Seepage Analysis Research Articles

Using H‐Convergence to Calculate the Numerical Errors for 1D Unsaturated Seepage Under Steady‐State Conditions

ABSTRACTUnsaturated zones are important for geotechnical design, geochemical reactions, and microbial reactions. The numerical analysis of unsaturated seepage is complex because it involves highly nonlinear partial differential equations. The permeability can vary by orders of magnitude over short vertical distances. This article defines and uses H‐convergence tests to quantify numerical errors made by uniform meshes with element size (ES) for 1D steady‐state conditions. The quantitative H‐convergence should not be confused with a qualitative mesh sensitivity study. The difference between numerical and mathematical convergences is stated. A detailed affordable method for an H‐convergence test is presented. The true but unknown solution is defined as the asymptote of the numerical solutions for all solution components when ES decreases to zero. The numerical errors versus ES are then assessed with respect to the true solution, and using a log–log plot, which indicates whether a code is correct or incorrect. If a code is correct, its results follow the rules of mathematical convergence in a mathematical convergence domain (MCD) which is smaller than the numerical convergence domain (NCD). If a code is incorrect, it has an NCD but no MCD. Incorrect algorithms of incorrect codes need to be modified and repaired. Existing codes are shown to converge numerically within large NCDs but generate large errors, up to 500%, in the NCDs, a dangerous situation for designers.

Numerical simulation of deposit-landslide instability induced by water level decrease: a case study of RS deposit in Lancang River

Changes in reservoir water level often trigger landslides along the reservoir banks, which are common geological hazards that significantly affect the construction and operation of hydropower projects. In this paper, the stability of the RS reservoir landslide in the southwestern region of China is investigated. A discrete element seepage analysis model is constructed based on the theory of changes in the infiltration surface of the deposit caused by water level drawdown. The model is then embedded into a continuous-discontinuous three-dimensional numerical simulation method to systematically investigate the influence of reservoir water level decrease on the stability of the RS deposit. The results indicate that, under the condition of a sudden drop in reservoir water level decrease, the deposit experiences destabilization failure. Its sliding velocities are mainly influenced by seepage forces and gravity, while sliding displacements are influenced by seepage forces and topographic conditions. The landslide process shows distinct stratification characteristics. The portion of the deposit that slides into the river channel is mainly distributed between an altitude of 2655 m and 2870 m. The research results provide a scientific basis for studying the mechanism of slope failure and landslide disaster chain under the condition of reservoir water level lowering.

A new tunnel drainage system using double-adhesive spray-applied membrane: key parameters and applicable scope

To address water leakage in tunnels with high water pressure, a new waterproof drainage system was proposed. The system uses a spray-applied material with double-adhesive properties as a waterproof layer, significantly reducing leakages, and incorporates a unique bottom drainage system to reduce water pressure. In order to check the effectiveness of the new drainage system and to analyze the effects of various structural measures on pressure reduction, a numerical seepage analysis was carried out under the conditions of a water head of 160 m and a surrounding rock permeability of 1 × 10−6 m/s. The results show that the maximum water pressure on the secondary lining is 0.6 MPa, which is about 60% reduction compared to a fully enclosed waterproof system and shows a significant pressure reduction. The spacing of the circumferential drainage pipe and the width of the drainage sheet significantly affect the drainage performance, while the arrangement of the drainage system and the size of the bottom drainage pipe have minimal impact. With full consideration of pressure reduction, cost efficiency and construction feasibility, it is recommended to use the following drainage scheme for iterative calculations during the design stage: “1” shaped arrangement, blind pipe diameter of 10 cm, width of drainage sheets of 0.8 m, and drainage spacing of 6 m. By combining the experimentally determined hydrostatic peel-off strength of 1.4 MPa for spray-applied membrane, the applicable scope of the new drainage system was acquired. The research results can provide valuable insights into the application of spray-applied waterproofing membrane in drainage tunnels with high water pressure.

