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Article

The Influence of Internal Erosion in Earthen Dams on the Potential Difference Response to Applied Voltage

by
Mingjie Zhao
1,
Pan Liu
1,
Li Jiang
1 and
Kui Wang
2,*
1
Key Laboratory of Hydraulic and Waterway Engineering of the Ministry of Education, Chongqing Jiaotong University, Chongqing 400074, China
2
Engineering Research Center of Diagnosis Technology and Instruments of Hydro-Construction, Chongqing Jiaotong University, Chongqing 400074, China
*
Author to whom correspondence should be addressed.
Water 2021, 13(23), 3387; https://doi.org/10.3390/w13233387
Submission received: 30 September 2021 / Revised: 23 November 2021 / Accepted: 26 November 2021 / Published: 1 December 2021
(This article belongs to the Special Issue Local Erosion of Hydraulic Structures and Flood Protection)
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Abstract

:
Internal erosion is widely perceived as contributing to the failure of earthen dams. To reduce the failure risk, timely monitoring of internal erosion is an effective method in observing their internal structure evolution. A set of earthen dam model experiments were conducted. Under an applied voltage, the response potential differences (PD) at the slope of the dam models were collected before and after the impoundment of the upstream reservoir. The discrepancy among the four dam models, the influence of soil moisture content on PD, and the impact of internal erosion on PD were studied. The results show that it is acceptable to employ different dam models to simulate the development of internal erosion, although the discrepancy among the models is inevitable. The moisture content of the soil significantly affects the PD response to applied voltage. The PD increases with an increase in soil moisture content until the soil is saturated. The change in PD is correlated with the development of internal erosion. With the progression of internal erosion, the starting position for the steep increase in PD distribution continues to move toward the dam toe. In addition, the electrode stability is noted to have an effect on measured PD, which requires further studies to be clarified. This study sets the stage for the PD-based monitoring method in observing the evolution of internal erosion in earthen dams.

1. Introduction

Earthen dams are widely constructed around the world to meet the demand of irrigation, hydroelectric generation, and flood control [1]. Due to low design standards [2], poor construction quality [3], and invasive wildlife activities [4], the various anomalous zones (including cracks, holes, and uncompacted zones) are generally inevitable in earthen dams [5,6,7]. Under seepage, these anomalous zones evolve into the high-permeability zones, which can easily trigger the hydraulic removal of soil particles, namely the initiation of internal erosion. As more particles are removed, the hydraulic gradient increases and the erosion continues toward the water source. This case allows for the formation of a larger void (i.e., pipe) and thus leads to a continuously increased flow. Eventually, the dam failures occur due to the collapse of the soil over the pipe. This process is also known as backward erosion, as described by Richards and Reddy [8].
According to statistics from Foster et al. [9], internal erosion is one of the main dam failure modes because it is responsible for approximately half of all dam failures and incidents. In particular, internal erosion is always linked to the leakage and failure of small earthen dams, which is due to a lack of filters and maintenance [10]. This indicates that internal erosion poses a serious threat to the stability and safety of earthen dams. Therefore, timely detection and monitoring of internal erosion are vital to understanding the structural evolution of earthen dams and to reduce the failure risk.
The investigations of internal erosion are generally limited by its hidden nature. Some traditional methods such as the use of various sensors are obviously not applicable. This is not only because of the limited detection range of the sensors and the time-consuming data process but also because it is difficult to install the sensors in the built dams [11]. On the contrary, geophysical methods are widely considered acceptable for detecting the erosion zones on account of their effectiveness, non-invasiveness, and non-destructiveness. The commonly used geophysical methods mainly involve seismic methods, ground-penetrating radar (GPR), the self-potential (SP) method, and electrical resistivity tomography (ERT). Many investigations have employed these methods to locate and characterize the anomalous zones and the preferential seepage paths [12,13,14,15,16]. Furthermore, the comprehensive method, integrated with two or more methods, was also developed in some in situ tests [17,18,19,20]. These investigations are capable of providing significant quantitative information for the engineering interventions in earthen dams, however, they are passive; that is, most of them are conducted after the formation of the anomalous zones or internal erosion.
Some active monitoring studies on time-lapse measurements for internal erosion in earthen dams (repeated measurements) have been reported in recent years. Among these studies, time-lapse ERT has received the most attention [21,22,23,24]. For example, Masi et al. [21] applied the time-lapse ERT to monitor the internal erosion induced by seepage flow, and pointed out that erosion evolution in dams and levees can be characterized and quantified by the time-lapse ERT. Similar conclusions have been drawn by Shin et al. [22] through a sandbox experiment, where the internal erosion in the earthen dam model can be effectively visualized by the time-lapse ERT. In addition to ERT, other monitoring parameters (e.g., self-potential and ambient seismic noise) have also been used for time-lapse measurements in similar studies [25,26,27,28,29]. Boleve et al. [25] and Ikard et al. [26] developed a method based on salt injection and time-lapse self-potential measurements to detect the preferential seepage pathways in porous media, which has great potential in detecting the seepage zones associated with internal erosion. Planes et al. [27] used ambient seismic noise to monitor the temporal changes in the earthen embankments during internal erosion, and it was found that the progress of internal erosion can be reflected by the reductions in surface wave velocity.
Since the above-mentioned studies are based on the changes in measurement results over time, the evolution information about internal erosion in the earthen dams can be captured. Nevertheless, due to the complexity of both internal erosion and field testing conditions, most existing time-lapse measurements still remain in experiment-scale research. Therefore, it is of crucial significance to build up a method for characterizing the evolution of earthen dam internal erosion.
This study aims to explore the influence of internal erosion in earthen dams on the potential difference (PD) response to applied voltage. For this reason, a set of experiments with four earthen dam models are conducted. In the experiment, the gravel-filled geotextile tubes at different length are buried in the models to simulate the internal erosion at four different stages. With the applied voltage, the response PDs at the downstream slope of the models are measured before and after the impoundment of the upstream reservoir. Based on the experiment results, we study the discrepancy among the four dam models and the influence of soil moisture content on PD, and mainly discuss the relation between the change in PD and the development of internal erosion.

