Аnalysis of methods of calculating road structures based by shear resistance in the soil

Introduction. Checking the soil of the subgrade and the layers of road pavement made of loosely cohesive materials by shear resistance is one of the three mandatory conditions for calculating road clothing according to strength criteria. The methodology for checking the soil of the subgrade and the sandy layers of the road pavement is constantly being modified, which is why changes concerning certain calculation details appear in each new version of the regulatory document. The purpose of this work is to analyze the advantages of the classical solution of A.M. Krivissky and to reveal the essence of the errors made in subsequent modifications of this calculation.Materials and methods. The analysis of solutions is carried out from the standpoint of compliance with the basics of mechanics. It is shown that the calculation of the total shear stress in the classical solution of A.M. Krivissky is performed in accordance with the principle of force superposition, which consists in calculating the components of the stress tensor from each force (time load and the own weight of the layer materials) separately, followed by summing the corresponding components. In this case, the active shear stresses from the temporary load and the own weight of the materials are calculated as the equivalent stress of the Mohr-Coulomb criterion. The calculation of these two components of the total shear stress is performed at the same value of the internal friction angle. Since the angle of inclination of the sliding surface to the main axes is determined by the sum or difference of 45 degrees and half of the internal friction angle, the tangential and normal stresses, which are components of the active shear stress, both from the temporary load and the own weight of the materials, are determined for the same shear surface rotated to the main axes at the same angle. In the current normative calculations, the active shear stresses from the temporary load and the own weight of the materials are determined at different angles of internal friction. This means that the active shear stresses from the temporary load and the own weight of the materials act on two different shear surface rotated to the main axes at different angles. Such stresses cannot be summed up or compared with each other. In addition to this error of the normative calculation methods, their other disadvantages are given.Results. As a result of a detailed analysis of the known modifications of the classical solution, obvious contradictions to the principles of continuum mechanics are established. As an alternative to modern calculation criteria for shear resistance, the article presents criteria for soil strength in which the shear stress exceeds the equivalent stress in the Mohr-Coulomb criterion. The principle of deducing formulas for calculating the first critical load and the total shear stress from the strength criteria under consideration is shown.Conclusion. Conclusions are drawn about the need to return to the classical solution obtained by specialists of the Leningrad School of the USSR, or to develop a fundamentally new solution based on a new plasticity condition in which the total shear stress exceeds the similar characteristic of the stress state of the original Mohr - Coulomb criterion.

Determination of Equivalent Mohr-Coulomb Criterion from Generalised Hoek-Brown Criterion

A new analytical solution is presented for determining equivalent Mohr-Coulomb (MC) shear strength parameters over an arbitrary interval of minor principal stress σ3 from the generalised Hoek-Brown (HB) criterion using least squares method. Comparison with several published examples demonstrates that the proposed solution had a capacity to accurately determine equivalent MC parameters over a given interval of σ3, as well as instantaneous MC parameters by using a very small interval of σ3. EMC parameters depended heavily on the interval of σ3, which highlighted the importance of intervals of σ3. A calculation case shows that the equivalent internal friction angle and cohesion over the interval of σ3 from tension cut-off σcut−off to maximum minor principal stress σ3max were approximately 12% smaller and 10.3% larger than those over an interval from tensile strength to σ3max, respectively. The proposed solution offers great flexibility for the application of the HB criterion with existing methods based on the MC criterion for rock engineering practice.

Evolution of Strength Parameters for Sandstone Specimens during Triaxial Compression Tests

Despite the lack of test data of the coefficient of pressure sensitivity α and the shearing cohesion k, the Drucker–Prager criterion is commonly applied for numerical analyses of geotechnical engineering. To bridge the gap between the wide application and insufficient knowledge of strength parameters of the Drucker–Prager criterion, this study presents experimentally calibrated strength parameters of this criterion for the first time. This paper proposes a new method to measure α and k in the Drucker–Prager criterion. The square root of the second invariant of the deviatoric stress tensor J 2 is linearly fitted with the first invariant of the stress tensor I 1 in the stress space. The parameters φ and c in the Mohr–Coulomb criterion and α and k in the Drucker–Prager criterion are calibrated to the same set of triaxial compression tests of sandstones. With these testing results, five pairs of conversion formulae (which are most commonly used in the literature) are examined and the most appropriate pair of conversion formulae is identified. With parameters indicating cohesive strength (c and k) and parameters indicating frictional strength ( φ and α ), the evolutions of different strength components are compared with those in the cohesion-weakening friction-strengthening model. With an increase in plastic deformation, the cohesive strength parameters c and k firstly increase to a peak value and then decrease. The frictional strength parameters φ and α gradually increase at a decreasing rate after the initial yield point.

