Drain Spacing Research Articles

Exploring energy efficiency and savings potential of a horizontal domestic drain water heat recovery system in high-rise apartment buildings

In residential buildings, domestic hot water (DHW) used for showering and handwashing produces significant amounts of hot drain water (DW), which is typically wasted. This study proposes a horizontal drain water heat recovery (DDWHR) unit to capture waste heat from DW and improve overall DHW system efficiency with the focus on thermal exchange in a compact installation suitable for high-rise apartment buildings. Experiments under different operating conditions were conducted to evaluate the DDWHR unit’s thermal performance and energy-saving potential. Results showed that the proposed DDWHR unit achieved energy efficiency of 90–95%, depending on operating conditions, due to high heat recovery rates. In the entire DHW system, the DDWHR unit demonstrated approximately 15% heating energy savings compared to conventional DHW setups. Also, nationwide adoption of the DDWHR unit in two-person apartments could reduce gas costs by about 14% annually. The findings of this study indicate that the horizontal DDWHR unit can effectively promote sustainable DHW use in high-rise residential buildings and offers a promising solution for improving energy efficiency in DHW systems.

A Novel Analytical Solution for Slurry Consolidation Induced by a Vacuum-Assisted Prefabricated Horizontal Drain

A Novel Analytical Solution for Slurry Consolidation Induced by a Vacuum-Assisted Prefabricated Horizontal Drain

Compressional rheology model for vacuum filtration-consolidation of sludge in geotextile tubes

Recently, the disposal of high-water-content dredged sludge through geotextile tubes with vacuum-assisted prefabricated horizontal drains (PHD) has gained growing popularity for its convenience and efficiency. However, existing simulations for this typical coupled filtration-consolidation process using conventional consolidation models exhibit deficiencies due to the absence of effective stress and invalidity of Darcy’s law in the particle-wandering filtration phase. In this study, based on the compressional rheology theory, a two-dimensional coupled filtration-consolidation model constituted by the compressive yield stress Py(ϕ) and hindered setting factor r(ϕ) is developed to elucidate the solid-solid and solid-fluid interactions during slurry dewatering. A novel approach for measuring consistent Py(ϕ) and r(ϕ) relationships is proposed. The numerical solution is derived utilizing the alternating direction implicit (ADI) difference method and verified against a classical one-dimensional compressional rheology model and a field trial. Further analysis suggests that constitutive parameters, e.g., gel point, affect the dewatering efficiency by determining the relative degree of soil disorder, obstruction to particle movement, and vacuum transmission effect, while design parameters, e.g., PHD spacing and tube height, impact the magnitude and radiation range of vacuum pressure to influence the overall efficiency.

About Filtration in a Geophysical Bridge with a Seepage Site

Based on the representation of a modular elliptic function in the form of a combination of simple algebraic formulas that conformally map the area of the velocity hodograph (curved triangle) onto a half-plane, a direct definition of filtration rates in a geophysical bridge is given. For the first time, a family of isotope lines of equal filtration rates was constructed for the inner area of the bridge in the absence of water in the downstream. For special cases, the values of the proposed formulas almost completely coincide with the hydromechanical solution of Masket M. (for 4 cases) and the numerical calculations of Khairullin Z.E. (for 2 cases). The well-known Nelson-Skornyakov F.B. formula for the output filtration rates through the lower face of the jumper, adopted by analogy with the flow outlet from the base of the flatbed into the horizontal drainage, gives an underestimation of the results by up to 45%, and therefore cannot be recommended for practical use.

