Tidal regime shift in Lingdingyang Bay,the Pearl River Delta: An identification and assessment of driving factors

Both natural changes (e.g., tidal forcing from the ocean and global sea level rise) and human-induced changes (e.g., dredging for navigation, sand excavation, and land reclamation) exert considerable influences on the long-term evolution of tidal regimes in estuaries. Evaluating the impacts of these factors on tidal-regime shifts is particularly important for the protection and management of estuarine environments. In this study, an analytical approach is developed to investigate the impacts of estuarine morphological alterations (mean water depth and width convergence length) on tidal hydrodynamics in Lingdingyang Bay, Southeast China. Based on the observed tidal levels from two tidal gauging stations along the channel, tidal wave celerity and tidal damping/amplification rate of different tidal constituents are computed using tidal amplitude and phase of tidal constituents extracted from a standard harmonic analysis. We show that the minimum mean water depth for the whole estuary occurred in 2006, whereas a shift in tidal wave celerity for the M₂ tide component occurred in 2009. As such, the study period (1990–2016) could be separated into pre-human (1990–2009) and post-human (2010–2016) phases. Our results show that the damping/amplification rate and celerity of the M₂ tide have increased by 31% (from 7 to 9.2 m⁻¹) and 28% (from 7 to 9 m·s⁻¹) respectively, as a consequence of the substantial impacts of human interventions. The proposed analytical method is subsequently applied to analyse the historical development of tidal hydrodynamics and regime shifts induced by human interventions, thus linking the evolution of estuarine morphology to the dominant tidal hydrodynamics along the channel. The observed tidal regime shift is primarily caused by channel deepening, which substantially enlarged the estuary and reduced effective bottom friction resulting in faster celerity and stronger wave amplification. Our proposed method for quantifying the impacts of human interventions on tidal regime shifts can inform evidence-based guidelines for evaluating hydraulic responses to future engineering activities.     

Analytical solutions for the consolidation of unsaturated foundation with prefabricated vertical drain

Based on the consolidation theory raised by Fredlund, the solutions for the equal-strain consolidation of unsaturated foundation with the prefabricated vertical drain considering smear effect and drain resistance are analytically formulated in this paper. Firstly, governing equations for excess pore pressures (i.e., excess pore-air and pore-water pressures) under the equal-strain hypothesis are derived with the introduction of radial boundary conditions. Afterwards, the obtained coupled equations are solved by applying general integration, decoupling process, and Fourier sine series expansion. The smear coefficients and factors of drain resistance corresponding to air and water phases are both captured explicitly in the final solutions. Furthermore, the degenerated solutions are employed to verify the reliability of the current solutions. Finally, a parametric study is conducted to study the consolidation characteristics of the proposed foundation model against modeling sizes (S and N), smear coefficients (α_a and α_w), and drain resistance factors (G_a and G_w).     

A comparison between the single ring pressure infiltrometer and simplified falling head techniques

Testing the relative performances of the single ring pressure infiltrometer (PI) and simplified falling head (SFH) techniques to determine the field saturated soil hydraulic conductivity, K_fs, at the near point scale may help to better establish the usability of these techniques for interpreting and simulating hydrological processes. A sampling of 10 Sicilian sites showed that the measured K_fs was generally higher with the SFH technique than the PI one, with statistically significant differences by a factor varying from 3 to 192, depending on the site. A short experiment with the SFH technique yielded higher K_fs values because a longer experiment with the PI probably promoted short‐term swelling phenomena reducing macroporosity. Moreover, the PI device likely altered the infiltration surface at the beginning of the run, particularly in the less stable soils, where soil particle arrangement may be expected to vary upon wetting. This interpretation was supported by a soil structure stability index, SSI, and also by the hydraulic conductivity data obtained with the tension infiltrometer, i.e. with a practically negligible disturbance of the sampled soil surface. In particular, a statistically significant, increasing relationship with SSI and an unsaturated conductivity greater than the saturated one were only detected for the K_fs data obtained with the PI. The SFH and PI techniques should be expected to yield more similar results in relatively rigid porous media (low percentages of fine particles and structurally stable soils) than in soils that modify appreciably their particle arrangement upon wetting. The simultaneous use of the two techniques may allow to improve K_fs determination in soils that change their hydrodynamic behaviour during a runoff producing rainfall event. Copyright © 2013 John Wiley & Sons, Ltd.     