Two-dimensional numerical analysis of seepage in an undersea mining area considering hydrochemical corrosion

The complex hydrogeological conditions and unique hydrochemical environment in the seabed rock often cause serious mine water inrush during undersea mining. With the exploitation of the undersea gold mining area in Sanshandao as the research background, a numerical analysis method for the seepage behavior of the surrounding rock in undersea gold mining considering the hydrochemical corrosion was put forward. A numerical simulation analysis of the undersea mining area in Sanshandao was conducted by the established method, and the results showed that mining the submarine ore body significantly changed the seepage field of the surrounding rock around the stope and water levels dropped obviously in the ore-controlling fault zone. Differences in the hydrochemical environment significantly influenced the distribution of the seepage field of the surrounding rock. The calculation results based on three fluids with different pH values show that the head variation range is the largest when pH = 2, followed by pH = 4, and pH = 7 has the smallest head variation range. The water inflow in the stope was also directly affected by the hydrochemical environment. With the change of pH, the water inflow at each boundary of the stope increases exponentially.

Confined seepage analysis of saturated soils using fuzzy fields

Seepage refers to the flow of water through porous materials. This phenomenon has a crucial role in dam, slope, excavation, tunnel, and well design. Performing seepage analysis usually is a challenging task, as one must cope with the uncertainty associated with the parameters such as the hydraulic conductivity in the horizontal and vertical directions that drive this phenomenon. However, at the same time, the data on horizontal and vertical hydraulic conductivities are typically scarce in spatial resolution. In this context, so-called non-traditional approaches for uncertainty quantification (such as intervals and fuzzy variables) offer an interesting alternative to classical probabilistic methods, since they have been shown to be quite effective when limited information on the governing parameters of a phenomenon is available. Therefore, the main contribution of this study is the development of a framework for conducting seepage analysis in saturated soils, where uncertainty associated with hydraulic conductivity is characterized using fuzzy fields. This method to characterize uncertainty extends interval fields towards the domain of fuzzy numbers. In fact, it is illustrated that fuzzy fields are an effective tool for capturing uncertainties with a spatial component, since they allow one to account for available physical measurements. A case study in confined saturated soil shows that with the proposed framework, it is possible to quantify the uncertainty associated with seepage flow, exit gradient, and uplift force effectively.

Analysis of hydraulic breakdown and seepage of tail sealing system in shield tunnel machines

The use of shield method in tunnel construction is limited by the engineering conditions of highwater pressure. This is mainly due to the uncertainty of the pressure-bearing capacity of the sealing chambers of the shield tail under different grades and conditions when subjected to different external water pressures. Therefore, it is crucial to determine the pressure-bearing capacity of the sealing chambers. However, there is a lack of studies on the calculating method of the pressure-bearing capacity, which requires more theoretical investigation. To explore the common patterns of multi-grade sealing-related parameters and quantify the pressure-bearing capacity of the sealing chambers, a breakdown and leakage model of the shield tail is proposed, targeting the basic sealing unit of the system. Based on non-Newtonian fluid dynamics and fractal theory of porous media, the model is used to calculate the breakdown pressure and grease seepage rate corresponding to tunneling and shutdown states. In addition, a hydraulic breakdown device of the sealing unit of the static shield tail is built to investigate the relationship between the shield tail clearance and the shield tail brush porous media area, which helps to verify the theoretical model. Finally, the analysis of sealing chamber geometry parameters, grease rheological parameters, and an environmental parameter using the proposed theoretical model shows that the pressure-bearing capacity of the shield tail can be improved by increasing the shield tail clearance and grease yield stress. It also shows that the length of the sealing chamber and the plastic viscosity of the grease do not have a significant effect on the breakdown pressure of the shield tail. The model proposed in this paper will provide ideas for the calculation of the pressure-bearing capacity of multi-grade sealing chambers in the future.