Impact of Subsurface Drainage System Design on Nitrate Loss and Crop Production

Subsurface (or tile) drainage offers a valuable solution for enhancing crop productivity in poorly drained soils. However, this practice is also associated with significant nutrient leaching, which can contribute to water quality problems at the regional scale. This research presents the findings from a 4-year tile depth and spacing study in central Illinois that included three drain spacings (12.2, 18.3, and 24.4 m) and two drain depths (0.8 and 1.1 m) implemented in six plots under the corn and soybean rotation system (plots CS-1 and CS-3: 12.2 m spacing and 1.1 m depth, plots CS-2 and CS-4: 24.4 m spacing and 1.1 m depth, and plots CS-5 and CS-6 18.3 m spacing and 0.8 m depth). Our observations indicate that drain flow and NO3-N losses were higher in plots with narrower drain spacings, while plots with wider drain spacing showed reduced drain flow and NO3-N losses. Specifically, plots set up with drain spacings of 18.3 m and 24.4 m showed significant reductions in drain flow compared to plots featuring a 12.2 m drain spacing. Likewise, plots characterized by 18.3 m and 24.4 m drain spacings (except CS-4) showed better NO3-N retention and lower leaching losses than those with 12.2 m spacing (CS-1 and CS-3). Crop yield results over a 3-year period indicated that CS-2 (wider spacing plot) showed the highest productivity, with up to 13.6% higher yield compared to other plots. Furthermore, when comparing plots with the same drainage designs, CS-2 and CS-4 showed 5.1% to 2.6% higher corn yield (3-year average) compared to CS-1 and CS-3, and CS-5 and CS-6, respectively. Overall, a wider drainage system showed the capacity to export lower nutrient levels while concurrently enhancing productivity. These findings represent that optimizing tile drainage systems can effectively reduce nitrate losses while increasing crop productivity.

Field Study of a Sustainable Land Reclamation Approach Using Dredged Marine Sediment Improved by Horizontal Drains under Vacuum Preloading

Field Study of a Sustainable Land Reclamation Approach Using Dredged Marine Sediment Improved by Horizontal Drains under Vacuum Preloading

Drainage estimation across mountainous regions from large-scale soil moisture observations

Drainage is a crucial soil hydrological process that governs the partitioning of rainfall into runoff, groundwater recharge, soil water storage and evapotranspiration. Despite its significance, the drainage process is poorly understood due to the difficulty in direct measurements and insufficient understanding of its underlying physical mechanisms. To address these challenges, we present an innovative, physically-based, data-driven approach, SM2D (Soil Moisture to Drainage), to estimate drainage. SM2D was applied and examined using soil moisture data from a large-scale observation network over mountainous areas during 2014–2020. The soil moisture threshold governing drainage initiation proves to be significantly lower than the commonly employed field capacity metric in hydrological models. This threshold is influenced by factors such as mean soil moisture, bulk density, residual soil moisture, soil organic carbon, and parameters n and α of soil retention curve. Notably, field capacity has minimal impact on this threshold. Additionally, our analysis reveals that the drainage process is more influenced by the Soil Water Storage Increment (SWSI) than by mean soil moisture (MSM) that has traditionally been recognized as a key factor in drainage control. In comparison to commonly used exponential equations and those in models such as the Soil & Water Assessment Tool (SWAT), SM2D demonstrates superior performance in estimating drainage. The exponential equation derived from the SWSI outperforms those derived from other soil moisture metrics, including the commonly utilized MSM, challenging prevailing norms in drainage equations. SM2D holds the potential to generate extensive drainage datasets from satellite or large-scale soil moisture observations, advancing large-scale hydrological studies.

Determining Groundwater Table in Slopes with Horizontal Drains and Design Framework for Length and Spacing

ABSTRACT Horizontal drains (HDs) are commonly implemented in slope stabilization to reduce the pore water pressure (PWP); however, they also cause complex three-dimensional (3D) variations in the groundwater table (GWT), which require intricate 3D flow models. To address this challenge, we propose a novel semi-empirical method based on a series of numerical simulations validated through numerical and field studies to determine the GWT of a slope with HDs. Subsequently, the proposed method was extended to calculate the average PWP (U) acting on a predefined slip surface via linear integration. The decrease of U (ΔU) resulting from HDs can be used to evaluate the performance of HDs. To create design charts that consider the impact of length and spacing of HDs on ΔU for a specific slope, we developed a Python-based computer program. Two case studies were conducted, which showed that ΔU increases with longer HDs and shorter spacing. The results also indicated that extending the HDs beyond a particular length does not significantly affect ΔU; it is highly sensitive to the spacing in short HDs and not sensitive in long HDs. Furthermore, we found that the total length of HDs required to achieve a target ΔU is less in wide spacings than in short spacings. In conclusion, long HDs with wide spacings are more effective and economical. Owing to the unique nature of each slope stability problem, this study offers a practical tool for analyzing the effectiveness of HDs instead of providing a general guide.

