Maximum Tensile Criterion Research Articles

Modeling of projectile penetrating fiber-reinforced concrete via the continuum discontinuum element method

In this paper, the projectile penetrating fiber-reinforced concrete (FRC) is modeled and simulated by the continuum discontinuum element method (CDEM) and a fiber-block interpolation coupling algorithm. The Mohr–Coulomb constitutive model is applied to the blocks to calculate the block forces, and the Mohr–Coulomb criterion and the maximum tensile criterion are applied to estimate the failure of contact surfaces. Numerical simulations of projectiles penetrating plain concrete and FRC with 1 to 3 vol% are performed. We verify the validity of the model by predicting the crack morphology and penetration depth for plain concrete and FRC, which are in agreement with experimental results. Detailed images of crack surfaces in the concrete blocks caused by projectile penetration are included. The effects of fiber content on crack width are analyzed. The results indicate that the normalized widths of the cracks approximately satisfy the Weibull distribution. Compared with plain concrete, the addition of fibers results in a reduction in both the expectation and variance of crack widths. However, the degree of reduction weakens as fiber content increased.

Initiation of hydraulically or drilling-induced tensile wall-fractures from arbitrarily inclined boreholes: Implications for constraints in the magnitudes of in-situ stresses

An accurate estimation of the magnitudes of three in-situ stresses can usefully improve the production performance of hydraulic fracturing and reduce the risk of wellbore instability. Considering two types of linear elastic stress around the non-perforated arbitrarily inclined borehole (plane strain and plane stress conditions), the theory of hydraulic fracturing, and the maximum tensile criterion, the generalized governing formulas are derived to explain the mechanism of hydraulically or drilling-induced longitudinal, oblique, and transverse tensile wall-fractures in arbitrarily inclined boreholes. These formulas provide useful implications for constraints on the magnitudes of in-situ stresses, which determine the initiation of different types of tensile wall-fractures under different faulting stress regimes. The present paper extends the initiating conditions of the common transverse tensile wall-fractures related to the works of Hossain et al. (2000) and Nelson et al. (2005). The prerequisite for the special transverse tensile wall-fractures that tensile fractures simultaneously initiated around a whole borehole wall (Huang et al., 2012) is generalized by introducing the concept of the turning locations. The formulas corresponding to the turning locations are provided under different faulting stress regimes, revealing that the work proposed by Huang et al. (2012) is only a particular case. It is found that the turning locations are related to the critical borehole inclination or azimuth angles. Overall, all the formulas in this study for longitudinal, oblique, and transverse tensile wall-fractures can be used to design hydraulic fracturing experiments and to determine the in-situ stress by using the information of drilling-induced tensile wall-fractures. Moreover, the governing formulas of the turning locations can also be used to optimize the borehole trajectory.

Analysis of instability mechanisms of natural fractures during the approach of a hydraulic fracture

A fluid-driven fracture propagation model dominated by viscosity-leak-off regime was presented to investigate the mechanical stability of natural fracture (NF) when hydraulic fracture (HF) approaches. The induced stresses generated by the approaching HF were calculated by a fully coupled integro-differential equation. The pore pressure effect caused by fracturing fluid leak-off was simulated based on dual porosity medium theory. The critical failure conditions of NF were determined based on maximum tensile criterion and Barton-Bandis criterion. The sensitivity of the stability of NF to in-situ stress anisotropy, approaching angle and distance, injection rate, fracturing fluid viscosity, and NF properties was analyzed in detail. Simulation results reveal that the shearing-mode failure of NF is obviously easier than the opening-mode failure, and the shear slip zone is much larger than the tensile failure zone. As HF approaches NF non-orthogonally, the induced debonding process is unstable, and the debonding zone is asymmetric with respect to the center of NF. The tensile-induced expansion zone is primarily located in the portion of NF ahead of the HF tip, however the shear-induced slip zone can even occur on NF behind of the HF tip. Induced stresses alone have negligible effect on the stability of the NF that is unconnected to the HF. The change in pore pressure due to leak-off effect dominates the final stimulated reservoir volume during large-scale fracturing. The instability of the NF dominates the propagation trajectory of the subsequent HF. A more suitable arrested/crossing condition by extending Gu-Weng criterion was established to predict the path of HF propagation.

A theoretical model for predicting the Peak Cutting Force of conical picks

In order to predict the PCF (Peak Cutting Force) of conical pick in rock cutting process, a theoretical model is established based on elastic fracture mechanics theory. The vertical fracture model of rock cutting fragment is also established based on the maximum tensile criterion. The relation between vertical fracture angle and associated parameters (cutting parameter n and ratio B of rock compressive strength to tensile strength) is obtained by numerical analysis method and polynomial regression method, and the correctness of rock vertical fracture model is verified through experiments. Linear regression coefficient between the PCF of prediction and experiments is 0.81, and significance level less than 0.05 shows that the model for predicting the PCF is correct and reliable. A comparative analysis between the PCF obtained from this model and Evans model reveals that the result of this prediction model is more reliable and accurate. The results of this work could provide some guidance for studying the rock cutting theory of conical pick and designing the cutting mechanism.