2. Materials and Methods

2.1. Experimental Setup

In order to measure the response PD of earthen dams to voltage excitation under seepage, four identical flumes are constructed. The schematic of a flume is illustrated in Figure 1. The inner dimensions of the flumes are 3.65 m (length) × 1 m (width) × 1 m (depth). Each flume consists of four clay-brick walls and a concrete floor, by which the flumes are able to withstand the compaction and stresses from the dam model. A tap is installed at the top of the upstream-side wall to provide the water source for the tests by connecting to the municipal water supply. A 2-cm-diameter hole is drilled in the lengthwise wall to drain the excess water from the upstream reservoir during the experiment. Since the hole aims to maintain a constant upstream water level, its height from the floor is specially designed to be 0.72 m (90% of the dam model height). An identical hole is also made at the bottom of the downstream-side wall for the purpose of draining the water seeping through the dam model. Both the two above-mentioned holes are connected to the polyvinyl chloride (PVC) pipe. The surface of the flumes is successively covered with the cement mortar and the waterproof material to prevent water penetration. In addition, the experiment is conducted one week after the construction of the flumes when the concrete has reached sufficient strength.
Four physical models of homogeneous earthen dams are constructed in layers in the flumes. For convenience, they are designated as DM 1, DM 2, DM 3, and DM 4, respectively. In the construction, the soil required for each layer is roughly calculated in amount and then poured into the flumes. Each layer is compacted with a wooden mallet to a thickness of 0.2 m. Three soil samples are taken from each compacted layer to determine the dry density, which is used to evaluate the compaction degree of the layer comprehensively. To avoid the separation of two successive layers, the surface of the completed layer is scarified prior to the construction of the latter one. The excess part from compacted soil is trimmed to obtain the desired dam geometry. The completed dam models are 0.8 m in height, 0.16 m in crest width and 1 m in length, with the upstream and downstream slope ratio of 1:2 and 1:1.8, respectively, as shown in Figure 1. A typical small-sized earthen dam with a height of 20 m and a crest width of 4 m is modeled with a scale of 1:25 in this study.
To simulate the different stages of internal erosion, a 4 cm-diameter geotextile tube filled by uniform gravel is embedded in DM 2, DM 3, and DM 4, with its central axis passing through the central cross-section of the dam model, as show in Figure 2. The three tubes are curved in the same extent, with their curvature increasing from the downstream end to the upstream end. The lengths of the tubes in DM 2, DM 3, and DM 4 are 50 cm, 90 cm, and 180 cm, respectively, which is the only difference among the three tubes. As a result, the tubes in DM 2 and DM 3 only extend to lower layers from the place near the dam toe (see Figure 2a,b), while that in DM 4 crosses through the dam (see Figure 2c).
For constructability, a plane coordinate system is induced in each flume, with its origin located at the midpoint of the dam toe line, horizontal axis (x-axis) pointing horizontally upstream, and vertical axis (y-axis) pointing upward. A series of reference points are employed to control the position of the tubes, as marked by the red dots in Figure 2. These reference points are distributed along the tube and located at the lowest point of each cross-section. Table 1 lists their values of x and y coordinates. More details on burying the tubes are as follows. After the first layer of the dam model is completed, a ditch is dug on its surface using a trowel (see Figure 3). The ditch is about 5 cm wide (slightly wider than the tube) and slants to the downstream. The position and depth of the ditch are determined by the reference points. The tube is then placed in the ditch. Finally, the soil dug out is backfilled and re-compacted. It should be pointed out that the above-mentioned steps are required to be repeated twice when DM 4 is constructed to the second and third layers. During the process, the unburied part of the tube is temporarily slung with a piece of string (see Figure 3c).
The data acquisition system consists of a 60-channel DUK-4 measuring instrument, the copper electrodes, and a power supply, which is developed by CGE (Chongqing) Geological Instrument Co., Ltd., Chongqing, China. The measuring instrument is integrated with a DC electrical meter and a control PC. The power supply is the high-performance lithium battery so as to allow the system to work continuously over 10 h, with the ability to provide an output voltage of 50 VDC, 100 VDC, and 200 VDC, respectively. In addition, the electrodes and the power supply are all connected to the measuring instrument via the cables. Using the system to transmit current and receive, the PD data from the downstream slope of the dam models are collected.

