Three-dimensional Failure Mechanism Research Articles

Lattice materials with pyramidal hierarchy: Systematic analysis and three dimensional failure mechanism maps

Sandwich core materials that offer superior mechanical properties at minimum weight are essential in designing high-performance sandwich structures. Hierarchical materials are ideal templates for this purpose. In this paper, we investigate the mechanical performance of a pyramidal–pyramidal hierarchical lattice material to highlight its potential as the core material for sandwich structures. Three-dimensional failure mechanism maps for the pyramidal–pyramidal hierarchical lattice material are developed under different loading conditions and the results are compared to finite element simulations. Next, we study the mechanical response and failure modes of a sandwich panel with self-similar pyramidal lattice core construction subjected to in-plane compression and three-point bending. The current study indicates that the pyramidal–pyramidal hierarchical configuration can improve the load bearing capacity and core buckling resistance of the sandwich structures at low density. The study provides insights into the role of structural hierarchy in tuning the mechanical response of the lattice materials and expands the application envelope of lightweight sandwich structures by effectively increasing the structural buckling resistance.

Three-dimensional Seismic Displacement Analysis of Rock Slopes based on Hoek-Brown Failure Criterion

Seismic force is one of the main factors resulting in the slip failure of steep rock slopes. In this paper, the seismic displacement analysis of rock slopes is carried out by virtue of the kinematical theorem of limit analysis and the Newmark method. It is assumed that the slope has a curvilinear cone-shaped failure mechanism and its materials are subjected to the Hoek-Brown failure criterion. The generalized tangential technique is employed to obtain equivalent parameters from the Hoek-Brown criterion. According to the three-dimensional failure mechanism, the internal energy dissipation and external work are respectively calculated, and the effect of horizontal seismic force is included by using the equivalent pseudo-static method. Subsequently, the yield acceleration is calculated for three-dimensional failure mechanism, and the results are shown to be valid when compared with the previous solutions. Parameter analysis is used to represent how the Hoek-Brown criterion parameters impact on the yield acceleration. The failure mechanism is also obtained during the process of limit analysis, and a dimensionless coefficient is adopted to investigate the influence of it on the seismic displacements of slopes. The results of calculations are given for a series of actual seismic waves and compared with the results calculated from empirical formula.

Three-dimensional limit analysis of seismic stability of tunnel faces with quasi-static method

Based on the existing research results, a three-dimensional failure mechanism of tunnel face was constructed. The dynamic seismic effect was taken into account on the basis of quasi-static method, and the nonlinear Mohr-Coulomb failure criterion was introduced into the limit analysis by using the tangent technique. The collapse pressure along with the failure scope of tunnel face was obtained through nonlinear limit analysis. Results show that nonlinear coefficient and initial cohesion have a significant impact on the collapse pressure and failure zone. However, horizontal seismic coefficient and vertical seismic proportional coefficient merely affect the collapse pressure and the location of failure surface. And their influences on the volume and height of failure mechanism are not obvious. By virtue of reliability theory, the influences of horizontal and vertical seismic forces on supporting pressure were discussed. Meanwhile, safety factors and supporting pressures with respect to 3 different safety levels are also obtained, which may provide references to seismic design of tunnels.

Three-dimensional numerical and analytical study of horizontal group of square anchor plates in sand

In this paper, numerical and analytical methods are used to evaluate the ultimate pullout capacity of a group of square anchor plates in row or square configurations, installed horizontally in dense sand. The elasto-plastic numerical study of square anchor plates is carried out using three-dimensional finite-element analysis. The soil is modeled by an elasto-plastic model with a Mohr-Coulomb yield criterion. An analytical method based on a simplified three-dimensional failure mechanism is developed in this study. The interference effect is evaluated by group efficiency η, defined as the ratio of the ultimate pullout capacity of group of N anchor plates to that of a single isolated plate multiplied by number of plates. The variation of the group efficiency η was computed with respect to change in the spacing between plates.