Prediction of Backward Erosion, Pipe Formation and Induced Failure Using a Multi‐Physics SPH Computational Framework

ABSTRACTSeepage‐induced backward erosion is a complex and significant issue in geotechnical engineering that threatens the stability of infrastructure. Numerical prediction of the full development of backward erosion, pipe formation and induced failure remains challenging. For the first time, this study addresses this issue by modifying a recently developed five‐phase smoothed particle hydrodynamics (SPH) erosion framework. Full development of backward erosion was subsequently analysed in a rigid flume test and a field‐scale backward erosion‐induced levee failure test. The seepage and erosion analysis provided results consistent with experimental data, including pore water pressure evolution, pipe length and water flux at the exit, demonstrating the good performance of the proposed numerical approach. Key factors influencing backward erosion, such as anisotropic flow and critical hydraulic gradient, are also investigated through a parametric study conducted with the rigid flume test. The results provide a better understanding of the mechanism of backward erosion, pipe formation and the induced post‐failure process.

Heterogeneous reservoir seepage characterized by geophysical, hydrochemical, and hydrologic methods

Seepage characterization from reservoirs is challenging for various environmental and water resource applications. Nonintrusive geophysical methods can achieve excellent detection results, but they cannot provide a quantitative description of the amount of seepage. Integrating geophysical methods with traditional hydrochemical and hydrologic methods enables simultaneous localization and quantitative analysis of heterogeneous reservoir seepage. Ground and waterborne electrical resistivity tomography are used to scan a reservoir under a typical cutoff wall antiseepage system, and the measurements reveal the northern preferential infiltration area. The hydrochemical results reveal that the seepage bypass of the cutoff wall has led to evident ion concentration variations in groundwater near the dam. Based on the geologic stratum information, the typical cutoff wall antiseepage system is divided into three scenarios for numerical simulation to calculate the seepage. The total seepage of the reservoir over 15 months is approximately 7.15 × 106 m3, which is consistent with traditional water budget methods. However, in the northern part of the reservoir, only 27% of the entire dam contributes 77% of the total seepage. All methods have confirmed that the heterogeneous seepage is caused by the absence of an antiseepage seal in the northern region, which should be a primary focus for future monitoring and operational efforts. With the geophysical results undergoing extensive cross-validation, the results from the preceding methods are comprehensively leveraged, effectively lowering uncertainties and overcoming the limitations of geophysical methods in quantitatively characterizing seepage.

Influence of 3D subsurface flow on slope stability for unsaturated soils

The occurrence of rainfall-induced slope failures has become more frequent due to the effect of climate change. Hence, various studies have been conducted to analyse the effect of rainfall infiltration on slope stability. Physically-based hydrological models have been commonly used with slope stability models such as the infinite slope model to develop slope susceptibility maps. However, a combination of three-dimensional (3D) water balance model with 3D limit equilibrium method (LEM) has not been commonly used. Hence, in this study, a water balance model, GEOtop was used to investigate the influence of subsurface flow in unsaturated soil under extreme rainfall conditions on regional slope stability in 3D directions. The results from the GEOtop model were used as inputs for 3D LEM slope stability analysis performed using the Scoops3D software to obtain the factor of safety (FOS) map for the region. Four slopes within the region were then selected to be modelled in the two-dimensional (2D) seepage and slope stability analyses, SEEP/W and SLOPE/W. Results from the detailed study showed that the pore-water pressures (PWPs) from the 3D water balance analyses were found to be higher than the 2D seepage analyses. Under similar PWP conditions, the FOS from the 2D slope stability analysis was observed to be lower than the 3D analysis for two out of the four slopes. However, the combined 3D water balance and slope stability analyses produced lower FOS compared to the 2D seepage and slope stability analyses due to the higher PWPs in the 3D water balance analyses. Therefore, this study highlights the importance of considering the 3D subsurface flow in unsaturated soil given that it has a significant influence on the FOS of slopes.