A simple expression for the bulk field capacity of a sloping soil horizon

Field capacity is a commonly used soil parameter in surface water hydrological models, loosely defined as the moisture content of a soil after drainage. The most commonly applied expression for field capacity is defined as the remaining water in a vertical soil column subject to 1/3 atm. of pressure head. While this quantification is sufficient in some cases, the definition is not consistent with the use of bulk field capacity in calculations of lateral drainage from hillslopes, as required by some surface soil parameterizations, nor does it address additional complications arising from differences in soil texture or sample size. Here, a simple alternative expression for bulk field capacity in a sloping or vertical soil is derived directly from Richards equation with the use of the Brooks‐Corey characteristics. It is demonstrated that this expression is consistent with data acquired from vertical soil columns, but may be extended to additional situations commonly found in surface water models and land surface schemes. The calculation of bulk field capacity requires only the Brooks‐Corey pore size distribution index, soil air‐entry pressure, and hillslope length and slope, and may be considered a physically based alternative to pedotransfer function or lookup table approaches. Copyright © 2010 John Wiley & Sons Ltd and Crown in the right of Canada.     

A high‐resolution local RBF collocation method for steady‐state poroelasticity and hydromechanical damage analysis

In this work, we describe a meshless numerical method based on local collocation with RBFs for the solution of the poroelasticity equation. The RBF finite collocation approach forms a series of overlapping nodal stencils, over which an RBF collocation is performed. These local collocation systems enforce the governing PDE operator throughout their interior, with the intersystem communication occurring via the collocation of field variables at the stencil periphery. The method does not rely on a generalised finite differencing approach, whereby the governing partial differential operator is reconstructed at the global level to drive the solution of the PDE. Instead, the PDE governing and boundary operators are enforced directly within the local RBF collocation systems, and the sparse global assembly is formed by reconstructing the value of the field variables at the centrepoint of the local stencils. In this way, the solution of the PDE is driven entirely by the local RBF collocation, and the method more closely resembles the approach of the full‐domain RBF collocation method. By formulating the problem in this fashion, high rates of convergence may be attained without the computational cost and numerical ill‐conditioning issues that are associated with the full‐domain RBF collocation approach. An analytical solution is formulated for a 2D poroelastic fluid injection scenario and is used to verify the proposed implementation of the method. Highly accurate solutions are produced, and convergence rates in excess of sixth order are observed for each field variable (i.e. pressure and displacement) and field‐variable derivative (i.e. pressure gradients and stresses). The stress and displacement fields resulting from the solution of the poroelasticity equation are then used to describe the formation and propagation of microfractures and microfissures, which may form in the presence of large shear strain, in terms of a continuous damage variable which modifies the mechanical and hydraulic properties of the porous medium. The formation of such hydromechanical damage, and the resulting increase in hydraulic conductivity, is investigated for a pressurised injection into sandstone. Copyright © 2014 John Wiley & Sons, Ltd.     

Using MODFLOW code to approach transient hydraulic head with a sharp‐interface solution

Saltwater intrusion problems have been usually tackled through analytical models because of its simplicity, easy implementation and low computational cost. Most of these models are based on the sharp‐interface approximation and the Ghyben–Herzberg relation, which neglects mixing of fresh water and seawater and implicitly assumes that salt water remains static. This paper provides insight into the validity of a sharp‐interface approximation defined from a steady state solution when applied to transient seawater intrusion problems. The validation tests have been performed on a 3D unconfined synthetic aquifer, which include spatial and temporal distribution of recharge and pumping wells. Using a change of variable, the governing equation of the steady state sharp‐interface problem can be written with the same structure of the steady confined groundwater flow equation as a function of a single potential variable (?). We propose to approach also the transient problem solving a single potential equation (using also the ? variable) with the same structure of the confined groundwater flow equation. It will allow solving the problem by using the classical MODFLOW code. We have used the parameter estimation model PEST to calibrate the parameters of the transient sharp‐interface equation. We show how after the calibration process, the sharp‐interface approach may provide accurate enough results when applied to transient problems and improve the steady state results, thus avoiding the need of implementing a density‐dependent model and reducing the computational cost. This has been proved by comparing results with those obtained using the finite difference numerical code SEAWAT for solving the coupled partial differential equations of flow and density‐dependent transport. The comparison was performed in terms of piezometric heads, seawater penetration, transition zone width and critical pumping rates. Copyright © 2014 John Wiley & Sons, Ltd.     