Upper-bound solutions for the face stability of a shield tunnel in multilayered cohesive–frictional soils

Tunneling in urban shallow soft ground is more frequently being carried out using the shield method. An important problem in the stability analysis of a tunnel face is to provide enough support pressure to the excavation face. Among the analytical approaches used to investigate the stability of a tunnel face, limit equilibrium methods or limit analysis methods are widely used. For cohesive–frictional soils, the results obtained from experimental tests and numerical simulations indicate that the failure soil in front of the tunnel face demonstrates two main features, i.e., a shear failure band in the lower part and a pressure arch effect in the upper part. Compared to the limit equilibrium methods, the limit analysis methods have a strictly theoretical basis and provide better results. To better interpret failure features, a new three-dimensional failure mechanism is proposed to analyze the limit support pressure of the tunnel face in multilayered cohesive–frictional soils based on limit analysis methods. The new failure mechanism is composed of five truncated cones that represent the shear failure band and a distributed force acting on the truncated cones that represents the pressure arch effect. The distributed force is calculated using Terzaghi earth pressure theory. The limit support pressures obtained from the new failure mechanism and the existing approaches are compared, and the new mechanism of this paper provides relatively satisfactory results for limit support pressures.

Reliability analysis of supporting pressure in tunnels based on three-dimensional failure mechanism

Based on nonlinear failure criterion, a three-dimensional failure mechanism of the possible collapse of deep tunnel is presented with limit analysis theory. Support pressure is taken into consideration in the virtual work equation performed under the upper bound theorem. It is necessary to point out that the properties of surrounding rock mass plays a vital role in the shape of collapsing rock mass. The first order reliability method and Monte Carlo simulation method are then employed to analyze the stability of presented mechanism. Different rock parameters are considered random variables to value the corresponding reliability index with an increasing applied support pressure. The reliability indexes calculated by two methods are in good agreement. Sensitivity analysis was performed and the influence of coefficient variation of rock parameters was discussed. It is shown that the tensile strength plays a much more important role in reliability index than dimensionless parameter, and that small changes occurring in the coefficient of variation would make great influence of reliability index. Thus, significant attention should be paid to the properties of surrounding rock mass and the applied support pressure to maintain the stability of tunnel can be determined for a given reliability index.

Seismic and static 3D stability of two-stage rock slope based on Hoek–Brown failure criterion

Two-stage slope is beneficial to improve slope stability in comparison with single-stage slope. Based on nonlinear Hoek–Brown criterion, a three-dimensional failure mechanism is employed to estimate the stability of two-stage rock slope, with the effect of seismic inertia force being taken into account. A generalized tangential technique is used to formulate the stability factor problem as a classical optimization problem corresponding to the dissipated energy. The upper-bound solutions are obtained by minimizing the objective function with respect to the location of sliding body center and the location of tangency point. The seismic inertia force is considered and incorporated into the objective function. In comparison with previously published solutions using the linear Mohr–Coulomb criterion, the validity of the present solutions is shown. The analytical expressions for two-stage slope are derived to estimate the seismic stability of slopes. Numerical results for different types of rocks are presented for practical use in engineering, and the effects of different parameters on slope stability are discussed.

Face Stability Analysis of Shield Tunnels in Homogeneous Soil Overlaid by Multilayered Cohesive-Frictional Soils

In order to better interpret failure features of the failure of soil in front of tunnel face, a new three-dimensional failure mechanism is proposed to analyze the limit support pressure of the tunnel face in multilayered cohesive-frictional soils. The new failure mechanism is composed of two truncated cones that represent the shear failure band and a distributed force acting on the truncated cones that represents the pressure arch effect. By introducing the concept of Terzaghi earth pressure theory, approximation of limit support pressures is calculated using the limit analysis methods. Then the limit support pressures obtained from the new failure mechanism and the existing approaches are compared, which show that the results obtained from the new mechanism in this paper provide relatively satisfactory results.