Evaluating installation of suction caisson in sand via accounting for soil seepage-deformation coupled process

Suction-assisted installation is one of the special features that distinguishes the suction caisson from other offshore foundations. Suction control during installation can be challenging, as it involves highly coupled processes between seepage flow and seabed soil deformations, including excessive soil deformation and plug formation under strong seepage actions that lead to early termination of the installation, as well as a seepage flow-induced reduction in caisson penetration resistance. However, existing methods for evaluating suction caisson installation are primarily based on pure seepage analysis while disregarding the above-coupled processes. This paper proposes an approach to evaluate suction caisson installation in sand by explicitly accounting for seepage-deformation coupling. For this purpose, pore pressure-deformation coupled finite element analyses are performed to investigate soil failure mechanism and evolving caisson penetration resistance subjected to suction. These analyses result in novel rules for assessing critical suction upon the rapid growth of soil deformation and describing the degradation of caisson penetration resistance. The latter two propositions lead to a new calculation method for determining the required suction for caisson installation. The performance of the calculation method is evaluated against field tests and centrifuge tests to illustrate the usefulness of considering coupled soil deformation-seepage process in designing caisson installation.

Seepage and Stability Analysis of Earth Dams’ Downstream Slopes, Considering Hysteresis in Soil–Water Characteristic Curves under Reservoir Water Level Fluctuations

Fluctuations in reservoir water levels have a significant impact on the seepage and slope stability of earth dams. The varying rate of the water level and soil–water characteristic curve (SWCC) hysteresis are the main factors affecting the seepage and the stability of dam slopes; however, they are not adequately considered in engineering practices. In this study, the SEEP/W module and the SLOPE/W module of Geo-studio were employed to analyze the seepage features and the stability of downstream slopes, taking into account the water level fluctuation rate and the SWCC hysteresis. The results reveal that the pore water pressure of the representative point forms a hysteresis loop when the water level fluctuates, which becomes smaller as the water level variation rate increases. Within the loop, the pore water pressure with a rising water level is greater than the value when the water level is dropping, and the desorption SWCC derives greater pore water pressures than the adsorption SWCC. Similarly, the safety factor (Fs) curves under the condition of water level fluctuations also form a hysteresis loop, which becomes smaller as the variation rate of the water level increases. When the water level fluctuation rate increases to 4 m/d, the two curves are tangent, meaning that the Fs with a rising water level is always greater than the value when the water level is dropping. The desorption SWCC derives a lower Fs value than the adsorption SWCC as the water level draws up, but this initiates no evident difference in the Fs value when the water level draws down. These findings can be used to inform the design and operation of earth dams under fluctuating water levels.

Non-parametric fragility curves for probabilistic risk assessment of rainfall-triggered landslides

Fragility analysis of slopes under rainfall condition express the conditional probabilities of exceeding prescribed slope limit states under a range of rainfall intensities, which is the basic and pivotal procedure in rainfall-triggered landslide risk assessment. Classical fragility analysis methods of slopes always develop fragility curves with the assumption of lognormal distribution. The validation of assuming the shape of fragility curves as lognormal distribution remains a open question in practice. In addition, the existing fragility analysis of slopes under rainfall condition have not dealt with the effect of spatially-variable geo-material parameters. In the present study, a novel fragility analysis methodology is proposed for the construction of non-parametric fragility curves of slopes under rainfall condition, in which the spatially-variable soil properties are taken into account. The non-parametric fragility curves are developed by the calculated slope failure probabilities under various rainfall intensities on the basis of probability density evolution theory, without restricting fragility functions to some assumed distribution models. With the proposed method and a set of probabilistic slope rainfall seepage and stability analyses, non-parametric fragility curves, fragility surface using two rainfall intensity measures and time-dependent fragility curves of a slope subjected to various rainfall scenarios are obtained for rainfall-triggered landslides risk assessment.