A Novel Approach to Detecting Blockages in Sewers and Drains: The Reflected Wave Technique

Blockages in sewers and drains often result in overflows and flooding that cause significant environmental pollution and public health risks, particularly in hospitals, where the consequences can be catastrophic. Due to their low “visibility”, sewers and drains are inherently difficult to monitor and maintain, resulting in a reactive management approach whereby maintenance or repair is carried out only after a system failure has occurred. This paper investigates the feasibility of applying the reflected wave technique, a unique sonar-like monitoring approach capable of identifying changes in the geometry of closed-pipe conduits, as a means of proactive system monitoring. The technique uses a 10 Hz sinusoidal air pressure wave which is transmitted into the drainpipe. When the pressure wave encounters a system boundary, a reflection is generated which alters the measured test pressure response. Analysis of the reflections generated by a changed system boundary, such as the formation of a blockage, can provide information related to the location of that boundary within the system. An experimental setup was developed to simulate a horizontal drain using standard pipework of 100 mm diameter and 70 m length. The technique was able to detect applied blockages with cross-sectional coverage of 30% and 75%, and lengths ranging from 30 mm to 3000 mm. Accuracy was improved when the pressure sensor was positioned closer to the blockage. When the sensor was 3.4 m from the blockage, location estimates were very accurate (−2% to 3% error). At a 14 m distance from the blockage, the error increased to between 4% and 33%. The accuracy of blockage detection and location improved with increasing blockage cross-sectional area and length. Overall, the reflected wave technique could provide a potentially continuous monitoring solution for blockage detection in sewers and drains.

Effect of Tile Drain Spacing on Nitrate Losses, Heavy Clay Soil Properties and Wheat Crop Productivity in Egypt

Effect of Tile Drain Spacing on Nitrate Losses, Heavy Clay Soil Properties and Wheat Crop Productivity in Egypt

Fully coupled finite strain consolidation analysis for soft clay treated by prefabricated horizontal drain with vacuum and heat preloading

This paper established a one-dimensional fully coupled finite strain consolidation analysis for soft clay treated by thermal prefabricated horizontal drain under vacuum and heat preloading with the consideration of thermal elastic viscoplastic (TEVP) behaviors of soft clay. Firstly, the governing equations for finite strain consolidation, heat conduction, and heat convention process have been carefully derived based on the well-established Gibson’s large strain consolidation theory and TEVP constitutive model. Secondly, the accuracy and reliability of the numerical method have been verified with benchmark cases and three physical model tests. Then, improvement of consolidation efficiency rate (IER) was defined and used to study the effect of three variables on consolidation efficiency. Last but not least, a graphical user interface (GUI) was provided to support researchers and engineers in utilizing the proposed numerical method for conducting consolidation analysis of soft soil treated in the same or similar fashion.

Classical solvability to the free boundary problem for a foam drainage equation. II. From the interface to the bottom

We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. in 1988 in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region below an interface to the bottom in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle. Moreover, the existence of its steady solution and its stability are shown.

Classical solvability to the free boundary problem for a foam drainage equation. I. From the top to the interface

We study a nonlinear partial differential equation describing the evolution of a foam drainage in one dimensional case which was proposed by Goldfarb et al. [Izv. Akad. Nauk SSSR Mekh. Ghidk. Gaza 2, 103–108 (1988)] in order to investigate the flow of liquid through channels (Plateau borders) and nodes (intersections of four channels) between the bubbles, driven by gravity and capillarity. Its mathematical studies so far are mainly restricted within numerical and particular solutions; as for mathematical analysis of it there are only a few. We prove that the free boundary problem for the foam drainage equation in the region from the top to the interface in a foam column admits a unique global-in-time classical solution by the standard classical mathematical method, the maximum principle and the comparison theorem. Moreover, the existence of its steady solution and its stability are discussed.

