Semi‐analytical solution to one‐dimensional consolidation for unsaturated soils with semi‐permeable drainage boundary under time‐dependent loading

This paper presents semi‐analytical solutions to Fredlund and Hasan's one‐dimensional consolidation of unsaturated soils with semi‐permeable drainage boundary under time‐dependent loadings. Two variables are introduced to transform two coupled governing equations of pore‐water and pore‐air pressures into an equivalent set of partial differential equations, which are easily solved by the Laplace transform. The pore‐water pressure, pore‐air pressure and settlement are obtained in the Laplace domain. Crump's method is adopted to perform the inverse Laplace transform in order to obtain semi‐analytical solutions in time domain. It is shown that the present solutions are more general and have a good agreement with the existing solutions from literatures. Furthermore, the current solutions can also be degenerated into conventional solutions to one‐dimensional consolidation of unsaturated soils with homogeneous boundaries. Finally, several numerical examples are provided to illustrate consolidation behavior of unsaturated soils under four types of time‐dependent loadings, including instantaneous loading, ramp loading, exponential loading and sinusoidal loading. Parametric studies are illustrated by variations of pore‐air pressure, pore‐water pressure and settlement at different values of the ratio of air–water permeability coefficient, depth and loading parameters. Copyright © 2017 John Wiley & Sons, Ltd.     

Computational model coupling mode II discrete fracture propagation with continuum damage zone evolution

We propose a numerical method that couples a cohesive zone model (CZM) and a finite element‐based continuum damage mechanics (CDM) model. The CZM represents a mode II macro‐fracture, and CDM finite elements (FE) represent the damage zone of the CZM. The coupled CZM/CDM model can capture the flow of energy that takes place between the bulk material that forms the matrix and the macroscopic fracture surfaces. The CDM model, which does not account for micro‐crack interaction, is calibrated against triaxial compression tests performed on Bakken shale, so as to reproduce the stress/strain curve before the failure peak. Based on a comparison with Kachanov's micro‐mechanical model, we confirm that the critical micro‐crack density value equal to 0.3 reflects the point at which crack interaction cannot be neglected. The CZM is assigned a pure mode II cohesive law that accounts for the dependence of the shear strength and energy release rate on confining pressure. The cohesive shear strength of the CZM is calibrated by calculating the shear stress necessary to reach a CDM damage of 0.3 during a direct shear test. We find that the shear cohesive strength of the CZM depends linearly on the confining pressure. Triaxial compression tests are simulated, in which the shale sample is modeled as an FE CDM continuum that contains a predefined thin cohesive zone representing the idealized shear fracture plane. The shear energy release rate of the CZM is fitted in order to match to the post‐peak stress/strain curves obtained during experimental tests performed on Bakken shale. We find that the energy release rate depends linearly on the shear cohesive strength. We then use the calibrated shale rheology to simulate the propagation of a meter‐scale mode II fracture. Under low confining pressure, the macroscopic crack (CZM) and its damaged zone (CDM) propagate simultaneously (i.e., during the same loading increments). Under high confining pressure, the fracture propagates in slip‐friction, that is, the debonding of the cohesive zone alternates with the propagation of continuum damage. The computational method is applicable to a range of geological injection problems including hydraulic fracturing and fluid storage and should be further enhanced by the addition of mode I and mixed mode (I+II+III) propagation. Copyright © 2016 John Wiley & Sons, Ltd.     

Daily salinity fluctuation alleviates salt stress on seedlings of the mangrove Bruguiera gymnorhiza

Salinity is a vital factor that regulates leaf photosynthesis and growth of mangroves, and it frequently undergoes large seasonal and daily fluctuations creating a range of environments – oligohaline to hyperhaline. Here, we examined the hypotheses that mangroves benefit opportunistically from low salinity resulting from daily fluctuations and as such, mangroves under daily fluctuating salinity (FS) grow better than those under constant salinity (CS) conditions. We compared growth, salt accumulation, gas exchange, and chlorophyll fluorescence of leaves of mangrove Bruguiera gymnorhiza seedlings growing in freshwater (FW), CS (15 practical salinity units, PSU), and daily FS (0–30 PSU, average of 4.8 PSU) conditions. The traits of FS-treated leaves were measured in seedlings under 15 PSU. FS-treated seedlings had greater leaf biomass than those in other treatment groups. Moreover, leaf photosynthetic rate, capacity to regulate photoelectron uptake/transfer, and leaf succulence were significantly higher in FS than in CS treatment. However, leaf water-use efficiency showed the opposite trend. In addition to higher concentrations of Na⁺ and Cl⁻, FS-treated leaves accumulated more Ca²⁺ and K⁺. We concluded that daily FS can enhance water absorption, photosynthesis, and growth of leaves, as well as alter plant biomass allocation patterns, thereby positively affecting B. gymnorhiza. Mangroves that experience daily FS may increase their adaptability by reducing salt build-up and water deficits when their roots are temporally subjected to low salinity or FW and by absorbing sufficient amounts of Na⁺ and Cl⁻ for osmotic adjustment when their roots are subsequently exposed to saline water.     

Numerical and theoretical research on stress distribution in the loosening zone of the trapdoor problem

The traditional theory of soil arching effect was developed on the assumption that stress distribution in the loosening zone is uniform. However, because of the deflection of principal stress' direction, the stress distribution in the loosening zone is actually ununiform. For the evaluation of principal stress axis deflection and stress redistribution, a discrete element method numerical model of trapdoor problem is established for the simulation of soil arching effect. Based on the numerical results, an arc shape of major principal stress trajectory and uniform horizontal stress distribution at the same depth of the loosening zone are adopted. An analytical model is raised to estimate the average loosening earth pressure acting on the trapdoor and stress distribution in the loosening zone at a limit state. In addition, comparison studies are carried out between the predictions of the proposed solutions and discrete element method numerical results as well as available model test results, thereby validating the accuracy of the proposed theoretical model. Both numerical and theoretical results indicate that the vertical stress distribution in the loosening zone is obviously ununiform. The load acting in the middle of loosening zone is transferred toward two sides so that the vertical stress distribution in loosening zone is concave.