimensional non-linear Tresca yield criterion. The clay layer is assumed to be completely saturated and subjected to undrained loading. The edge discontinuities of the Tresca surface was smoothened by providing a C 2 rounded surface at the vicinity of the sharp corners of the regular hexagon lying on the octahedral plane. No inherent assumption of hoop stress was considered in the present analysis. The clay has been considered to be heterogeneous where the cohesion increases linearly with depth. The study is useful in providing the methodology for simulating the axisymmetric structures and providing the design chart for the bearing capacity factors for circular piles in clays whose cohesion increases linearly with depth.

Determination of Mohr–Coulomb Parameters from Nonlinear Strength Criteria for 3D Slopes

Many experimental data have illustrated that the strength envelops for soils are not linear. Nevertheless, the linear Mohr–Coulomb (MC) strength parameters are widely applied for the conventional method, software codes, and engineering standards in the slope design practice. Hence, this paper developed the 3D limit analysis for the stability of soil slopes with the nonlinear strength criterion. Based on a numerical optimization procedure written in Matlab software codes, the equivalent MC parameters (the equivalent friction angle and the equivalent cohesion) from the nonlinear strength envelopes were derived with respect to the least upper-bound solutions. Further investigations were made to assess the influences of nonlinear strength parameters and slope geometries on the equivalent MC parameters. The presented results indicate that the equivalent MC parameters are closely related to the nonlinear strength parameters. As the inclination angle increases, the equivalent friction angle becomes bigger, but the equivalent cohesion becomes smaller. Besides, 3D effects on the equivalent MC parameters were found to be slight. The presented approach for the determination of MC strength parameters is analytical and rigorous, and the approximate MC strength parameters in the provided design tables can be alternative references for practical use.

Upper bound solution of surrounding rock pressure of shallow tunnel under nonlinear failure criterion

The nonlinear Baker failure criterion is introduced into the upper-bound limit analysis to examine the face stability of a shallow tunnel. The tunnel face under the ultimate limit state is analyzed from the perspective of energy balance. The work rates of external forces and internal energy dissipation are calculated. An analytical solution of necessary face pressures is derived. The optimal upper-bound solution of the face pressures is obtained by optimization. The results show that the three dimensionless parameters A, T, n of nonlinear Baker failure criterion have different effects on the necessary face pressures and the pattern failure mechanisms ahead of tunnel face. A is the most important one; n takes the second place, and T is the least one. The computed necessary face pressures are nonlinearly increasing when A is reduced. Combined with the actual monitoring data of Taxia tunnel, the calculation results in this paper is verified. It is suggested that the tunnel face supports should be strengthened timely in soft rocks to prevent the occurrence of face collapse.

Face stability analysis for a shield-driven tunnel with non-linear yield criterion

The aim of this work was to investigate the face stability of a tunnel driven by a pressurised shield for cases of collapse failure and blow-out failure based on the kinematic approach of limit analysis. For the analyses, the soil material was assumed to follow the non-linear Mohr–Coulomb failure criterion. Advanced rotational failure mechanisms were applied to the face stability analysis. The numerical results, optimised using Matlab, were close to the existing solutions, proving that this approach is reliable. The influences of two parameters (the tunnel buried depth C and the initial cohesion co) on the critical support pressures and the shapes of the failure mechanisms for collapse failure and blow-out failure were investigated. The results of the collapse failure and blow-out failure showed that the critical support pressures and the shapes of failure mechanisms were significantly influenced by these parameters and the non-linear failure criterion should be considered in practice to improve the accuracy of the critical support pressures.

