Linear Strength Envelope Research Articles

Evaluating the active earth pressure exerted by granular soils with nonlinear strength behaviour using the slice-based limit equilibrium method

ABSTRACT Conventional earth pressure theories are generally applicable to soils with a linear strength envelope. Preferred granular backfill, however, usually exhibits a decreasing peak friction angle with an increasing normal effective stress. In this study, the slice-based limit equilibrium method is used to evaluate the active earth pressure applied by soils that exhibit nonlinear strength behaviour. The force and moment equilibrium equations for a differential soil slice are introduced, and the boundary conditions for the active earth pressure problems are specified. The mathematical nature of the active earth pressure is explored. It is found that the active earth pressure corresponds to a stationary point on a saddle surface. Seeking the active earth pressure is equivalent to identifying the maximum from a series of local minima. By introducing a combination of two functions for the inter-slice force angle distribution, the local minimisation process for each possible failure surface is implemented by varying the combination factor within its valid range. The proposed solution strategy is compared with existing methods and reasonable agreement is obtained. The influences of the inter-slice force angle distribution on the resultant active earth pressure and its position of application are also studied by using three different combination functions.

Comparison of crack processes in single-flawed rock-like material using two bonded–particle models under compression

The parallel bond model (PBM), one type of basic bonded particle model (BPM), has been diffusely studied in natural rock and rock-like material. It is well-known that BPMs yield unrealistically low ratios of compressive to tensile strength (UCS/TS), friction angles and linear strength envelopes. The flat-joint model (FJM) overcomes those intrinsic deficiencies with a special structure. Thus, FJM can provide satisfactory replication of the mechanical behavior of rock-like materials. In this paper, rock-like material samples containing a single flaw were constructed with flaw angles of 0°, 30°, 45°, 60°, and 90° measured from the horizontal. The PBM and FJM were used to simulate this rock-like material. The results of the numerical simulations were compared with observations from physical tests, including strength, main types of microcracks, macroscopic fracture zones, and location and sequence of the first and secondary cracks. The results demonstrate that (1) the flaw inclination angle had a significant effect on strength; (2) the FJM results showed better agreement with respect to the main types of microcracks and macroscopic fracture zones, reproducing vertical tension failure dominance over shear failure in the rock-like material, contrary to the PBM results; and (3) using the FJM to capture the initiation location, direction, and sequence of the first and secondary cracks is recommended.

A cone surface in three-dimensional analyses of slopes with tension cut-off

A three-dimensional limit analysis of slopes is presented in this paper, based on a right circular cone failure surface. The associated translational mechanism appears to yield better assessment of the safety in isotropic rock than the traditional wedge-type mechanism. The strength of a bonded geomaterial was described using a linear strength envelope truncated in the tensile regime. The tensile strength cut-off so introduced constitutes a non-linear portion of the strength envelope, and it allows constructing failure mechanisms that include rupture modes, in addition to the shear deformation mode. Consequently, the mechanisms in materials with tension cut-off are more critical than those in materials with a traditional linear strength envelope. It is also demonstrated that the failure mechanism based on the right circular cone failure surface in vertical slopes yields results as good as or better than the more complex rotational mechanisms, although the difference is not very significant.

Revising the unified hardening model by using a smoothed Hvorslev envelope

The original unified hardening (UH) model, in which a straight Hvorslev envelope was employed to determine the potential peak stress ratio of overconsolidated soils, is revised using a smoothed Hvorslev envelope (Hermite-Hvorslev envelope). The strength at the intersection between the straight Hvorslev envelope and the critical state surface (i.e. Mohr-Coulomb envelope) can be undefined due to the discontinuous change in the slope of the two linear strength envelopes mentioned above. A smoothed Hvorslev envelope is derived through Hermite interpolation to ensure a smooth change between the proposed Hvorslev envelope and the zero-tension surface as well as a smoothed transition between the proposed Hvorslev envelope and the critical state surface. The Hermite-Hvorslev envelope is then integrated into the original UH model, and then the UH models with four different functions of the Hvorslev envelope are compared with each other. The UH model revised by the Hermite-Hvorslev envelope can well predict the mechanical behaviors of normally consolidated and overconsolidated soils in drained and undrained conditions with the same parameters in the modified Cam-Clay model.

