Drainage Boundary Research Articles

An explicit one‐dimensional consolidation solution with semi‐permeable drainage boundary for unsaturated soil

SummaryExisting solutions for analyzing one‐dimensional (1‐D) consolidation of unsaturated soil are only derived to cater to two extreme drainage conditions (fully drained and undrained). This study presents a new explicit solution for 1‐D consolidation of unsaturated soil with semi‐permeable drainage boundary. Based on the assumptions of two independent stress variables and the governing equations proposed by Fredlund, the eigenfunction expansion method is adopted to develop an explicit analytical solution to calculate excess pore‐water and pore‐air pressures in an unsaturated soil when it is subjected to external loads. The developed general solutions are expressed in terms of depth, z, and time, t. For the semi‐permeable drainage boundary, eigenvalues and eigenfunctions in the space domain are developed. The technique of Laplace transform is used to solve the coupled ordinary differential equations in the time domain. The newly derived explicit solution is verified with the existing semi‐analytical method in the literature, and an excellent agreement is obtained. Compared with the semi‐analytical solution, the newly derived analytical solution is more straightforward and explicit so that this solution is relatively easier to be implemented into a computer program to carry out a preliminary assessment of 1‐D consolidation of unsaturated soil.

Semianalytical Solutions to the Consolidation of Drainage Well Foundations in Unsaturated Soils with Radial Semipermeable Drainage Boundary under Time-Dependent Loading

Abstract This paper presents semianalytical solutions to the consolidation of drainage well foundations in unsaturated soils with radial semipermeable drainage boundary subjected to time-dependent ...

3D numerical investigation of the coupled interaction behavior between mechanized twin tunnels and groundwater – A case study: Shiraz metro line 2

Mechanized tunneling method using Tunnel Boring Machine (TBM) is being extensively employed in urban areas, especially when excavation takes place underneath the groundwater table. In this study, three-dimensional coupled Finite Element Analyses (FEA) have been performed to investigate the interaction mechanism between mechanized twin tunnels construction of Shiraz metro (line 2) and groundwater. Firstly, two soil constitutive models (Mohr-Coulomb and Modified Cam-Clay model) of Shiraz lean clay are validated against drained triaxial compression test data. Varying the permeability of the grout layer within the specified range, the base numerical model is then calibrated by the field data of ground surface settlements. Parametric studies are conducted subsequently to evaluate the effects of influencing factors involved in the coupled FEA of twin tunnels, including the drainage boundary condition of the grout layer, the position of groundwater level, and the rest interval between excavations of twin tunnels. The numerical results indicate that the ground surface settlements and internal forces of existing segmental lining are greatly influenced by the drainage condition of the grout layer. Also highlighted is the marked effect of the drainage condition of the grout layer in the numerical prediction of the interaction behavior between mechanized twin tunnels and groundwater in different cases of the groundwater level and the rest interval between excavations of twin tunnels.

Genetic Structure of Smallmouth Bass in the Lake Michigan and Upper Mississippi River Drainages Relates to Habitat, Distance, and Drainage Boundaries

AbstractAnalysis of genetic connectivity helps to define stock boundaries and provides information on interpopulation dynamics, such as migration and spawning site fidelity. We used 16 microsatellite loci to describe the genetic population structure of 1,215 Smallmouth Bass Micropterus dolomieu from 32 sites throughout the upper Mississippi River and Lake Michigan watersheds. We found that Smallmouth Bass populations formed two genetically distinct units separated by the Mississippi River–Lake Michigan drainage boundary. Smallmouth Bass from the Lake Michigan drainage could be parsimoniously grouped into two or six genetically distinct units that largely corresponded with either river or lake habitats, while fish from the Mississippi River drainage grouped into two, six, or nine genetic units that were mostly associated with watershed boundaries. In the Lake Michigan and Mississippi River drainages, relative migration was limited between lake and river sites, suggesting that gene flow between neighboring sites with different habitat attributes can be low. Our research provides a higher‐resolution assessment of Smallmouth Bass genetic structure in a core portion of the species’ range and provides strong evidence that Smallmouth Bass populations are structured at small spatial scales that are potentially associated with habitat type. These results demonstrate the importance of evaluating genetic structure at small spatial scales and adopting management strategies that preserve genetic diversity of black bass populations at both the watershed level and the habitat level.