Analytical solutions for Euler‐Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads

In this paper, the dynamic response of an infinite beam resting on a Pasternak foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The mechanical resistance of the Pasternak foundation is modeled using two parameters, that is, one accounts for soil resistance due to compressive strains in the soil and the other accounts for the resistance due to shear strains. Because the Winkler model only represents the compressive resistance of soil, comparatively, the Pasternak model is more realistic to consider shear interactions between the soil springs. The governing equation of the beam is simplified into an algebraic equation by employing integration transforms, so that the analytical solution for the dynamic response of the beam can be obtained conveniently in the frequency domain. Both inverse Laplace and inverse Fourier transforms combined with convolution theorem are applied to convert the solution into the time domain. The solutions for several special cases, such as harmonic line loads, moving line loads, and travelling loads are also discussed and numerical examples are conducted to investigate the influence of the shear modulus of foundation on the beam responses. The proposed solutions can be an effective tool for practitioners. Copyright © 2017 John Wiley & Sons, Ltd.     

An analytical model for vapor‐phase volatile organic compound diffusion through landfill composite covers

One‐dimensional mathematical models for vapor‐phase volatile organic compound (VOC) diffusion through composite cover barriers are presented. An analytical solution to the model was obtained by the method of separation of variables. The results obtained by the proposed solution agree well with those obtained by a numerical analysis. Based on the proposed analytical model, the VOC breakthrough curves of five different composite covers are compared. The effects of degree of saturation of geosynthetic clay liner (GCL) or compacted clay liner (CCL) on VOC migration in the composite covers are then presented. Results show that the composite cover barriers provide much better diffusion barriers for VOC than the single CCL. The top surface steady‐state flux for a composite barrier, consisting of a 1.5 mm geomembrane (GM) and a 20 cm CCL, can be 8.3 times lower than that for a 30 cm CCL. The surface steady‐state flux for the case with (1.5 mm GM + 6 mm GCL) was found to be 2.3 times lower than that for the case with (1.5 mm GM + 20 cm CCL). The degree of saturation S_r of the CCL has a great influence on VOC migration in composite covers when S_r is larger than 0.5. The steady‐state flux at the surface of GM for the case with S_r = 0.7 can be 1.8 times lower than that for the case with S_r = 0.2. The proposed analytical model is relatively simple and can be used for verification of complicated numerical models, analysis of experimental data and performance assessment of composite cover barriers. Copyright © 2016 John Wiley & Sons, Ltd.     

A general solution for groundwater flow in an estuarine's leaky aquifer system after considering aquifer anisotropy

This paper presents an analytical model for describing the tidal effects in a two‐dimensional leaky confined aquifer system in an estuarine delta where ocean and river meet. This system has an unconfined aquifer on top and a confined aquifer on the bottom with an aquitard in between the two. The unconfined and confined aquifers interact with each other through leakage. It was assumed that the aquitard storage was negligible and that the leakage was linearly proportional to the head difference between the unconfined and confined aquifers. This model's solution was based on the separation of variables method. Two existing solutions that deal with the head fluctuation in one‐dimensional or two‐dimensional leaky confined aquifers are shown as special cases in the present solution. Based on this new solution, the dynamic effect of the water table's fluctuations can be clearly explored, as well as the influence of leakage on the behaviour of fluctuations in groundwater levels in the leaky aquifer system. Copyright © 2015 John Wiley & Sons, Ltd.     

Timoshenko beam solution for the response of existing tunnels because of tunneling underneath

An analytical solution for the deflection and internal forces of an existing tunnel because of tunneling underneath is presented. The existing tunnel is modeled as a Timoshenko beam resting on a Winkler foundation, which takes into account the contribution of shear deformation to the total deflection of the existing tunnel. The validity of the analytical solution is verified by a centrifuge test, and the merit of this analytical method is confirmed by comparison with the conventional Euler–Bernoulli beam model. Influential factors on the behavior of the existing tunnel are investigated by consideration of the variations of subgrade modulus, ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Results show that the proposed analytical method is a valid and effective method to evaluate shearing‐induced deformation in existing tunnels with large diameters. Results also show that the pattern and the amplitude of the response of the existing tunnel are affected largely by ground loss induced by the new tunnel construction, vertical clearance between the new tunnel and the existing tunnel, and relative existing tunnel–soil stiffness. Copyright © 2015 John Wiley & Sons, Ltd.