2.2. Soil Materials

Due to low construction standard in the last century, problematic materials were widely used to construct the earthen dams in China. These materials were soil formed by mudstone, sandstone, or mudstone–sandstone mixture, and were internally unstable in essence. To keep its typicality, the soil in this experiment is originally collected from a strongly-weathered mudstone formation in Chongqing, China, with a natural moisture content of 2.57%. The particles with a diameter of 0–40 mm are then selected as the dam materials (see Figure 4a). The particle size distribution of the soil is obtained based on sieving method, as is presented in Figure 4b. The detailed particle size groups with the contents are as follows: 0–0.075 mm (6.7%); 0.075–0.25 mm (5.5%); 0.25–0.5 mm (4.9%); 0.5–1 mm (5.1%); 1–2 mm (6.1%); 2–5 mm (18.6%); 5–10 mm (21.3%); 10–20 mm (24.6%); 20–40 mm (7.2%). The geometrical and mechanical properties are summarized in Table 2. Based on X-ray diffraction, the mineral and chemical composition of the soil are summarized in Table 3 and Table 4, respectively. In addition, the optimum moisture content is determined as 10.3% through the proctor compaction test, and the corresponding maximum dry density is 2.12 g/cm3.
In general, both the geometric factors [30,31,32,33,34,35] and the mechanical factors [36,37,38,39,40,41] are recognized to affect the internal erosion of soil. The geometric factors determine the potential for internal instability, while the mechanical factors dictate the onset of internal instability [42,43]. Unlike the mechanical factors, the geometric factors are regarded as the essential preconditions for internal instability, which involve some intrinsic properties of the soil, including the particle size distribution, the gradation, the particle shape, etc. [44]. Based on several typical geometric criteria proposed by Istomina [30,31], Liu [31], and Kenney and Lau [32,33], a series of assessments for the internal stability of the soil used in this experiment are conducted. Results show that the soil is internally unstable, as shown in Table 5, which is considered to provide a soil potential condition for internal erosion simulation.
In order to improve the quality of compaction, the soil is spread out on the ground near the flumes and sprayed with an appropriate amount of water before building the dam models. The soil is sufficiently turned over to make moisture uniformly distributed.

2.3. Test Procedure

Four dam models are tested through the same procedure, which consists of three basic steps. The first step is to set up the data acquisition system. Firstly, three parallel survey lines, named L1, L2, and L3, respectively, are set on the dam model from the crest to the dam toe at an interval of 0.3 m. The line L2 is in the central cross-section of the dam model. Nineteen electrodes are then inserted with spacing of 0.1 m along each survey line. The insertion depth of each electrode is strictly controlled. Finally, the electrodes are connected to the DUK-4 measuring instrument.
The second step is to measure the background potential difference (BPD) of the dam model, i.e., the PD when there is no seepage. Grounding measurements are conducted using the measuring instrument to assess the contact between each inserted electrode and the soil, as well as to examine the stability of the instrument. The lines L1, L2, and L3 are utilized in turn. For some electrodes, a small amount of water is added to the soil to improve the contact conditions [45]. In the end, under the condition of a 50-VDC voltage applied by the power supply, the PD data are collected using the Wenner configuration. In order to capture the surface information of the dam model, the separation factor (n-factor) is set to 1.
The third step is to measure the PD of the dam model during the seepage (see Figure 5). Given that the survey lines L1 and L3 are symmetrical in location, measurement of L3 is canceled to speed up the test process. The step starts with the filling of the upstream reservoir. The water is released into the flume from the tap. During this process, several large plastic buckets holding water are used to help shorten the filling time. Once the level reaches to 0.72 m, grounding measurements are carried out along L1 and L2, with the purpose of eliminating the looseness of the electrodes. Due to the high moisture content of the soil, some electrodes located near the dam toe are unable to stand and, accordingly, are no longer retained. As a result, ten electrodes are left for measurements along L1 and L2. The PD is then measured with the same configuration, separation factor, and voltage as those in step 2. As the water continuously flows in, the level remains constant due to the tap control and the drainage hole. Subsequently, the grounding measurements and the data collection are repeated once an hour. For each time, the PDs are compared with the former measured values. The test is terminated when the data remain almost constant. In addition, it is noted that the voltage loss in this experiment is ignored since the power supply is charged after each measurement.