Semi-analytical solutions to the two-dimensional plane strain consolidation for unsaturated soil with the lateral semi-permeable drainage boundary under time-dependent loading

Abstract Using Fourier sine series expansion and Laplace transform, semi-analytical solutions for the two-dimensional plane strain consolidation problem of unsaturated soils are presented subjected to time-dependent loading with the lateral semi-permeable drainage boundary (LSDB), which is the third boundary and can be used to consider the smear effect of the vertical drain. Then, degenerated and numerical solutions are provided to verify the validity of the proposed solutions. Finally, the consolidation property involving the LSDB and time-dependent loading is depicted and analyzed, and the consolidation behavior is shown to result from the application of the LSDB and loading.

A grid-based distributed hydrological model for coal mined-out area

Water-conducting cracks and mined-out area caused by coal mining change the regional hydrological processes. To address this issue, this research proposed a grid-based distributed hydrological model for coal mined-out area (GDHCMA), and validated the model in one representative coal mining watershed (Wujiayao watershed in China). The impact of coal mining on wet front depth was further analyzed based on the GDHCMA model. The results revealed that: (1) ground subsidence or cracks induced by coal mining accelerate the leakage of water flow into the mined-out area or replenish the groundwater reservoir, thereby reducing the flood peak flow; (2) The parameters of GDHCMA model was calibrated by the Shuffled Complex Evolution (SCE) global search algorithm and the model showed high accuracy before and after coal mining. During the pre-coal mining period, the calculated NSE (Nash-Sutcliffe efficiency coefficient) was above 0.9, and the error percentage of peak flow and flood volume was less than 15%; During the coal mining period, the main improvement is that the lower boundary conditions for the calculation of unsaturated soil infiltration are treated with free drainage boundaries. The calculated mean NSE is 0.95, the error percentages of flood peak and flood volume are less than 10%, and the peak time error is 0. (3) The leading factors affecting the downward depth of the wetting front are rainfall, soil type, the coal mined-out area etc. The above are of great practical significance for studying the mechanism of the coal mining on the water cycle.

Three-dimensional response to a partially penetration well pumping in a general anisotropic three-layer aquifer system

Three-dimensional response to well pumping in a multilayer aquifer system with rigorous treatment of interfacial flow attracts great attention among the subsurface hydrologists because of its theoretical importance and practical merits. In this study, a general theory of three-dimensional groundwater flow to a well of infinitesimal radius in an anisotropic three-layer aquifer system is developed with a constant-rate pumping in the lower layer, and associated semi-analytical solutions of drawdowns in individual layers are obtained. This theory discards many previous assumptions for studying a multilayer aquifer system such as simplified flow configuration in the aquitard, treatment of cross-formation flow as a volumetric averaged term adding to the governing equations of aquifer flows, and sometimes negligence of vertical flow components in the aquifers. Additionally, this theory considers three types of commonly used top boundary conditions: A water table with delayed gravity drainage boundary condition (Case 1), a constant-head top boundary condition (Case 2), and a no-flow top boundary condition (Case 3). The dimensionless drawdown solutions in Laplace domain are obtained and inverted numerically to calculate the time-domain solutions. The solution encompasses existing solutions for a two-layer or a single-layer (e.g. unconfined or confined) aquifer system as subsets. The developed solutions are tested extensively with a finite-element numerical solution using COMSOL and other existing solutions, and a sensitivity analysis is performed to prioritize the influences of different parameter groups. The results of this study can be used to predict the pumping induced drawdown at any position with an observation well, and to estimate the hydraulic parameters of the lower pumped layer and upper layer, as well as the middle layer. The developed theory provides a basis for other potential applications such as geotechnical engineering and groundwater management.

Analytical solution for classical one-dimensional thaw consolidation model considering unfrozen water effect and time-varying load

A one-dimensional thawing process of frozen soil under a uniform initial temperature and a step increase of boundary temperature is investigated. The classical thaw consolidation model developed by Morgenstern and Nixon is extended by including unfrozen water in frozen soil and time-varying loads under two types of drainage boundaries. It is proven that the thawing front advances in proportion to the square root of time even with the unfrozen water effect included. It is also indicated that a certain form of superposition principle is applicable to the consolidation process even with the presence of a moving interface. An analytical solution for the external load in the form of a power function is developed using the similarity transformation technique, and this solution can be applied to construct the analytical solution for an arbitrary external load using the superposition principle. A numerical solution for the problem is also developed. Computational examples are presented. First, the correctness of the analytical solution and the numerical solution is verified. Second, thaw consolidation processes under an instant load and a corresponding exponential load are compared and discussed. Third, the effects of unfrozen water and drainage types on the thaw consolidation behavior are investigated.

