This article presents a procedure for designing rockfill toe protections with a highly permeable downstream shoulder to avoid mass sliding in dams during extremely high through-flow episodes. This accidental through-flow may be caused by reasons such as overtopping or leakage flow due to the loss of sealing at the impervious element of the dam or its foundation. The proposed protection is located at the downstream toe of the dam, and it is composed of highly permeable material, typically compacted rockfill. This material can be different from the rockfill forming the downstream shoulder of the main dam. The work is a result of a combination of numerical and experimental research carried out to analyze the influence of the geometry of the toe protection for given material properties of both dam shoulder and protection, when they can be considered highly isotropic. As a result of these studies, a design methodology is obtained. A series of validation tests are presented to support the reliability of the method.

Introduction and background

During the last decades, the social demand for dam safety standards has significantly increased, especially in most developed countries. This has yielded new and more demanding dam regulations and technical guidelines, some of them imposing the need of protecting existing dams [1,2]. The dam protection techniques involve different adaptations of the designs of the dams to protect them against foreseeable failure mechanisms so as to improve their safety [3,4]. There are different types of dam protections, mainly depending on the type of dam, the associated failure mechanisms, and the specified degree of protection [5]. In the particular case of rockfill or earthfill dams, the development of heavy through-flows within the downstream shoulder due to overtopping or extremely high leakages (Fig. 1) is the main cause of their partial or total failure [6]. Reinforced rockfill, riprap, and gabions, among others, have been the most common rockfill dam protections used in the past [7–11]. In addition to this, countries such as Norway or Sweden are currently using rockfill protections on the downstream slope in rockfill dams where potential risk for loss of life and significant downstream damage is high. This is the case of, for example, Suorva, Seitevare and Trängslet Dams in Sweden, and Svartevann Dam in Norway. So-called “rockfill toe berms” are installed on these three Swedish dams, whereas rip-rap is placed on the downstream slope of the Norwegian dam. These particular types of protection have been recommended by their respective National Dam Safety Guidelines [2,12] to improve the stability of dams against accidental leakage [13–16].

The probabilistic analysis of slope stability is a topic that has been widely studied in the literature. Works in this domain have mainly considered uncertainties relating to soil mechanical properties obtained from geotechnical investigations. These uncertainties essentially stem from inherent spatial variability and measurement errors [1,2], to which can be added limited site investigation data and the assumptions included in the stability model [3]. Among these sources of uncertainties, some studies have shown that spatial variability is the most important [4–6]. Therefore, it is the aspect on which research studies have focused most [2,3,7–16]. Thus, the theory of random fields [17] is best suited for modeling the spatial variability of properties of continuous media like soils. In recent years, much research has integrated this kind of modeling in embankment slope stability analysis covering different aspects. For example, Gaouar et al. [18] and Auvinet and Gonzalez [19] studied the reliability of hypothetical earth dams using random fields of undrained shear strength. Nishimura et al. [47] employed the Swedish weight sounding test to identify the spatial correlation structure of the materials of an earth-fill dam. Zheng et al. [48] conducted a Bayesian updating approach with monitoring data to improve the predictions of embankment settlements. Cho [11] used direct MCS to investigate the effect of the spatial variability of shear strength parameters on the failure surface with 1-D random fields and LEM. Others have paid attention to the influence on both seepage and slope stability of the characteristics of random fields like: (i) correlation length [2,20]; (ii) the coefficient of variation (CoV) [14]; (iii) the choice of the autocorrelation function (ACF) used to represent spatial variability [3,16]. Finally, Liu et al. [3] proposed a numerical procedure to combine Subset Simulations (SS) with the Kriging method for assessing the reliability of an embankment slope in spatially variable soils. Most of these studies used the limit equilibrium method (LEM) to assess slope stability. However, with the rapid development of computational tools, FEM is increasingly used in geotechnics. This is particularly true concerning sliding stability analyzes [21] which have been extensively combined with the strength reduction method (SRM), based on Zienkiewicz’s work [22]. SRM has since been used for slope stability analyzes by many authors like Matsui and San [23], Griffiths and Lane [24], Cheng et al. [25], Huang and Jia [26] and others. Combined with SRM technique, FEM is used as an alternative to LEM because it presents several advantages that are described in detail in [24,25]: (i) no assumptions are needed concerning the failure surface, (ii) no assumptions on inter-slice side forces are needed, since there is no concept of slices, and (iii) soil behavior can be modeled in terms of stresses/strains. Furthermore, several studies have shown that LEM and SRM give similar FoS [24,25], except in some specific cases pointed out by Cheng et al. [25]. Different methods are used in the literature to evaluate reliability in geotechnical issues. Some authors used first-order, second-moment (FOSM) methods [2,7,27], whereas others used the FORM method [11,20,28]. MCS is nevertheless the method used most for probabilistic slope stability analysis [3,8,9,13,15,16]. MCS is a simple and robust tool for simulating the statistical distribution of FoS, although it requires considerable computational effort in terms of calculation time [13,15]. Regarding earthfill dams, large quantities of geotechnical data are available in the form of design studies, construction controls and monitoring measurements [29,30]. These data are still not well exploited in studies relating to the reliability of earth dams (or for that of concrete dams [33]), although some authors have underlined the benefits of carrying out a geostatistical analysis on them [31,32]. However, the probabilistic assessment of geotechnical properties generally depends on the type of soils and considerations found in the literature, such as in the work of Phoon and Kulhawy [5,6].