Face Stability Analysis for a Shield-Driven Tunnel in Anisotropic and Nonhomogeneous Soils by the Kinematical Approach

AbstractThe stability on a tunnel face is of great practical significance for safe construction in tunnel engineering. In this work, an advanced three-dimensional (3D) failure mechanism is extended to the face stability analysis of a tunnel driven in anisotropic and nonhomogeneous soils using the kinematic approach of limit analysis. The results obtained from the presented approach are in good agreement with the existing ones, showing that this method can be further applied to the proposed situation in this paper. Two common examples of cohesion variation, a linear variation with depth and a layered soil, are then analyzed. The numerical results show that both anisotropy and nonhomogeneity have a significant impact on the critical face pressure, especially when the cohesion is relatively large or when there is a weaker layer. Therefore, these two factors should be taken into account in tunnel design.

Three-dimensional face stability analysis of pressurized tunnels driven in a multilayered purely frictional medium

This paper aims at presenting a three-dimensional (3D) failure mechanism for a circular tunnel driven under a compressed air shield in the case of a dry multilayered purely frictional soil. This mechanism is an extension of the limit analysis rotational failure mechanism developed by Mollon et al. (2011a) in the case of a single frictional layer. The results of the present mechanism are compared (in terms of the critical collapse pressure and the corresponding shape of the collapse mechanism) with those of a numerical model based on Midas-GTS software. Both models were found to be in good agreement. Furthermore, the proposed mechanism has the significant advantage of reduced computation time when compared to the numerical model. Thus, it can be used in practice (for preliminary design studies) in the case of a multilayered soil medium.

Sleeper End Resistance of Ballasted Railway Tracks

This paper describes model tests used to investigate how ballast shoulder width and height contribute to a railway sleeper’s resistance to lateral movement for a range of shoulder widths and heights. Deflection and resistance were measured and photographs taken during the tests.The photographs were analyzed using a digital image correlation technique to identify the zones of ballast surface disturbance, which demonstrated that a bulbed failure volume was mobilized at the ultimate limit state. An idealized three-dimensional failure mechanism is proposed, and resistances are calculated using the limit equilibrium approach. The calculation provides a reliable estimate of the measured resistance. The work identifies the optimum shoulder width and height. The calculations are extended to demonstrate that when a number of sleepers are moved simultaneously, the sleeper end resistance may be one-third less per sleeper than that indicated in tests on an isolated sleeper. Image analysis and limit equilibrium calculations show that this is caused by overlapping of mobilized failure volumes from adjacent sleepers.

Limit analysis of roof collapse in tunnels under seepage forces condition with three-dimensional failure mechanism

The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.

Three-dimensional failure mechanism of a rectangular cavity in a Hoek–Brown rock medium

• For deep cavities, three-dimensional rotational failure mechanism is proposed for calculating the work rate of external force and the internal energy dissipation.

Bearing capacity of square spudcan of jack-up rig based on a three-dimensional failure mechanism

The methods currently used in prediction of the jack-up spudcan penetration depth usually ignored the geometric features of the spudcan. This simplification to a certain extent caused a deviation, especially for the spudcan of special geometric characteristics. For a special square spudcan of the jack-up rig, in this paper, a method was proposed for prediction of the penetration depth. This method was deduced according to the limit equilibrium theory based on the three-dimensional failure mechanism of the subsoil constructed in this paper. By use of large amounts of data, including solutions recommended in other literatures, results of the static load tests that have been published and results of the model experiment carried out in this paper for the special square spudcan, comparisons and discussions were also conducted and presented.

Analysis of Face Stability during Excavation of Double-O-Tube Shield Tunnel

This paper focuses on the face stability analysis of Double-O-Tube shield tunnel. This kind of analysis is significant to ensure the safety of workers and reduce the influence on the surrounding environment. The key point of the stability analysis is to determine the supporting pressure applied to the face by the shield. A collapse failure will occur when the supporting pressure is not sufficient to prevent the movement of the soil mass towards the tunnel. A three-dimensional collapse failure mechanism was presented in this paper. Based on the mechanism of a single circular shield tunnel, the mechanism of Double-O-Tube shield tunnel was established by using the fact that both of the mechanisms are symmetrical. Then by means of the kinematic theorem of limit analysis, the numerical results were obtained, and a design chart was provided. The finite difference software FLAC3D was applied to investigate the face failure mechanism of DOT shield tunnel established in this paper; the critical supporting pressures of the collapse failure mechanism in different strata (sand and silt) were calculated. Through comparative analysis, the theoretical values were very close to the numerical values. This shows that the face failure mechanism of DOT shield tunnel is reasonable, and it can be applied to the sand and silt strata.