ROHSA: Regularized Optimization for Hyper-Spectral Analysis

Context. Extracting the multiphase structure of the neutral interstellar medium is key to understanding star formation in galaxies. The radiative condensation of the diffuse warm neutral medium producing a thermally unstable lukewarm medium and a dense cold medium is closely related to the initial step leading the atomic-to-molecular (HI-to-H2) transition and the formation of molecular clouds. Up to now, the mapping of these phases out of 21 cm emission hyper-spectral cubes has remained elusive mostly due to the velocity blending of individual cold structures present on a given line of sight. As a result, most of the current knowledge about the HI phases rests on a small number of absorption measurements on lines of sight crossing radio sources. Aims. The goal of this work is to develop a new algorithm to perform separation of diffuse sources in hyper-spectral data. Specifically the algorithm was designed in order to address the velocity blending problem by taking advantage of the spatial coherence of the individual sources. The main scientific driver of this effort was to extract the multiphase structure of the HI from 21 cm line emission only, providing a means to map each phase separately, but the algorithm developed here should be generic enough to extract diffuse structures in any hyper-spectral cube. Methods. We developed a new Gaussian decomposition algorithm named ROHSA based on a multi-resolution process from coarse to fine grid. ROHSA uses a regularized nonlinear least-square criterion to take into account the spatial coherence of the emission and the multiphase nature of the gas simultaneously. In order to obtain a solution with spatially smooth parameters, the optimization is performed on the whole data cube at once. The performances of ROHSA were tested on a synthetic observation computed from numerical simulations of thermally bi-stable turbulence. We apply ROHSA to a 21 cm observation of a region of high Galactic latitude from the GHIGLS survey and present our findings. Results. The evaluation of ROHSA on synthetic 21 cm observations shows that it is able to recover the multiphase nature of the HI. For each phase, the power spectra of the column density and centroid velocity are well recovered. More generally, this test reveals that a Gaussian decomposition of HI emission is able to recover physically meaningful information about the underlying three-dimensional fields (density, velocity, and temperature). The application on a real 21 cm observation of a field of high Galactic latitude produces a picture of the multiphase HI, with isolated, filamentary, and narrow (σ ~ 1−2 km s−1) structures, and broader (σ ~ 4−10 km s−1), diffuse, and space-filling components. The test-case field used here contains significant intermediate-velocity clouds that were well mapped out by the algorithm. As ROHSA is designed to extract spatially coherent components, it performs well at projecting out the noise. Conclusions. In this paper we introduce ROHSA, a new algorithm that performs a separation of diffuse sources in hyper-spectral data on the basis of a Gaussian decomposition. The algorithm makes no assumption about the nature of the sources, except that each one has a similar line width. The tests we made shows that ROHSA is well suited to decomposing complex 21 cm line emission of regions of high Galactic latitude, but its design is general enough that it could be applied to any hyper-spectral data type for which a Gaussian model is relevant.

Three-dimensional upper bound limit analysis of a deep soil-tunnel subjected to pore pressure based on the nonlinear Mohr-Coulomb criterion

In this work, the three-dimensional failure mechanism of a deep soil-tunnel is established based on the nonlinear Mohr-Coulomb criterion and the upper bound theorem of the limit analysis subjected to the effects of pore water pressure. The formulas of the height, width and upper bound surface of a three-dimensional collapse of a deep soil-tunnel are derived from the three-dimensional failure mechanisms. The correctness and effectiveness of the proposed method is confirmed by comparing the results with those of existing studies. Then, the change rule of the geotechnical and geometrical parameters on the influence of the collapsing range and weight are studied. The results indicate that the pore water pressure has a significant influence on the range and weight of a tunnel collapse, but the initial cohesion determines the change rule of the pore pressure coefficient on the influence of the collapsing weight. The work in this study provides a reliable theoretical method for the optimization of the support designs of deep soil-tunnels.

Functional Catastrophe Analysis of Progressive Failures for Deep Tunnel Roof Considering Variable Dilatancy Angle and Detaching Velocity

The phenomena of progressive failures are very common and important in geotechnical engineering. In this paper, a reliable prediction model is proposed to interpret the progressive failure phenomenon of roof collapse in deep tunnels using the functional catastrophe theory. The progressive collapse mechanisms and collapsing block shapes of deep circular tunnels under conditions of plane strain are investigated. The analytical solutions for the shape curves of the collapsing blocks of circular tunnels are derived based on the nonlinear power-law failure criterion considering variable dilatancy angle and detaching velocity. Moreover, criterions with variable dilatancy angle on progressive failure occurrence for deep tunnels are obtained. Then, the analytical predictions obtained in this paper are compared with experimental testing results, which indicate that the impacts of variable detaching velocity on the shape curves of the several continuous collapsing blocks should be considered to obtain more consistent prediction results with the corresponding experimental testing results.

Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Reliability-based design (RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown (HB) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated HB parameters m and σc, and corresponding predicted axial strength. The results suggest that within- and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile (both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and σc suitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an HB criterion. The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion. These criteria are presented in terms of characteristic parameters mk and σck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the HB criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering (ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.

Limit Equilibrium Analysis of Slope Stability with Coupling Nonlinear Strength Criterion and Double-Strength Reduction Technique

Currently, the strength parameters are reduced by a uniform coefficient for the traditional strength-reduction technique in the slope stability analysis. However, observations proved that the contributions of the strength parameters on slope stability are different from each other when the slope reaches the limit equilibrium (LE) state, which means that the strength parameters should be reduced with their own reduction coefficient. Thus, based on the assumptions of stresses on slip surfaces and the overall mechanical equilibrium conditions of the slope sliding body, this work establishes the LE solution for slope stability under the double-strength reduction (DSR) technique. In the LE stress-based analysis, the loop iteration strategy is given to solve the LE stability of slope with the nonlinear strength criterion. Moreover, a new method (i.e., the square root method) is proposed to calculate the slope comprehensive factor of safety (FOS) for evaluating the slope stability with application of the DSR technique. Thus, by comparing and analyzing some slope examples, the accuracy of the present method is verified. Furthermore, from the obtained stability charts of slope under the DSR technique, the study shows that if the characteristic stability number is less than 0.04 for clay soil, then the internal friction angle would have a larger contribution to the slope stability than cohesion; whereas if the characteristic stability number is more than 1.00, then the larger contributor on the slope stability would be the cohesion.

A novel transversely isotropic strength criterion for soils based on a mobilised plane approach

The peak shear strength rules of transversely isotropic soils are stress state dependent and dependent on relative orientation between bedding plane and principal stress. Accordingly, the shear strength of transversely isotropic soils exhibits two primary characteristics: (a) the strength curve on the deviatoric plane is asymmetrical with respect to three principal stress axes; (b) the shear strength changes with the direction angle of the bedding plane when the intermediate principal stress coefficient is a constant. In this paper, the mobilised plane is introduced and used to reveal the failure mechanism of soils. By projecting the microstructure tensor of transversely isotropic soils onto the normal of the mobilised plane, the directionality of the transversely isotropic soils is introduced into the friction rules on the mobilised plane, and a transversely isotropic strength parameter is proposed. The proposed strength parameter can extend isotropic strength criteria into transversely isotropic strength criteria. This mobilised plane approach is used to establish a novel transversely isotropic non-linear unified strength criterion (TI-NUSC). The difficulty in establishing a unified description of the asymmetrical strength curve and its evolution with direction angle is overcome by the established criterion. Comparisons between available test results and the TI-NUSC show that the TI-NUSC can successfully describe these two primary peak strength characteristics.

Granular hyperelasticity with inherent and stress-induced anisotropy

A hyperelasticity for granular medium is proposed in this study, considering the inherent and stress-induced anisotropy. The nonlinear elastic behavior is described by defining an elastic potential energy model in terms of the elastic strain invariants that are coupled with a fabric tensor accounting for the transverse isotropy of granular solids formed under gravity. Such an approach provides a unified consideration on the stress-induced and inherent anisotropic behavior of the nonlinear elasticity and its stability. The six independent constants of the elastic modulus tensor of granular medium consolidated under different stress levels and consolidation stress ratios are well predicted using the granular hyperelasticity. Furthermore, the proposed anisotropic model of elastic potential results in a state region within which the thermodynamic stability is broken and thus naturally enables the predictions of the mechanically instable behavior of transversely anisotropic granular solids. From such a thermodynamic perspective, the state boundary of granular medium corresponds to the states at which the positive definiteness of the Hessian matrix of the elastic potential density function is violated and is used to define the strength criterion. Therefore, the proposed granular hyperelasticity in this study provided a generalized approach predicting the nonlinear elasticity and strength criterion of granular medium.