3. Experimental Results

3.1. BPD of the Dam Models

In this experiment, the midpoint between every two adjacent electrodes is defined as the recording point for PD. Figure 6 plots the BPD collected along the three survey lines from the four dam models, for a total of 12 data sets. It can be observed that the BPD along each survey line shows a stationary trend. For the same dam, the means of BPD along the three survey lines are approximately equal. In addition, DM 1 holds the smallest fluctuation among the four dam models.

3.2. PD of the Dam Models under Seepage

Although the four dam models are similar to each other, the discrepancy among them can lead to errors in results. In this paper, the PD is determined by subtracting the BPD from the directly measured PD with the aim to minimize the impacts of the model variability.
The PDs from each dam model under seepage are plotted in Figure 7. For DMs 1, 2, and 3, the PDs obtained after 2 h are coincident with those obtained after 3 h. That implies that the total time for the formation of steady-state seepage from the beginning of water storage are 2 h for DMs 1, 2, and 3. Likewise, it takes 3 h for DM 4 to form steady-state seepage. It is also noted that the variation trends of PDs are similar when the steady-state seepage is formed: the PD first varies slightly, then increases abruptly, and finally varies mildly again with the increase in the distance to dam crest.
Figure 7 also shows the spatial distribution of the PD at different time moments. At the initial moment, the PDs show a mild fluctuating trend for all dam models with only a slight increment trend near the waist of the downstream slope (about 0.55~0.65 m from the dam crest). The cause of such a phenomenon is that the transient seepage has been generated in the dam model before the first measurement. The data obtained after 1 h show that the point where the PD starts to increase moves towards the dam crest. As the seepage continues, the point where the PD starts to increase moves furtherly towards the dam crest until the formation of steady-state seepage (2 h for DMs 1, 2, and 3 and 3 h for DM 4). After that, the distributions of PDs remain largely the same.

4. Discussion

4.1. Discrepancy of Dam Models

For convenience, the erosion path is commonly designed to be straight in existing experiments to study the hydraulic properties and mechanical properties [11,46,47,48,49]. For example, Hanson et al. [46] and Ali et al. [47] placed the continuous steel pipe through the physical earthen dam model for simulating the internal erosion process, and then pulled the steel pipe out to initiate internal erosion. Although this straight plan is a passable imitation, the curve plan is employed in this experiment to reconstruct the developed zone during the internal erosion process. As reported by some numerical simulation studies [50,51], the curve plan models the development scenarios with the curvature increasing from the downstream toe towards the upstream.
However, it is of significant difficulty to imitate the erosion behavior under the curved developing path in a physical dam model. As a challenge for the experimental setup, pulling out the curved pipe from the model can easily induce a slump of the soil over the pipe. To avoid this, four dam models with geotextile tubes at different length are constructed in this study, with an attempt to reproduce the dam at four stages in the internal erosion process, namely, (a) non-erosion, (b) onset of erosion, (c) progressional erosion, and (d) formation of penetrating pipe. Due to the discrepancy among the four dam models, extra attention should be paid to the background data. The main purpose of measuring the BPD is to investigate the discrepancy among the four models, which determines the comparability and availability of the measurement results.
Table 6 summarizes the statistics of the BPD. It can be found that the range (difference between the maximum and minimum), standard deviation, and coefficient of variation for DM 1 are smaller than those for the other three dam models, suggesting that DM 1 is more uniform. The BPD means for every line on DMs 1, 2, and 3 are around 2 V, while those on DM 4 are relatively lower (around 1.8 V). That may be caused by the difference in model compactness. Under the applied voltage, this difference leads to the different proportions of current flow via the liquid phase pathway, solid–liquid phase pathway, and solid phase pathway. The soil electrical conductivity of DM 4 is therefore affected, showing a BPD difference of approximately 0.2 V. In addition, Table 6 shows that the range of DM 3 is larger than that of DM 2 and DM 4, which can also be attributed to the difference in model compactness.
The differences in the means in Table 6 are evaluated using Tukey’s HSD. It is found that only the differences between the means of L1 on DM 2 and L1 on MD 4, L1 on DM 2 and L2 on MD 4, and L2 on DM 3 and L2 on MD 4 are significant at α level of 0.05, while those of the other 63 pairwise comparisons are not significant at α level of 0.05. This indicates that there are no significant differences among the four dam models in general. In addition, the CVs of the experimental BPD are evaluated according to DB 50/143-2003 [52], a code for the investigation of geological hazard prevention in China. Based on the requirement that the CV value of a geotechnical parameter must be less than 30%, the differences in BPD among the four models are within an acceptable level. Thus, it can be concluded that they are in a nearly identical state.
Moreover, a limitation of the curve plan is that the focus is placed on the hydraulic properties of internal erosion, with a neglect of the mechanical properties, such as the particle loss.