New exact solutions of the conformable space-time two-mode foam drainage equation by two effective methods

In this article, the two-mode foam drainage equation in terms of time and space conformable sense has been investigated. Two effective methods, the generalized exponential rational function method (GERFM) and the improved version of the Bernoulli sub-equation function method (IBSEFM), are used to get new solutions of underlying equation. The fractional travelling wave transformation is applied to convert nonlinear partial differential equations to nonlinear ordinary differential equations. Proposed methods successfully extract trigonometric, hyperbolic and exponential solutions. Some of the obtained solutions are visualized to understand the effect of fractional orders of time and space derivatives on the wave profile and the dynamic behavior of the solutions.

Two-Dimensional Hydrodynamic Simulation of the Effect of Stormwater Inlet Blockage on Urban Waterlogging

The drainage capacity of stormwater inlets, which serve as the connection between the surface and the underground drainage system, directly affects surface runoff and the drainage capacity of underground drainage systems. However, in reality, stormwater inlets are often blocked due to the accumulation of leaves, human waste disposal and other factors, resulting in a greatly reduced drainage capacity of the drainage network and, in turn, urban waterlogging disasters. In view of the problem of stormwater inlet blockage, employing a typical waterlogging point in the Lianjiang Middle Road area of Fuzhou city as the research object, the stormwater inlet equivalent drainage method was adopted in this paper to characterize the drainage capacity of the pipe network and enable the control of the stormwater inlet blockage state. Coupled with the stormwater inlet drainage equation, an improved ITF-FLOOD two-dimensional hydrodynamic model was constructed, and the influence of stormwater inlet blockage on urban waterlogging under different rainfall return periods was simulated and analyzed. With increasing rainfall return period, the influences of stormwater inlet blockage on both the maximum area and the depth of accumulated water in the study area gradually decreased compared with those of a nonblocked stormwater inlet, and the growth proportions decreased from 43.35% and 34.58% under the 1-year rainfall scenario to 3.34% and 9.76% under the 50-year rainfall scenario, respectively. However, in terms of the change in the accumulated water level, stormwater inlet blockage will cause an increase, and the influence will always be significant. Overall, stormwater inlet blockage aggravated the waterlogging risk and the extent of waterlogging. Therefore, the results provided a reference for the construction of an urban waterlogging model and have certain guiding significance for waterlogging prevention and control in the study area prone to stormwater inlet blockage.

Evaluating the effect of different diaphragm wall cracking scenarios on seepage and slope stability in Earth dams using experimental and numerical modeling approaches

BackgroundSeepage control measures are essential in earth dams to enhance their safety against seepage and slope failures. A diaphragm is a thin impervious wall that is used in the core area of the dam to prevent the seepage of water. Any crack in the diaphragm can reduce its efficiency and threaten the safety and stability of the dam. Extensive evaluation of the influence of diaphragm fracturing on dam safety is required to establish a safe design and offer the appropriate measures. This study investigates the effect of diaphragm cracking on the safety of the dam for seepage and slope stability. A permeability tank is first used to validate the numerical model; then, different scenarios for cracked diaphragm walls are studied numerically. The crack’s height, width, direction, and number are all investigated. The effect of having a downstream horizontal blanket drain with cracked internal diaphragms is also evaluated.ResultsThe results showed that the internal diaphragm enhances the safety of earth dams as it reduced the seepage discharge by 98% and increased the downstream slope safety by 34%. Considering the development of a crack in the internal diaphragm, the most critical location was at the base of the dam, wider cracks were more destructive, and the most critical direction was the horizontal crack. The fracturing of the diaphragm at multiple locations proved to be detrimental to the safety of the dam. Having three cracks caused the seepage discharge to reach 74% of its value for no diaphragm, the pore water pressure to raise drastically, and the downstream critical factor of safety to be higher than the case of no diaphragm by 8% only.ConclusionsAccording to the findings, it is advised to continuously monitor the components of diaphragm-type earth dams and perform the necessary maintenance works whenever any sign of damage or water seepage appears. Furthermore, using a well-graded horizontal drain of sufficient length and high permeability with the internal diaphragm is highly recommended as a mitigation measure if diaphragm fracturing occurs. This helps to quickly release the seeping water and keep the phreatic line away from the downstream slope.Graphical abstract

Experimental and numerical modeling on vacuum consolidation behavior of staged-filled soil slurry with prefabricated horizontal drain and flocculant

