An analytical solution for deforming twin‐parallel tunnels in an elastic half plane

The interaction between twin‐parallel tunnels affects the tunnelling‐induced ground deformation, which may endanger the nearby structures. In this paper, an analytical solution is presented for problems in determining displacements and stresses around deforming twin‐parallel tunnels in an elastic half plane, on the basis of complex variable theory. As an example, a uniform radial displacement was assumed as the boundary condition for each of the two tunnels. Special attention was paid to the effects of tunnel depth and spacing between the two tunnels on the surface movement to gain deep insight into the effect of the interaction between twin‐parallel tunnels using the proposed analytical approach. It is revealed that the influence of twin tunnel interaction on surface movements diminishes with both the increase of the tunnel depth and the spacing between the two tunnels. The presented analytical solution manifests that, similar to most of the existing numerical results, the principle of superposition can be applied to determine ground deformation of twin‐parallel tunnels with a certain large depth and spacing; otherwise, the interaction effect between the two tunnels should be taken into account for predicting reliable ground movement. Copyright © 2014 John Wiley & Sons, Ltd.     

A two‐dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing

Within the framework of our discontinuous deformation analysis for rock failure algorithm, this paper presents a two‐dimensional coupled hydromechanical discontinuum model for simulating the rock hydraulic fracturing process. In the proposed approach, based on the generated joint network, the calculation of fluid mechanics is performed first to obtain the seepage pressure near the tips of existing cracks, and then the fluid pressure is treated as linearly distributed loads on corresponding block boundaries. The contribution of the hydraulic pressure to the initiation/propagation of the cracks is considered by adding the components of these blocks into the force matrix of the global equilibrium equation. Finally, failure criteria are applied at the crack tips to determine the occurrence of cracking events. Several verification examples are simulated, and the results show that this newly proposed numerical model can simulate the hydraulic fracturing process correctly and effectively. Although the numerical and experimental verifications focus on one unique preexisting crack, because of the capability of discontinuous deformation analysis in simulating block‐like structures, the proposed approach is capable of modeling rock hydraulic fracturing processes. Copyright © 2014 John Wiley & Sons, Ltd.     

Response of soil aggregate disintegration to the different content of organic carbon and its fractions during splash erosion

Aggregate disintegration is a critical process in soil splash erosion. However, the effect of soil organic carbon (SOC) and its fractions on soil aggregates disintegration is still not clear. In this study, five soils with similar clay contents and different contents of SOC have been used. The effects of slaking and mechanical striking on splash erosion were distinguished by using deionized water and 95% ethanol as raindrops. The simulated rainfall experiments were carried out in four heights (0.5, 1.0, 1.5 and 2.0 m). The result indicated that the soil aggregate stability increased with the increases of SOC and light fraction organic carbon (LFOC). The relative slaking and the mechanical striking index increased with the decreases of SOC and LFOC. The reduction of macroaggregates in eroded soil gradually decreased with the increase of SOC and LFOC, especially in alcohol test. The amount of macroaggregates (>0.25 mm) in deionized water tests were significantly less than that in alcohol tests under the same rainfall heights. The contribution of slaking to splash erosion increased with the decrease of heavy fractions organic carbon. The contribution of mechanical striking was dominant when the rainfall kinetic energy increased to a range of threshold between 9 J m⁻² mm⁻¹ and 12 m⁻² mm⁻¹. This study could provide the scientific basis for deeply understanding the mechanism of soil aggregates disintegration and splash erosion.     

Water mining from the deep critical zone by apple trees growing on loess

There have been significant recent advances in understanding the ecohydrology of deep soil. However, the links between root development and water usage in the deep critical zone remains poorly understood. To clarify the interaction between water use and root development in deep soil, we investigated soil water and root profiles beyond maximum rooting depth in five apple orchards planted on farmland with stand ages of 8, 11, 15, 18, and 22 years in a subhumid region on the Chinese Loess Plateau. Apple trees rooted progressively deeper for water with increasing stand age and reached 23.2 ± 0.8 m for the 22‐year‐old trees. Soil water deficit in deep soil increased with tree age and was 1,530 ± 43 mm for a stand age of 22 years. Measured root deepening rate was far great than the reported pore water velocity, which demonstrated that trees are mining resident old water. The deficits are not replenished during the life‐span of the orchard, showing a one‐way mining of the critical zone water. The one‐way root water mining may have changed the fine root profile from an exponential pattern in the 8‐year‐old orchard to a relative uniform distribution in older orchards. Our findings enhance our understanding of water‐root interaction in deep soil and reveal the unintended consequences of critical zone dewatering during the lifespan of apple trees.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.