4.2. Influence of Soil Moisture Content on PD

In this experiment, the artificial upstream reservoir causes the seepage across through the dam model. The soil below the phreatic surface is saturated, resulting in a significant increase in the moisture content of the soil on the seepage surface. Due to the lack of the special drainage facility (e.g., drainage mound) at the dam toe, the phreatic surface is higher than that in the general case, and the upper boundary of the seepage surface extends to the waist of the slope. From the experimental results (see Figure 7), the PD at the waist of the slope increases, while that near the dam crest changes little. Therefore, it can be concluded that the increase in the moisture content causes the increase in the PD, which is consistent with the results in the previous study [53]. The main reason is that the increase in the moisture content in the soil promotes the development of a liquid phase pathway, leading to more charge transfer under the applied voltage. The conclusion can also be supported by the spatial distribution of the PD at different time instants. From the transient-state seepage to the steady-state seepage, the phreatic surface in the dam model is rising until in a stable elevation, leading to an increase in the moisture content of the soil on the slope. In addition, the PD varies mildly after an intense increase, indicating that the moisture content no longer has an effect on PD when the soil is saturated.
It is worth noting that a few abnormal data, particularly the PDs at 0.25-m-distance to the dam crest (see Figure 7c) and at 0.55-m-distance to the dam crest (see Figure 7f), are slightly inconsistent with the general trend. That can be attributed to the electrode stability, according to the study by LaBrecque et al. [54]. A double layer forms at the soil–electrode boundary as the electrode is used, which determines the measurement error for the electrode. The formation of the double layer may be influenced by the micro or subtle variations in the electrode’s surface, although they are the same in material, size, and appearance. As a result, certain electrodes show a different performance. Moreover, such behavior of an electrode can also be caused by the evolution of the layer over time. In this study, since the electrodes are stationary during the test, the only change is the water content in the soil. Therefore, we consider that the increase in water content not only promotes the development of a liquid phase pathway but also affects the contact conditions between the soil and electrode and, thereby, the double layer.
For the earthen dam models studied in this paper, there is a remarkable correlation between the seepage and the PD response to applied voltage. Both the values and the range of the PD at the waist of the downstream slope increases with the evolution of seepage (from the transient-state seepage to the steady-state seepage). The primary reason is the rise of the phreatic surface. Therefore, the PD can be used to understand the seepage state in earthen dams and, thereby, assess the seepage risk.