A 3D fractional elastoplastic constitutive model for concrete material

The core mission to establish elastoplastic constitutive model is how to determine the magnitude and direction of plastic strain increment for material under the given load. Fractional derivative provides a powerful tool for determining the nonorthogonal direction of a certain differentiable function. A three-dimensional (3D) fractional plastic flow rule suitable for concrete material is presented for the first time utilizing fractional derivative. The direction of plastic strain increment is determined by the proposed fractional plastic flow rule. A closed form yield function is developed in the transformed stress (TS) space based on the nonlinear unified strength criterion, and further used to describe the plastic strain induced by hydrostatic loading. A united hardening/softening function proposed by the authors in previous works is adopted to describe the pre-peak hardening and post-peak softening behaviour of concrete. Furthermore, a 3D fractional elastoplastic constitutive model for concrete material is presented. Only nine material parameters with the clear physical meaning are need for the proposed model, and the determination method of each material parameter is given. A series of test results of concrete with different strength under biaxial and triaxial stress conditions are used to assess the performance of proposed model.

Determination of economic losses of gas transportation companies from accidents on gas transmission pipelines

Selection of information was conducted to streamline the theoretical provisions and develop practical recommendations for determining the economic losses of gas transportation companies from accidents and failures on gas transmission pipelines, caused, in particular, by corrosion damage to a pipeline. The classification of losses due to the influence of corrosion on the linear part of gas transmission pipelines was considered. It was clarified that the structure of losses of gas transportation enterprises from corrosion during the operation of the linear part of gas transmission pipelines includes the cost of protecting the elements of structures from corrosion; losses from corrosion of metals. It was proved that the size of economic losses from accidents and failures on gas transmission pipelines to a large extent depends on the quality of the anti-corrosion protection system (measures, methods, ways and means of control), and also on observance of the rules of safe operation. The method of calculating economic losses, caused by accidents and failures on gas pipelines (taking into account the cost of compensation for losses from environmental pollution) is proposed, which takes into account the approach of neural networks and has advantages over the existing ones, as it characterizes: nonlinear quality criterion; the influence of energy characteristics of the interphase layers and aggressive agents on the corrosion processes in metal; nonlinear character of the monitoring system. On the basis of neural networks, a method of controlling the parameters, characterizing the technical state of steel structures in the oil and gas industry was developed, taking into account the nonlinear model for optimizing information and financial flows. The approach of neural networks can reduce errors in estimating the parameters of a nonlinear model that describes the system for monitoring underground pipelines.

Experimental verification of a progressive damage model for composite pinned-joints with different clearances

A new 3-D progressive damage model (PDM) was developed with the aid of ABAQUS software, nonlinear Hashin failure criteria and Riccio property degradation rules to predict failure mode and load of pinned joints in cross-ply glass fiber/epoxy composites. A series of ASTM tests (tensile, compressive and shear) were conducted on a unidirectional laminates to find the lamina properties, which were used as input to the PDM. The strength of pinned joints with pin-hole clearance of 0, 50, 100, 200, 300 µm was measured experimentally in accordance with ASTM5961. The Failure modes of the mechanical and pinned joint tests are agreed well with those reported by the ASTM standards. The developed PDM successfully predicted the ultimate strength of the composite pinned joints with a maximum error of 4.7%. Increasing the pin-hole clearance from 0 to 300 µm reduces the half of the contact length by 17.8% and increases the contact pressure by 26.6%. Accordingly, the 4% hole deformation strength, first-peak bearing strength, the measured ultimate strength and the predicted ultimate strength were decreased respectively by 20.9%, 34.0%, 14.2% and 8.8%.

Instability of catenary-type flexible risers conveying fluid in subsea environments

As water depths for oil and gas exploration and extraction increase, structures such as flexible risers, mooring lines, and umbilical cables are increasingly being used for subsea environments. Compared to conventional fixed-type structures and vertical risers, the dynamics of flexible risers is significantly more complex. In particular, the flexible structures may be prone to dynamic instabilities. The goal of the present paper is to provide a comprehensive study of the dynamics, stability, and vibration of flexible risers. We use Kirchhoff's theory of an extensible, flexible rod that resists torsion to develop a set of nonlinear equations for the dynamics of risers. The resulting model incorporates drag and the effects of the fluid being transported internally. Using a nonlinear stability criterion, our analyses show the nonlinear stability of a simple catenary-type riser modeled either as an inextensible or extensible string. For the more advanced rod models, we use a linear stability analysis to show how the internal fluid being conveyed can destabilize certain static configurations.