One‐dimensional consolidation of soil under multistage load based on continuous drainage boundary

SummaryIn engineering practice, a rapid loading rate can result in ground failure when the strength of soft soils is relatively low, and a multistage loading scheme is always utilized to deal with this situation. Firstly, under a multistage load and the continuous drainage boundary, an analytical solution of excess pore‐water pressure and consolidation degree is obtained by virtue of the superposition formula of excess pore‐water pressure, and a more general continuous drainage boundary under arbitrary time‐dependent load is developed. Then, a comparison with existing analytical solutions is conducted to verify the present solution. A preliminary attempt on applying the continuous drainage boundary into the finite element model is made, and the feasibility of the numerical model for the one‐dimensional consolidation under the continuous drainage boundary is verified by comparing the results calculated by FEM with that from present analytical solution. Finally, the consolidation behavior of soil is investigated in detail for different int erface parameters or loading scheme. The results show that, in land reclamation projects, a horizontal drain should be placed close to the boundary with a smaller interface parameter to improve the consolidation efficiency. The degree of consolidation is also related to the applied time‐dependent load and interface parameters.

European minnows through time: museum collections aid genetic assessment of species introductions in freshwater fishes (Cyprinidae: Phoxinus species complex)

Massive fish introductions have taken place throughout much of the world, mostly over the last 70 years, and present a major threat to the genetic diversity of native fishes. Introductions have been reported for European Phoxinus, a ubiquitous small cyprinid that populates a wide variety of habitats. Species delineation in European Phoxinus has proven difficult with one reason being ranges of distribution that often traverse drainage boundaries. The present study combines recent samples with museum samples to better understand the current distribution of Phoxinus species and their distributions prior to the massive introductions of fishes in Europe, and to evaluate the use of museum specimens for species distribution studies. For these purposes, genetic lineages from sites collected prior to 1900 (n = 14), and between 1900 and 1950 (n = 8), were analysed using two mitochondrial and nuclear markers. Although possible fish introductions were detected, our results show that the distribution of genetic lineages of museum samples is comparable to that of the extant lineages of European Phoxinus present in those areas. These observations suggest that in the studied ranges the distribution of Phoxinus lineages has been driven by natural processes.

Asymptotic state model of saturated low liquid-limit clay under partial drainage condition

To investigate the drainage boundary influence on the strength characteristics of saturated clay, triaxial tests of saturated clay under undrainage, partial drainage, and complete drainage conditions are performed by using the GDS-DYNTTS apparatus. The partial drainage tests are conducted by controlling the strain increment ratio of the volume strain to axial strain as a constant value. The drainage boundary effects on the mechanical properties of the saturated clay are investigated considering the pore water pressure, effective stress path, and asymptotic behavior of the effective spherical stress-effective deviator stress plane. The asymptotic state constitutive equations are established by incorporating the strain increment ratio into the stress path constitutive model according to the asymptotic state and dilatancy characteristics of the saturated clay. The rationality of the model is verified by comparison with experimental results for the pore pressure and effective stress path. The experimental data show that the strain increment ratio of the saturated clay ratio should be less than 0.3. The drainage conditions affect the dilatancy of the normal consolidated clay, effective stress path, and shear strength of the clay. An increase in the strain increment ratio corresponds to a decrease in the pore water pressure and the effective stress ratio of the saturated low liquid-limit clay. The saturated clay specimen remains in a critical state for a long period of time when the axial strain of the specimen reaches 3%, and changes in the drainage condition can inhibit or accelerate soil failure.

Evaluation of Liquefaction Potential in Saturated Sand under Different Drainage Boundary Conditions—An Energy Approach

Drainage conditions are supposed to have significant influence on sand liquefaction behavior. An infiltration device was utilized in cyclic triaxial tests to reproduce different drainage conditions by altering dry density of the within silt. Permeability coefficient ratio (kp) was utilized for quantifying the drainage boundary effect. Cyclic triaxial tests were conducted on saturated Fujian standard sand samples. Test results were used to evaluate the liquefaction potential by using the energy approach. It can be concluded that, if kp increases slightly bigger than zero, excess pore water pressure (EPWP) will respond more fiercely, and the dissipated energy that triggers sand liquefaction will be less. By considering kp, an energy-based database was built by taking kp into consideration and different neural network (NN) models were constructed to predict liquefaction potential by energy approaches accurately under different drainage boundary conditions. It was suggested that the neuro-fuzzy (NF)-based NN model has more satisfactory performance.