4.3. Influence of Internal Erosion on PD

As mentioned before, the two survey lines L1 and L2 are set on the downstream slope of the dam models in the experiment. The only difference between the two lines is that L2 is located over geotextile tube. Therefore, the obtained PDs for L1 and L2 can be used to investigate the influence of internal erosion on PD. Figure 8 presents the PDs for L1 and L2 under the steady-state seepage. For comparison purposes, the results for L1 and L2 from each dam model are plotted on the same subfigure.
As expected, the results for L1 and L2 on DM 1 vary little, owing to the absence of the geotextile tube in this model. A steep increase in PD can be identified in both Figure 8b (DM 2) and Figure 8d (DM 4). For the steep increase in PD, the starting position on L1 is closer to the dam crest than that on L2. This indicates that the phreatic line in the model cross-section where L2 is located moves downward due to the presence of the geotextile tube. Given the symmetry of the dam model, we consider that there is a V-shaped phreatic surface in the two dam models. However, although the length of the geotextile tube in DM 3 lies between that of the geotextile tube in DM 2 and DM 4, the starting position on L1 is in coincidence with that of L2 for DM 3, producing a horizontal phreatic surface. The explanation we can give is that the results may be influenced by the boundary effect. Due to the leakage near the flume wall, the phreatic line in the model cross-section where L1 is located falls down, which results in the starting position on L1 moving downward along the slope.
Under the steady-state seepage, a high-permeability zone is induced by the simulated erosion zone in the model. The formation of the V-shaped phreatic surface means that the seepage flowing is concentrated in the high-permeability zone, which is consistent with the existing investigation [51]. Compared to that in the dam model with no erosion, the seepage field in the dam model with erosion changes, which leads to a remarkable change in the moisture content of the soil on the slope. Since the PD of the soil is sensitive to the moisture content, the PD at the slope can be considered as a key parameter in the identification of erosion zones in earthen dams.
The normalized PDs for L2 on the four dam models under the steady-state seepage are plotted as shown in Figure 9. From Figure 9, the significant difference in the results among the four dam models is the starting position of the steep increase in PD. With an increase in the length of the simulated erosion zone, the starting position on the slope gradually moves toward the toe. This implies that the phreatic surface moves downward, and the distribution range of the saturated soil on the slope decreases. Therefore, there is a noticeable change in the distribution of PD due to the different length of the erosion zone.
In summary, the experimental results show that the PD is highly correlated with internal erosion. Affected by the erosion, the starting position for the steep increase in PD moves toward the dam toe, and this change is a continuing process in the same way as the development of erosion. Both the existence and the development of erosion can be reflected by the PD at the slope of the dam models, which provides implications for developing a PD-based method for monitoring the erosion in earthen dams. Moreover, being the same as the index, the starting position for the steep increase in PD plays a key role in the monitoring.

5. Conclusions

In order to trace the progression of internal erosion using the potential difference (PD), a set of laboratory experiments are carried out with four physical models of earthen dams to study the relation between the PD and the internal erosion. Considering the notable characteristic that the flow concentrates strongly towards the erosion pipe, the geotextile tubes filled by uniform gravel are installed in the dam models to simulate the zone affected by internal erosion. Under the applied voltage, the response PDs at the slope of the dam models are collected before and after the impoundment of the upstream reservoir. The discrepancy among the four dam models, the influence of soil moisture content on PD, and the impact of internal erosion on PD are investigated and discussed. The main conclusions are as follows:
(1)
Employing different dam models to simulate the development of internal erosion is acceptable. Due to the inevitable discrepancy among the models, extra attention should be paid to the background data of target measurement parameters, which determine the availability of the measurement results.
(2)
The moisture content of the soil has a significant effect on the PD response to applied voltage. The PD increases with an increase in soil moisture content until the soil is saturated, which is helpful to understand the change in the seepage state in earthen dams.
(3)
There is a remarkable correlation between the internal erosion and the PD response to applied voltage. Induced by the internal erosion, the starting position for the steep increase in PD moves toward the dam toe. This change is a continuing process as the erosion develops. The progression of internal erosion can be effectively traced through analyzing the PD. In the measured PD, the starting position for the steep increase is a reliable identification indicator, which lays a foundation for developing a PD-based approach to the monitoring and early warning of internal erosion in earthen dams.
(4)
It is noted that a measurement error can be induced by electrode stability. In addition, an error may be induced due to the mechanical properties of internal erosion, which is neglected in this study. These can provide a direction for further investigations.

Author Contributions

Methodology, M.Z. and K.W.; formal analysis, P.L. and L.J.; investigation, P.L. and L.J.; data curation, P.L.; writing—original draft preparation, P.L.; writing—review and editing, K.W.; project administration, M.Z. and K.W.; funding acquisition, M.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Natural Science Foundation of China, grant number 51879017 and Chongqing Research Program of Basic Research and Frontier Technology, grant number cstc2017jcyjBX0066.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Not applicable.

Acknowledgments

The authors acknowledge the financial support from the National Natural Science Foundation of China (Grant No. 51879017), and Chongqing Research Program of Basic Research and Frontier Technology (Grant No. cstc2017jcyjBX0066).

Conflicts of Interest

The authors declare no conflict of interest.