Assessment of instability initiation in exposed salt rock roofs

Stability of rocks is the main requirement for the safe operation of mines. For this purpose, certain measures are applied for the protection and support of underground openings, including roof support design and roof arrangement in the most stable rocks. Stability assessment of underground excavations is largely related to their roof stability. Determination of possible instability conditions in mine roofs governs the choice of support system design and parameters of mine excavations. The Upper Kama Potash Salt Deposit represents a stratified layer of solid salt rocks. Roof instability develops as stratification and roof collapse. The Mohr–Coulomb criterion of coherent rocks is currently used to estimate parameters of a possible damage zone in the exposed roof. This criterion allows evaluating shear plane angles in roof rocks and, as a result, finding parameters of the possible collapse zone. The experience of mining operations in the Upper Kama deposit shows different failure conditions as against the Mohr–Coulomb criterion as the stress state is scarcely included in the criterion used. This study is an attempt to assess parameters of rock exposures by solving a Lame problem in terms of a single mine excavation. The analytical results were compared with the parameters obtained from the plane elasticity solutions by the finite element method. Based on the implemented studies, an engineering approach is developed for the assessment of anticipated instability parameters in exposed roofs in horizontal excavations driven in salt rocks.

Unit weight patterns of overlying rocks above commercial-value salt strata in the Upper Kama deposit

Stability of rocks is the main requirement for the safe operation of mines. For this purpose, certain measures are applied for the protection and support of underground openings, including roof support design and roof arrangement in the most stable rocks. Stability assessment of underground excavations is largely related to their roof stability. Determination of possible instability conditions in mine roofs governs the choice of support system design and parameters of mine excavations. The Upper Kama Potash Salt Deposit represents a stratified layer of solid salt rocks. Roof instability develops as stratification and roof collapse. The Mohr–Coulomb criterion of coherent rocks is currently used to estimate parameters of a possible damage zone in the exposed roof. This criterion allows evaluating shear plane angles in roof rocks and, as a result, finding parameters of the possible collapse zone. The experience of mining operations in the Upper Kama deposit shows different failure conditions as against the Mohr–Coulomb criterion as the stress state is scarcely included in the criterion used. This study is an attempt to assess parameters of rock exposures by solving a Lame problem in terms of a single mine excavation. The analytical results were compared with the parameters obtained from the plane elasticity solutions by the finite element method. Based on the implemented studies, an engineering approach is developed for the assessment of anticipated instability parameters in exposed roofs in horizontal excavations driven in salt rocks.

Failure in Confined Brazilian Tests on Sandstone

Strength of rocks in the confined tension region, where the minimum principal stress is tensile, has only infrequently been measured and is not well understood. Quasi-static confined Brazilian tests under a range of confining stresses (2.76 to 27.58 MPa) where used to determine the strength of sandstone in the confined tension region. The test results indicate that the strength in the confined tension region was a strong function of the intermediate principal stress: increasing the intermediate principal stress significantly increased the strength of the sandstone. The strength data were well fit by the Mogi–Coulomb criterion, which accounts for the intermediate principal stress. Unconfined Brazilian strength data were not well fit to the Mogi–Coulomb criterion derived from the confined Brazilian test data, consistent with a transition from tensile to shear processes dominating failure with increasing confining pressure. Observations of post-failure fracture surfaces reveal more indication of shear processes with increasing confining pressure. Numerical simulations from combined finite-discrete element method are compared to the experimental results and reflect similar conditions for failure compared to the experimental tests in the confined tension region.