Semi‐analytical solutions of two‐dimensional plane strain consolidation in unsaturated soils subjected to the lateral semipermeable drainage boundary

SummaryThe study presents semi‐analytical solutions of two‐dimensional plane strain consolidation problem in unsaturated soils incorporating the lateral semipermeable drainage boundary by adopting Fourier sine series and Laplace transform. The two‐dimensional plane strain consolidation equations in the form of two‐order partial differential equations with three variables are firstly converted to two‐order partial differential equations with two variables, which are similar to those of one‐dimensional consolidation problem. The four‐order ordinary differential equations about excess pore‐air and excess pore‐water pressures are got by applying Laplace transform and the substitution method. Then, the solutions of excess pore pressures and settlement are achieved in the Laplace transform domain. Afterwards, on the basis of Crump's method, the inverse Laplace transform is conducted to obtain the analytical solutions in time domain. The comparison is conducted to verify the exactness of the obtained solutions, and the two‐dimensional plane strain consolidation property with the lateral semipermeable drainage boundary is illustrated and discussed. Parametric studies are demonstrated for the excess pore pressures and normalized settlement with the change of the boundary parameters, air‐water and lateral‐vertical permeability coefficients, and the distance and depth. It can be found that the lateral semipermeable drainage boundary impedes the consolidation rate obviously, and when different investigated parameters are adopted, the consolidation property is similar to each other under the later permeable and semipermeable drainage boundary conditions.

Continent‐Wide, Interferometric SAR Phase, Mapping of Antarctic Ice Velocity

AbstractSurface ice velocity is a fundamental characteristic of glaciers and ice sheets that quantifies the transport of ice. Changes in ice dynamics have a major impact on ice sheet mass balance and its contribution to sea level rise. Prior comprehensive mappings employed speckle and feature tracking techniques, optimized for fast‐flow areas, with precision of 2‐5 m/year, hence limiting our ability to describe ice flow in the slow interior. We present a vector map of ice velocity using the interferometric phase from multiple satellite synthetic aperture radars resulting in 10 times higher precision in speed (20 cm/year) and direction (5°) over 80% of Antarctica. Precision mapping over areas of slow motion (<1 m/year) improves from 20 to 93%, which helps better constrain drainage boundaries, improve mass balance assessment, evaluate regional atmospheric climate models, reconstruct ice thickness, and inform ice sheet numerical models.

Consolidation solution of soil around a permeable pipe pile

In practice, how to quickly improve the bearing capacity of piles in a short time is of great significance. In view of this, a technique of setting grooves and installing PVDs (prefabricated vertical drains) at the surface of the pile is proposed in this investigation to accelerate the consolidation of the surrounding soil. A radial and circular consolidation model is established for permeable piles. The finite cosine transform, finite Weber transform, and discretization method are used to obtain a semi-analytical solution for the consolidation model with a mixed drainage boundary condition at the surface of the pile. The sensitivity of the consolidation process to the strip number and the width of PVDs is discussed. The results show that the technique of installing PVDs in piles could potentially improve the bearing capacity. When the area of drainage channels is fixed, the bearing capacity of permeable piles can be more effectively improved by using a higher strip number of PVDs and a smaller PVD width.

Analisa Perhitungan Muka Air Rata-Rata Di Lahan Gambut Dengan Tanggul Keliling Dalam Rangka Mengurangi Kebakaran

Peatland fires encourage the government to restore peat function as natural water storage. One of the measures taken is to build a circumference dike to hold water to reduce excessive drainage. However, there is no study yet of the planned average water level that has to be maintained from the construction of circumference dike. Therefore, the aim of this study is to calculate the average water level on peatlands inside the circumference dike. The methods used consist of hydrological analysis, spatial analysis, and water level analysis. The results of the analysis shows that the average water level in normal years tends to be above the surface, except in the second half of August to the first half of November. In the second half of September to the second half of October, the peat has the potential to be burned. In a dry season the water tends to fall decline to the drainage boundary of peatland which is at -1.5 m which occurs in the second half of March to December. In the second half of February until December peatland has potential to be burned. From this research, it can be concluded that the calculations using this method is similar with in-situ observation data and can be used to calculate the average water level of peat with the same conditions in other locations.