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Water 13 03387 g001 550
Figure 1. Schematic of a flume and a dam model constructed in the experiment.
Figure 1. Schematic of a flume and a dam model constructed in the experiment.
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Water 13 03387 g002 550
Figure 2. Cross-section and front view of dam models with geotextile tubes of different lengths. (a) DM 2 with a 50-cm-long geotextile tube. (b) DM 3 with a 90-cm-long geotextile tube. (c) DM 4 with a 180-cm-long geotextile tube. The description of the same details among the three subfigures is only added to one of them to avoid repetition.
Figure 2. Cross-section and front view of dam models with geotextile tubes of different lengths. (a) DM 2 with a 50-cm-long geotextile tube. (b) DM 3 with a 90-cm-long geotextile tube. (c) DM 4 with a 180-cm-long geotextile tube. The description of the same details among the three subfigures is only added to one of them to avoid repetition.
Water 13 03387 g002
Water 13 03387 g003 550
Figure 3. Geotextile tube arrangements in different dam models. (a) DM 2; (b) DM 3; (c) DM 4; (d) The three tubes used and the gravel encased in the tubes.
Figure 3. Geotextile tube arrangements in different dam models. (a) DM 2; (b) DM 3; (c) DM 4; (d) The three tubes used and the gravel encased in the tubes.
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Water 13 03387 g004 550
Figure 4. Soil used for dam models. (a) Photographs of each particle group. (b) Particle size distribution.
Figure 4. Soil used for dam models. (a) Photographs of each particle group. (b) Particle size distribution.
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Water 13 03387 g005 550
Figure 5. Photograph taken from the measurement on one of the dam models after the impoundment.
Figure 5. Photograph taken from the measurement on one of the dam models after the impoundment.
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Water 13 03387 g006 550
Figure 6. BPD for the different dam models. (a) DM 1; (b) DM 2; (c) DM 3; (d) DM 4. The D refers to the distance to dam crest along the downstream slope. The black square symbols, the red circle symbols, and the blue triangle symbols represent the BPD for survey lines LI, L2, and L3, respectively.
Figure 6. BPD for the different dam models. (a) DM 1; (b) DM 2; (c) DM 3; (d) DM 4. The D refers to the distance to dam crest along the downstream slope. The black square symbols, the red circle symbols, and the blue triangle symbols represent the BPD for survey lines LI, L2, and L3, respectively.
Water 13 03387 g006
Water 13 03387 g007a 550Water 13 03387 g007b 550
Figure 7. Distributions of PD for different survey lines on the four dam models under seepage. (a) L1 on DM 1; (b) L2 on DM 1; (c) L1 on DM 2; (d) L2 on DM 2; (e) L1 on DM 3; (f) L2 on DM 3; (g) L1 on DM 4; (h) L2 on DM 4. The D refers to the distance to dam crest along the downstream slope. The black square symbols, the red circle symbols, the blue triangle symbols, the green inverted triangle symbols, and the purple rhombus symbols represent the PD for 0 h, 1 h, 2 h, 3 h, and 4 h after filling the reservoir, respectively.
Figure 7. Distributions of PD for different survey lines on the four dam models under seepage. (a) L1 on DM 1; (b) L2 on DM 1; (c) L1 on DM 2; (d) L2 on DM 2; (e) L1 on DM 3; (f) L2 on DM 3; (g) L1 on DM 4; (h) L2 on DM 4. The D refers to the distance to dam crest along the downstream slope. The black square symbols, the red circle symbols, the blue triangle symbols, the green inverted triangle symbols, and the purple rhombus symbols represent the PD for 0 h, 1 h, 2 h, 3 h, and 4 h after filling the reservoir, respectively.
Water 13 03387 g007aWater 13 03387 g007b
Water 13 03387 g008 550
Figure 8. Distributions of PD for survey lines on the different dam models under the steady-state seepage. (a) DM 1; (b) DM 2; (c) DM 3; (d) DM 4; The D refers to the distance to dam crest along the downstream slope. The black square symbols and the red circle symbols represent the PD for LI and L2, respectively.
Figure 8. Distributions of PD for survey lines on the different dam models under the steady-state seepage. (a) DM 1; (b) DM 2; (c) DM 3; (d) DM 4; The D refers to the distance to dam crest along the downstream slope. The black square symbols and the red circle symbols represent the PD for LI and L2, respectively.