A reduced-order model approach for fuzzy fields analysis

Characterization of the response of systems with governing parameters that exhibit both uncertainties and spatial dependencies can become quite challenging. In these cases, the accuracy of conventional probabilistic methods to quantify the uncertainty may be strongly affected by the availability of data. In such a scenario, fuzzy fields become an efficient tool for solving problems that exhibit uncertainty with a spatial component. Nevertheless, the propagation of the uncertainty associated with input parameters characterized as fuzzy fields towards the output response of a model can be quite demanding from a numerical point of view. Therefore, this paper proposes an efficient numerical strategy for forward uncertainty quantification under fuzzy fields. This strategy is geared towards the analysis of steady-state, linear systems. To reduce the numerical cost associated with uncertainty propagation, full system analyses are replaced by a reduced-order model. This reduced-order model projects the equilibrium equations into a small-dimensional space constructed from a single analysis of the system plus sensitivity analysis. The associated basis is enriched to ensure the quality of the approximate response and numerical cost reduction. Case studies of heat transfer and seepage analysis show that with the presented strategy, it is possible to accurately estimate the fuzzy responses with reduced numerical effort.

Probabilistic analysis of seepage and temperature fields in geothermal extraction process based on discrete fracture network (DFN) model

Enhanced geothermal system is currently the most efficient technology of exploiting geothermal energy from high-temperature rock reservior in deep earth. However, due to the uncertainty of geological structural discontinuities, such as natural or artificial fractures, great challenges are encountered in conducting the precise evaluation of heat extraction within enhanced geothermal system. In this paper, a probability analysis is carried out to incorporate the uncertainty of the fracture network into the analysis of the spatial-time evolution on the seepage and temperature fields, based on a discrete fracture network based modeling scheme developed by the authors. The developed finite element model of the fractured reservior exhibits two-phase structure consisting of rock matrix and fractures, which are practically discretized into triangular elements and zero-thickness elements, respectively. The approach demonstrates a favorable comparison with the results obtained from the thereotical and other numerical solution. Monte Carlo simulation technique is then employed to probabilistically analyze the evolution of coupled thermal–hydraulic behavior, which involves 1000 different realizations considering the uncertainty of fracture structure. The results illustrate that the coefficient of variation of the seepage field decreases from 0 to 0.29 at 1 a to 0.06 to 0.15 at 50 a, averaging at 0.07, and the peak coefficient of variation of the temperature field decreases from 0.61 to 0.52, averaging at 0.27. The uncertainty of the temperature field is varying against time and prominent around the proximity to the advancing cold front, upper and lower boundaries, primarily associated with variations in fractures and constraint of boundary conditions. The existence of highly permeable fractures leads to a pronounced heterogeneity in the seepage and temperature fields within enhanced geothermal system. Furthermore, the importance of taking the uncertainty of the fracture structure into account for geothermal reservoir evaluation is highlighted, to enhance the reliability of numerical modeling for geothermal process prediction.

Study on the water retention curve of shredded municipal solid waste considering the compressibility of specimens based on the centrifuge method.

The water retention curve (WRC) of municipal solid waste (MSW) is the important hydraulic parameter for the study of unsaturated seepage analysis in landfills. Due to the compressibility and degradability of the waste, the search for a method to quickly and accurately test its water retention curve (WRC) is a current problem that needs to be solved. In this paper, considering the volume change of the waste specimens in test, the test principle of centrifuge testing of WRC is corrected to make it applicable to the testing of waste WRC. In addition, the WRCs of 20 MSW specimens with typical landfill compositions and porosities are measured using the corrected centrifuge test. The effects of compositions and porosities of waste specimens on WRC parameters were analyzed. The results are summarized as follows. Disregarding the height reduction of specimens resulted in overestimated matric suction values and underestimating volume water content values. By comparing uncorrected and corrected values, the maximum difference of the matric suction and volumetric water content reach 233kPa and 11%, respectively. This study can provide a reference for accurately measuring the WRC of MSW using a centrifuge. For the waste specimen without kitchen and yard waste, composition had less of an effect on the WRC of waste compared to porosity. The effect of the content of the non-absorbable fraction on the residual volumetric water content θr and the parameter nv in the van Genuchten model was significant. The initial porosity n had a great effect on the parameter α.