A Study of Three Intrinsic Problems of the Classic Discrete Element Method Using Flat-Joint Model

Discrete element methods have been proven to offer a new avenue for obtaining the mechanics of geo-materials. The standard bonded-particle model (BPM), a classic discrete element method, has been applied to a wide range of problems related to rock and soil. However, three intrinsic problems are associated with using the standard BPM: (1) an unrealistically low unconfined compressive strength to tensile strength (UCS/TS) ratio, (2) an excessively low internal friction angle, and (3) a linear strength envelope, i.e., a low Hoek–Brown (HB) strength parameter m i . After summarizing the underlying reasons of these problems through analyzing previous researchers’ work, flat-joint model (FJM) is used to calibrate Jinping marble and is found to closely match its macro-properties. A parametric study is carried out to systematically evaluate the micro-parameters’ effect on these three macro-properties. The results indicate that (1) the UCS/TS ratio increases with the increasing average coordination number (CN) and bond cohesion to tensile strength ratio, but it first decreases and then increases with the increasing crack density (CD); (2) the HB strength parameter m i has positive relationships to the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle, but a negative relationship to the average coordination number (CN); (3) the internal friction angle increases as the crack density (CD), bond cohesion to tensile strength ratio, and local friction angle increase; (4) the residual friction angle has little effect on these three macro-properties and mainly influences post-peak behavior. Finally, a new calibration procedure is developed, which not only addresses these three problems, but also considers the post-peak behavior.

Behaviour of a cemented clay

A series of 18 triaxial CIUP (undrained isotropically consolidated with pore pressure measurement) tests of fissured cemented Neogene lacustrine clay from northern Bohemia is analyzed, with special reference to the shear strength. The effects of sample disturbance, swelling, and cementation are shown to be the principal factors affecting the shear envelope. During the prepeak stage of testing, destruction of the cementation of some specimens occurs, which is reflected in the wavy form of the stress–strain diagrams. The linear strength envelopes were found to be arranged according to the amount of disturbance (as expressed in the magnitude of swelling). Cemented and uncemented specimens differ when pore-water pressure and stress–strain diagrams are compared. Key words : Miocene clay, undisturbed samples, triaxial test, structural bonds, cementation, sample disturbance.

Response of MDOF Systems to Multiple Support Seismic Excitation

The response of general multiple‐degrees‐of‐freedom (MDOF) systems subjected to several components of earthquake at multiple support points is obtained using a random‐vibration formulation. The excitation is modeled as a colored, correlated, vector‐valued, nonstationary random process. A new filter is used, such that the excitation may have multiple predominant frequencies and a wide range of spectral shapes. The time history of the RMS excitation at support points which is the output of the filter is prescribed directly. The corresponding input of the filter, a fictitious piecewise linear strength envelope, is generated accordingly before engaging the filter with the system. This filter also allows the support motion to be prescribed in terms of displacement, velocity, or acceleration, which is not true for other filters that are popular and widely in use. Finally, the correlation between any two components can also be prescribed as a function of time. The concept of “pseudo‐static displacement” used by ...

RMS Response of Cascaded MDOF Subsystem to Multiple Support Excitation

The RMS response of a general multiple degrees of freedom (MDOF) cascaded secondary system attached at several points to a primary system is obtained using time domain random vibration formulation. The primary system is excited by ground motion at multiple support points. This in turn excites the subsystem at the attachment points. To analyze a primary system, filter parameters are chosen to represent the spectral shapes of earthquakes. The output of the filter, i.e., the time histories of RMS ground excitation at support points and their cross‐correlation, is directly prescribed. Fictitious piecewise linear strength envelopes, which represent the corresponding input of the filter, are generated accordingly before engaging the filter to the system. The time history of the RMS modal coordinates of the supporting system and their cross‐correlation are evaluated and stored as input to its subsystems. To analyze a subsystem, filter parameters are chosen to represent the spectral shapes of the modal coordinates of the supporting system, with a predominant frequency equal to the corresponding natural frequency of the primary system. Piecewise linear strength envelopes are generated as the diagonal terms to match the RMS time histories of modal coordinates and the cross‐terms to match the time histories of cross‐correlation between corresponding modal coordinates. This formulation enables one to independently analyze and design various multiply supported cascaded subsystems attached to a primary system.