Improved Double-Layer Soil Consolidation Theory and Its Application in Marine Soft Soil Engineering

Marine soft soil foundation is a double-layer foundation structure with a crust layer and soft substratum. Moreover, it is common that there are various forms of drainage. Accordingly, based on Terzaghi’s consolidation theory and the continuous drainage boundary conditions theory of controllable drainage conditions, an improved double-layer soil consolidation theory considering continuous drainage boundary conditions was proposed. To improve the computational efficiency and accuracy, the Laplace transform and the Stehfest algorithm was used to deduce the numerical solution of the improved double-layer soil consolidation theory considering continuous drainage boundary conditions and to compile a computer program. Subsequently, the theory was validated and analyzed by the degenerated model of the perfectly permeable boundary conditions and the semi-permeable boundary conditions, respectively, which showed that this theory has higher accuracy. Simultaneously, the analysis of double-layer consolidation settlement under continuous drainage boundary conditions for marine soft soil foundation of Guangxi Binhai Highway was carried on. The result showed that the consolidation settlement calculated by the improved double-layer consolidation theory presented is basically consistent with the field measurement results, and that the correlation coefficient between them is higher. Accordingly, the research results can provide useful basic information for marine soft foundation engineering.

Internal fluctuations in green roof substrate moisture content during storm events: Monitored data and model simulations

Understanding how the moisture content in a green roof substrate varies during a storm event is essential for accurately modelling runoff detention. In this paper, a green roof test bed installed with moisture probes at three depths was used to understand how moisture content varies during storms. Detailed studies were conducted on five selected storm events. Physical characterisation tests and field-data based calibrations were performed to acquire the model parameters. Two alternative detention models, based on Reservoir Routing and Richard’s Equation, were validated against the measured green roof runoff and temporary moisture storage data. Once the moisture content exceeds local field capacity, its response at different depths occurs simultaneously during storms, although the recorded data indicate a vertical gradient in the absolute values of local field capacity. Both Reservoir Routing and Richard’s Equation can provide reasonable estimations of the runoff and the vertical moisture content profiles, although Richard’s Equation exhibited stronger vertical water content gradients than were observed in practise. The vertical water content profile is not sensitive to the soil water release curve, although the hydraulic conductivity function influences both the vertical water content profile and runoff rate. The modelled results are highly sensitive to the bottom boundary condition, with a constant suction head boundary condition providing a more suitable option than a free drainage boundary condition or a seepage boundary condition.

Analytical model for consolidation settlements under centrifuge environment

Accurate estimation of consolidation settlements is of great engineering interest to address the problem of ground subsidence. Centrifuge consolidation testing in the laboratory is gaining importance due to the requirement of shorter testing time in predicting consolidation settlement. An analytical model is presented for estimating the rate of consolidation settlements using a one-dimensional large-strain consolidation framework in a centrifuge environment. The model accounts for soil self-weight, relative velocity of the fluid and solid phases, different soil compressibility and hydraulic conductivities, and variation of acceleration factor along the specimen length. Development of the proposed model is first presented and is followed by a numerical solution of the model for different drainage boundary conditions using the finite-difference approach. A comparison of the proposed model with the currently available piecewise-linear model, CC1, on Singapore marine clay data shows that the proposed model uses very large time steps in the time marching process after satisfying the stability and convergence criteria. The proposed model is computationally superior to the existing fully numerical approach. Numerical simulations with different centrifuge parameters show that the approximation of the constant acceleration factor over the sample depth overestimates the settlements nearly 45% for a chosen initial specimen height and at a given centrifuge time. The proposed model is capable of simulating consolidation settlements of different clays whose constitutive parameters vary widely.

One‐dimensional self‐weight consolidation with continuous drainage boundary conditions: Solution and application to clay‐drain reclamation

SummaryTraditional consolidation theories cannot provide good predictions of consolidation settlement in land reclamation because of their assumptions that the influence of soil's self‐weight is often neglected, and the drainage boundary is considered as fully pervious/impervious. In view of these limitations, an analytical solution is derived for one‐dimensional self‐weight consolidation problems with a continuous drainage boundary using the finite Fourier sine transform method. Following the classical Terzaghi's small strain theory, the soil's self‐weight is considered to produce consolidation settlement in dredged materials with a constant coefficient of consolidation. The continuous drainage boundary can essentially describe the time‐dependent variation of drainage capacity at the interface between two adjacent soil layers. By reducing the interface parameters, the effectiveness of the calculation is demonstrated against the Terzaghi's solution. The influence of interface parameters and soil's self‐weight stress coefficient on self‐weight consolidation is discussed. As expected, the rate of consolidation considering the self‐weight stress is faster, although the dependency of consolidation rate on the material property of void ratio is neglected. Moreover, the plane of maximum excess pore‐water pressure is estimated as a function of time factor, based on which a design chart is developed to optimize the layout of horizontal drains in land reclamation.