Experimental and Seepage Analysis of Gabion Retaining Wall Structure for Preventing Overtopping in Reservoir Dams

Recently, heavy rains caused by climate change have resulted in dam failures due to overtopping. This study presents a design method aiming to prevent overtopping failures by applying gabion retaining walls at the dam crest. Simulations, experiments, and measurements were conducted to evaluate the effectiveness of this design. The design framework aims to establish a system in which gabion retaining walls prevent overtopping when water levels exceed the crest of the dam, efficiently draining seepage water into the dam body through vertical filters. Research findings indicate that implementing dam crest core and geomembrane design effectively prevents seepage and saturation of the downstream slope during overtopping events. Notably, the reservoir dam operates in a stable manner, as seepage water passing through the dam body is directed solely to the toe drain. Overall, this design approach suggests its potential as a practical solution by significantly reducing hazards resulting from heavy rainfall.

Inversion of the Permeability Coefficient of a High Core Wall Dam Based on a BP Neural Network and the Marine Predator Algorithm

The parameters’ inversion of saturated–unsaturated is important in ensuring the safety of earth dams; many scholars have conducted some research regarding the inversion of hydraulic conductivity based on seepage pressure monitoring data. The van Genuchten model is widely used in saturated–unsaturated seepage analysis, which considers the permeability connected to the water content of the soil and the soil’s shape parameters. A BP neural artificial network is a mature prediction technique based on enough data, and the marine predator algorithm is a new nature-inspired metaheuristic inspired by the movement of animals in the ocean. The BP neural artificial network and marine predator algorithm are applied in the permeability coefficient inversion of a core-rock dam in China; the results show that in the normal operation status, the BP network shows better accuracy, and the average of the absolute error and variance of the absolute error are both minimum values, which are 2.21 m and 1.43 m, respectively. While the water storage speed changes, the marine predator algorithm shows better accuracy; the objective function is calculated to be 0.253. So, the marine predator algorithm is able to accurately reverse the desired results in some situations. According to the actual condition, employing suitable methods for the inverse permeability coefficient of a dam can effectively ensure the safe operation of dams.

Simple method to determine coefficient of permeability of unsaturated soil

This study introduces a novel transient method for determining the unsaturated coefficient of soil permeability, requiring the measurement of volumetric water content and corresponding pore-water pressures at three distinct points. This distinctive advantage of the method lies in eliminating the need to measure or control the flux at any point within the soil profile. The proposed method was validated through numerical simulations that performed one-dimensional seepage analysis, followed by a comparison of the calculated unsaturated coefficients of permeability with the input data. The strong agreement between the compared results validates the feasibility of the proposed method for determining the unsaturated coefficient of soil permeability. Moreover, a spatial interval of less than 5 cm is recommended to ensure accurate results for the unsaturated coefficient of permeability when employing this method.

Thermodynamic Analysis of Coupled Seepage and Thermal Conduction Effects in Earth-Rock Dams

Thermodynamic Analysis of Coupled Seepage and Thermal Conduction Effects in Earth-Rock Dams

Seepage handling using secant pile as a solution to replace curtain grouting and dam stability evaluation to optimize work on the Margatiga Dam construction project

Based on the results of a soil investigation using the bore log method carried out by the Consultant, it was found that the foundations of the spillway building and intake building are in a geological condition that is composed predominantly of sand and porous deposits or easily absorbs water, as well as rocks with the characteristics of fine tuff rock, indicating that the foundation The building is prone to seepage. The seepage treatment contained in the contract is the curtain grouting method 20 meters deep with a distance of 2 meters between points. It is necessary to carry out trial grouting in 3 location zones to be sure. Therefore, it is necessary to analyze the secant pile design. In the work on filling the dam body on the left and right sides, a review needs to be carried out to optimize the implementation of the work because it has a safety factor that is too high than the required safety factor. Secant pile design planning and cross-section evaluation calculations use software to help calculate seepage and stability analysis. Based on the results of modeling analysis calculations and evaluation of cost and implementation time calculations that meet the criteria, it is recommended to handle seepage using secant piles, namely with dimensions of 80 cm, overlap of 15 cm and a depth of up to -10 elevation and recommendations for the cross-section of the dam body, namely by modifying the slope of the section.