Water 13 03387 g008
Water 13 03387 g009 550
Figure 9. Distributions of PD for L2 on the different dam models. The D refers to the distance to dam crest along the downstream slope. The black square symbols, the red circle symbols, the blue triangle symbols, and the green inverted triangle symbols represent the PD for DM 1, DM 2, DM 3, and DM 4, respectively.
Figure 9. Distributions of PD for L2 on the different dam models. The D refers to the distance to dam crest along the downstream slope. The black square symbols, the red circle symbols, the blue triangle symbols, and the green inverted triangle symbols represent the PD for DM 1, DM 2, DM 3, and DM 4, respectively.
Water 13 03387 g009
Table
Table 1. Coordinates of the reference points.
Table 1. Coordinates of the reference points.
Dam ModelReference PointCoordinatesLayer
DM 2P1, P2, P3, P4(18 cm, 10 cm), (40 cm, 10 cm),
(53 cm, 11 cm), (64 cm, 12 cm)		1st layer
DM 3P1, P2, P3, P4, P5, P6(18 cm, 10 cm), (40 cm, 10 cm),
(53 cm, 11 cm), (64 cm, 12 cm),
(85 cm, 15 cm), (102 cm, 18 cm)		1st layer
DM 4P1, P2, P3, P4, P5, P6, P7, P8, P9(18 cm, 10 cm), (40 cm, 10 cm),
(53 cm, 11 cm), (64 cm, 12 cm),
(85 cm, 15 cm), (102 cm, 18 cm),
(127 cm, 24 cm), (152 cm, 34 cm),
(174 cm, 72 cm)		1st layer
2nd layer
3rd layer
Table
Table 2. Geometrical and mechanical properties of soil used for dam model preparation.
Table 2. Geometrical and mechanical properties of soil used for dam model preparation.
GsCuCcd10 (mm)d20 (mm)d30 (mm)d60 (mm)d70 (mm)
2.7243.863.720.180.752.37.910.6
Gs = the specific gravity; Cu = coefficient of uniformity; Cc = coefficient of curvature; d10, d20, d30, d60, and d70 = diameter of the 10%, 20%, 30%, 60%, and 70% mass passing, respectively.
Table
Table 3. Mineral composition of soil used (in %).
Table 3. Mineral composition of soil used (in %).
QuartzIlliteAlbiteChloriteKaoliniteCalciteHematite
48.822.017.95.52.71.81.2
Table
Table 4. Chemical composition of soil used (in %).
Table 4. Chemical composition of soil used (in %).
SiO2Al2O3K2ONa2OMgOFe2O3CaOCr2O3
70.7816.692.602.121.971.201.010.17
Table
Table 5. Assessments of internal stability for the soil.
Table 5. Assessments of internal stability for the soil.
AuthorsCriteriaStability Assessment
Istomina (Original) [30]Cu > 20, internally unstableInternally unstable
(Cu = 43.86)
10 < Cu < 20, transitional
Cu < 10, internally stable
Istomina [31]p < 25%, internally unstableInternally unstable
(p = 15%)
25% < p < 35%, transitional
p > 35%, internally stable
Liu [31]p < 25%, internally unstableInternally unstable
(p = 24.6%)
25% < p < 35%, transitional
p > 35%, internally stable
Kenney and Lau (Original) [32](H/F)min < 1.3, internally unstableInternally unstable
((H/F)min = 0.47)
(H/F)min > 1.3, internally stable
Kenney and Lau (Modified) [33](H/F)min < 1, internally unstableInternally unstable
((H/F)min = 0.47)
(H/F)min > 1, internally stable
Table
Table 6. Statistics of the BPD.
Table 6. Statistics of the BPD.
Dam ModelSurvey LineMax./Min. (V)Range (V)Mean (V)SD 1 (V)CV 2 (%)
DM 1L12.24/1.720.522.000.168.0
L22.35/1.750.601.950.168.2
L32.36/1.870.492.030.136.4
DM 2L12.53/1.540.992.200.2812.7
L22.51/1.441.072.010.3215.9
L32.58/1.381.201.890.3317.5
DM 3L12.47/1.091.381.960.3517.9
L22.72/1.631.092.070.2914.0
L32.86/1.231.632.040.4220.6
DM 4L12.21/1.440.771.800.2312.8
L22.16/1.250.911.700.2514.7
L32.28/1.320.961.870.3016.0
1 SD = Standard deviation; 2 CV = Coefficient of Variation.
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Zhao, M.; Liu, P.; Jiang, L.; Wang, K. The Influence of Internal Erosion in Earthen Dams on the Potential Difference Response to Applied Voltage. Water 2021, 13, 3387. https://doi.org/10.3390/w13233387

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Zhao M, Liu P, Jiang L, Wang K. The Influence of Internal Erosion in Earthen Dams on the Potential Difference Response to Applied Voltage. Water. 2021; 13(23):3387. https://doi.org/10.3390/w13233387

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Zhao, Mingjie, Pan Liu, Li Jiang, and Kui Wang. 2021. "The Influence of Internal Erosion in Earthen Dams on the Potential Difference Response to Applied Voltage" Water 13, no. 23: 3387. https://doi.org/10.3390/w13233387

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