Three-Dimensional Face Stability Analysis of EPBS Tunnels

A three-dimensional (3D) failure mechanism, based on the framework of the kinematical approach of limit analysis theory, is applied to calculate the face supporting pressure of a circular tunnel driven by the Earth Pressure Balance Shield (EPBS). The geometry of the mechanisms considered is composed of a sequence of truncated rigid cones. The numerical results obtained are presented.

Limit analysis of cantilever retaining walls with spaced piles

A modified method is proposed for designing cantilever retaining walls with spaced piles. The approach used is based on a new translational three-dimensional failure mechanism within the framework of the upper-bound theorem of limit analysis. Numerical optimisation of the mechanism is performed by a minimisation procedure for the critical three-dimensional passive earth pressure coefficient. Internationally accepted analytical methods for designing these types of retaining structure assume a simplified rectilinear earth pressure distribution, not only for non-spaced piles but also for spaced piles, where the earth pressure distribution is multiplied by the pile spacing. The results of the proposed method indicate that the pile-to-pile spacing, depending on the input soil parameters, strongly influences the shape of the three-dimensional failure mechanism and the passive pressure along the embedment depth to the point of moment equilibrium. Distribution of the passive earth pressure is no longer rectilinear, but the earth mass contributing to the soil–pile interaction on the dredged side of the embedment depth is reduced, which leads to longer piles and higher inner forces in the retaining structure.

A Mechanical Model of the End Anchorage Zone of Prestressed Concrete Members

It is expected that recent development of mechanical models will soon supersede previous empirical methods of detailing. In this study, a mechanical model is proposed to analyze the behavior of the anchorage zone of prestressed concrete members. The main characteristics of the proposed model lies in its rational consideration of material properties such as concrete strength in biaxial stress state and that of local zone reinforced by spirals. The shear friction strength of concrete surrounding a spiral is also considered. The computational results of the proposed model as well as the existing Strut-and-Tie model(STM) and nonlinear finite element analysis are compared with experimental results. The results of the comparison revealed that the proposed model showed better prediction of the failure mode as well as the failure load. Additionally, the proposed model also explained the three-dimensional failure mechanism very well, while other methods based on two-dimensional analysis could not do so well.

Performance prediction of TBM disc cutting on granitic rock by the linear cutting test

This paper aims to estimate the TBM disc cutter performance on Hwandeung Granite, one of the representative rock types in Korea by the Linear Cutting Machine. In the Linear Cutting test, the digital photogrammetric technique was newly adopted to measure three-dimensional cutting volumes and to apply them to the derivation of design parameters of TBM cutterhead. In this study, a series of linear cutting tests by a TBM disc cutter with the diameter of 17 inches were carried out by varying cutter spacing as well as cutter penetration conditions. From the tests, the optimum ratio of cutter spacing and penetration depth was derived for Hwandeung Granite. However, experimental results showed that three-dimensional cutting volumes measured by the photogrammetrical technique were not very close to those that were simply calculated from mechanical set-up values of each linear cutting test. Considering that the cutting procedure of a TBM disc cutter is not one-dimensional but three-dimensional failure mechanism, the use of three-dimensional cutting volumes as a performance parameter of a TBM disc cutter is indispensable to design a more accurate and reliable TBM cutterhead. (A) This paper was presented at Safety in the underground space - Proceedings of the ITA-AITES 2006 World Tunnel Congress and the 32nd ITA General Assembly, Seoul, Korea, 22-27 April 2006. For the covering abstract see ITRD E129148. Reprinted with permission from Elsevier.