The large-scale troughs on Asteroid 4 Vesta are opening-mode fractures

<p>The Dawn mission at Asteroid 4 Vesta revealed two sets of enormous linear structures. Both sets are troughs—linear, negative-relief landforms—with one spanning around at least two-thirds of the equator and the other set incompletely preserved in the northern hemisphere. A previous study evaluated the cross-sectional geometries of the troughs and interpreted them as analogous to grabens, which are landforms caused by normal faults. However, for the troughs to be large-scale opening-mode fractures, i.e., joints, was heretofore not considered. To distinguish between normal faulting and jointing, we investigated the map patterns, cross-sectional geometries, and variations of relief and width along the length of these troughs. Relief and width are meaningful measurands that causally relate to the vertical displacement of faults or aperture of joints, respectively. Their distributions along the trough length should thus reveal differences in fracturing behavior. In addition, we derived strength-depth profiles to characterize the rheologic structure of Vesta’s lithosphere and determine the predicted fracturing behavior in its brittle regime.</p><p>We mapped all large-scale troughs on Vesta, including four equatorial and two northern troughs, and no map patterns diagnostic for faulting were identified. The troughs are bounded by scalloped rims and mainly show V- and bowl shapes in cross-section. The variation of reliefs of the two-opposing trough-bounding scarps reveals that the relief maxima for each of the investigated troughs are located off-center, and at different locations along the trough they bound. In contrast, we found that both the individual and cumulative variations in trough width have their maxima near the center of the trough. These map patterns and geomorphologic characteristics are largely inconsistent with the mechanics of graben formation but instead point to an origin by opening-mode fracturing. Moreover, our calculations of lithospheric strength evolution that enable assessments of fracturing behavior reveal that Vesta’s lithosphere has been dominated by a thick brittle portion throughout its history. Solutions to the Coulomb criterion considering a range of strengths properties of intact to fractured basaltic materials are in support of jointing as the major fracturing mode in at least the upper ~14 km of Vesta’s lithosphere.</p>

A New Unified Solution for Deep Tunnels in Water-Rich Areas considering Pore Water Pressure

Pore water pressure has an important influence on the stresses and deformation of the surrounding rock of deep tunnels in water-rich areas. In this study, a mechanical model for deep tunnels subjected to a nonuniform stress field in water-rich areas is developed. Considering the pore water pressure, a new unified solution for the stresses, postpeak zone radii, and surface displacement is derived based on a strain-softening model and the Mogi-Coulomb criterion. Through a case study, the effects of pore water pressure, intermediate principal stress, and residual cohesion on the stress distribution, postpeak zone radii, and surface displacement are also discussed. Results show that the tangential stresses are always larger than the radial stress. The radial stress presents a gradually increasing trend, while the tangential stress presents a trend of first increasing and then decreasing, and the maximum tangential stress appears at the interface between the elastic and plastic zones. As the pore water pressure increases, the postpeak zone radii and surface displacement increase. Because of the neglect of the intermediate principal stress in the Mohr-Coulomb criterion, the postpeak zone radii, surface displacement, and maximum tangential stress solved by the Mohr-Coulomb criterion are all larger than those solved by the Mogi-Coulomb criterion. Tunnels surrounded by rock masses with a higher residual cohesion experience lower postpeak zone radii and surface displacement. Data presented in this study provide an important theoretical basis for supporting the tunnels in water-rich areas.

Determination of Critical Criterion of Tensile-shear Failure in Brazilian Disc Based on Theoretical Analysis and Meso-macro Numerical Simulation

To define the critical criterion between tensile failure and shear failure of Brazilian disc is crucial for determination of tensile strength under combination of tensile and compressive stresses. Although Griffith's tensile failure criterion is consistent with theoretical solution of radial splitting disc, there are still some shortcomings in which the compression-tension ratio is regarded as a constant and the critical criterion only depend on single parameter of tensile strength. Therefore a critical criterion for tensile-shear failure including tensile truncation was proposed firstly based on Mohr-Coulomb criterion. Then, a new calculation method of shear strength parameters was deduced based on the critical state stress circle. Finally, effective diameter and range of compression-tension ratio of Brazilian disc under tensile failure are proposed, and failure process of Brazilian disc from meso to macro is carried out based on numerical simulation. The results show that the modified Mohr-Coulomb criterion can be determined by two indexes of compressive strength and tensile strength. The deduced compression-tension ratio is in good agreement with experiment results. The accuracy of tensile strength test results is closely related to this ratio. When the ratio is greater than 6, failure of rock can be regarded as ideal tensile failure. If the ratio is less than 6, wedge-shape failure in loading area is the main failure type. On this condition, even if radial crack occurs, it is still not considered to be caused by pure tension.