The vacuum-assisted prefabricated horizontal drain offers a promising method for strengthening soil slurry, allowing simultaneous filling and vacuum-dewatering via staged construction. However, there is limited research on the unique characteristics of staged filling. This study aims to investigate the vacuum consolidation process of staged-filled soil slurry through laboratory model tests and numerical simulations, also assessing the impact of anionic polyacrylamide. Comparative analyses are conducted between vacuum consolidation with and without anionic polyacrylamide, as well as self-weight consolidation without anionic polyacrylamide. Results reveal contour lines of excess pore pressure, water content, and soil strength forming an ellipse around the prefabricated horizontal drain board. During the consolidation process, a higher degree of consolidation, lower water content, and higher soil strength were observed closer to the prefabricated horizontal drain board. After treatment, the uppermost filling layer exhibits an average water content that was approximately 40% higher than the lower filling layer, and its average strength was about 60% lower. This discrepancy is primarily due to the absence of sealing on the top surface and the relatively short vacuum consolidation time caused by staged filling. The introduction of anionic polyacrylamide-induced flocculation significantly improves the initial consolidation rate but minimally affects the dewatering capacity of vacuum preloading. Using flocculant can enhance both the staged filling rate and soil strength (by 1–2 times). Additionally, employing a staggered arrangement between different prefabricated horizontal drain layers is advisable to prevent top-down penetration in areas with low soil strength.

Study of design parameters for staged-filled slurry treated by prefabricated horizontal drains under vacuum preloading

The method of using Prefabricated Horizontal Drains (PHDs) placed in layers under vacuum preloading can significantly speed up consolidation of staged-filled soil slurry. The PHDs can settle with the soil slurry and maintain their shape/pattern and dewatering capacity largely in comparison with Prefabricated Vertical Drains (PVDs). This study presents a field trial focused on treating dredged sediments using PHDs under vacuum preloading for land reclamation purposes. The staged filling involved in the field trial is analyzed using a finite strain consolidation model based on the piecewise-linear finite-difference method. Then, the effects of horizontal and vertical spacings of PHDs on settlement and vacuum consolidation rate are evaluated, considering various combinations of variables for staged-filled soil. It is found that for soils with low compressibility, the consolidation rate is primarily affected by the vertical spacing of PHD layers. For soils with higher compressibility, the consolidation rate is more significantly affected by the horizontal spacing of PHDs, and the final settlement after vacuum preloading is mainly influenced by the vertical spacing of PHD layers. This study provides practical recommendations for cost-effective design of horizontal and vertical spacings of PHDs in efficiently treating soil slurry with different compressibility and initial conditions.

Experimental Study on the Hydraulic Performance of the Horizontal Main Drain of Building Drainage Systems Affected by Surfactants Sodium Dodecyl Benzene Sulfonate and Alkyl Ethoxylate-9

Experimental Study on the Hydraulic Performance of the Horizontal Main Drain of Building Drainage Systems Affected by Surfactants Sodium Dodecyl Benzene Sulfonate and Alkyl Ethoxylate-9

Experimental study on dewatering and reinforcement of dredged slurry treated by PHDs-PVDs under step vacuum preloading

Nowadays, the utilization of prefabricated vertical drains (PVDs) or prefabricated horizontal drains (PHDs) in combination with vacuum preloading (VP) has emerged as a prevalent and effective strategy for treating dredged slurry. Nevertheless, both of these methods possess certain inherent limitations. In this study, three groups of parallel model experiments are conducted to compare the effectiveness of PVDs, PHDs and PHDs-PVDs under step VP in treating dredged slurry. Firstly, the water discharge, settlement and pore water pressure are monitored during the experiments. Then, the shear strength and water content of the soil at various locations after experiments are measured and the soil profiles at different cross sections are gauged. Additionally, soil excavation is conducted to evaluate the deformation characteristics of PHDs and PVDs. Finally, a scanning electron microscopy analysis is to assess the clogging of filter membranes. The results indicate that the proposed method can combine the advantages of both PHDs and PVDs, effectively enhancing the treatment effectiveness of the slurry. These findings elucidate the dewatering and reinforcement mechanism of PHDs-PVDs-VP and provide valuable insights for its practical engineering application.