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In rock grouting, idealized 2D-radial laminar flow of yield stress fluids (YSF) is a fundamental flow configuration that is used for cement grout spread estimation. A limited amount of works have presented analytical and numerical solutions on the radial velocity profiles between parallel disks. However, to the best of our knowledge, there has been no experimental work that has presented measured velocity profiles for this geometry. In this paper, we present velocity profiles of Carbopol (a simple YSF), measured by pulsed ultrasound velocimetry within a radial flow model. We describe the design of the physical model and then present the measured velocity profiles while highlighting the plug-flow region and slip effects observed for three different apertures and volumetric flow rates. Although the measured velocity profiles exhibited wall slip, there was a reasonably good agreement with the analytical solution. We then discuss the major implications of our work on radial flow.

The situation that the grouting borehole doesn’t intersect with natural fractures of rock masses is often met in practical grouting project. Hence, it’s very necessary to discuss whether the rock masses around borehole will split under the grouting pressure and the corresponding splitting orientation. After the splitting crack finishes propagation, we can estimate whether it will penetrate with original fractures, and it’s favorable for grouting theory analysis and numerical simulation and so on. According to this, the splitting criterion and splitting orientation are proposed with and without considering ground stress, respectively. In the meantime, under the situation of splitting, the singularity of crack-tip’s stress field is simulated by 6 nodes singular isoparametric element through secondary development of large-scale finite element analysis software-ANSYS. The stress intensity factor is introduced and the propagation of the splitting crack is simulated to obtain the final propagation length, which has significant guiding meaning to grouting theory and the practical grouting projects.

Snow avalanches cause fatalities and economic loss worldwide and are one of the most dangerous gravitational hazards in mountainous regions. Various flow behaviors have been reported in snow avalanches, making them challenging to be thoroughly understood and mitigated. Existing popular numerical approaches for modeling snow avalanches predominantly adopt depth-averaged models, which are computationally efficient but fail to capture important features along the flow depth direction such as densification and granulation. This study applies a three-dimensional (3D) material point method (MPM) to explore snow avalanches in different regimes on a complex real terrain. Flow features of the snow avalanches from release to deposition are comprehensively characterized for identification of the different regimes. In particular, brittle and ductile fractures are identified in the different modeled avalanches shortly after their release. During the flow, the analysis of local snow density variation reveals that snow granulation requires an appropriate combination of snow fracture and compaction. In contrast, cohesionless granular flows and plug flows are mainly governed by expansion and compaction hardening, respectively. Distinct textures of avalanche deposits are characterized, including a smooth surface, rough surfaces with snow granules, as well as a surface showing compacting shear planes often reported in wet snow avalanche deposits. Finally, the MPM modeling is verified with a real snow avalanche that occurred at Vallée de la Sionne, Switzerland. The MPM framework has been proven as a promising numerical tool for exploring complex behavior of a wide range of snow avalanches in different regimes to better understand avalanche dynamics. In the future, this framework can be extended to study other types of gravitational mass movements such as rock/glacier avalanches and debris flows with implementation of modified constitutive laws.

This chapter explores on a number of automated attainable regions (AR) construction schemes. Research in AR theory has witnessed a shift toward the development of numerical AR construction algorithms, with less emphasis placed on general AR theory. Visualization of the data is an important part of AR theory when starting out, as it allows for the interpretation of the rate field, where plug flow reactors (PFRs), continuous‐flow stirred tank reactors (CSTRs), and differential sidestream reactors (DSRs) can be observed how they interact in state space. However, the types of systems that are often encountered in practice are seldom cast in two or three dimensions only. The recursive constant control (RCC) method demonstrates how the DSR expression may be used to achieve effluent concentrations belonging to both PFRs and CSTRs. A trade‐off between construction time and computational accuracy must often be established when implementing the RCC algorithm in practice.

This chapter explains the aspects of higher dimensional attainable regions (AR) theory to a number of problems. These problems are organized into the following three sections: higher dimensional constructions in concentration space; residence time constructions involving temperature; application of AR theory to batch reactors. Three‐dimensional Van de Vusse kinetics has been used extensively in AR research papers in the past. AR practitioners often use the system as an ‘acid test’ for many AR construction algorithms and hypotheses. The extreme points of the AR boundary are composed of plug flow reactor (PFR) trajectories; one can use concentrations belonging to the CSTR locus as feed points for PFRs. The required reactor structure in this instance is then a CSTR followed by a PFR for the three‐dimensional Van de Vusse kinetics. Critical CSTRs investigates the existence of any critical continuous‐flow stirred tank reactor (CSTR) points in the benzene toluene xylene (BTX) system.