According to statistics from the National Bureau of Statistics of the People’s Republic of China (MWR and NBS, 2013), there are currently more than 98000 reservoirs in China, with a total capacity of over 900 billion cubic meters. Of these reservoirs dams, up to 90% are embankment dams. However, due to historical reasons (e.g., inadequate survey and design, poor construction quality, and improper management), more than 36% of these dams and reservoirs are in dangerous conditions, with various degrees of risk, which not only limit the use of the reservoirs and maximization of economic benefits, but may also cause potentially catastrophic consequences like life loss and property damage if they are wrecked. For these reasons, dam safety and danger condition evaluation are of the utmost importance (Hartford and Baecher, 2004; Jiang and Fan, 2008). Moreover, according to the International Commission on Large Dams (ICOLD, 1973), nearly 50% of earth dam disasters in China and one-third in the world are caused by flood overtopping, seepage, and piping, and other causes make up the rest (Hege, 1997; Jin, 2008). In principle, an earth dam is considered to be destroyed after suffering flood overtopping, which might lead to unexpected consequences. Therefore, it is important and urgent to improve danger degree analysis and assessment, thus offering a scientific basis and reference for risk management and security decision-making. In the case of modification of dangerous dams, including repairs and reconstruction, economic feasibility and social safety goals need to be addressed. When evaluating the priority of earth dam rehabilitation, it is necessary to estimate the danger degree of these dams and reservoirs and sort them, in order to determine the urgency of reinforcement, which will contribute to reasonable allocation of limited resources. Thus, danger degree evaluation is a potentially useful approach. On the other hand, a flood-water resources utilization strategy with higher standards has been put forward to meet the requirements of rapid industrial and agricultural development. Fortunately, reservoirs are one of the most efficient types of infrastructure for integrated water resources development and management, and flood-limiting water level (FLWL) during the flood season is an important parameter in reservoir operation and the key to coordinating the contradiction between flood risk and reservoir benefit (Eum and Simonovic, 2010; Yun and Singh, 2008). In addition, an annual fixed FLWL for the whole flood season may reduce electricity generation, because of the lower water level. In this case, water shortage may occur when the flood season is delayed or ends prematurely, which prevents the reservoir from refilling to the normal water level by the end of the flood season. Sub-season flooding and the corresponding FLWL for flood control have been proposed to coordinate flood control and water resources utilization. When the highest water level in front of the dam exceeds the elevation of the dam crest, it will lead to earth dam overtopping and cause earth dam failure. Higher standards for flood water resources utilization seek a more suitable scheduling solution for reservoir optimal operation. The scheduling solution with optimal utilization of water resources, including flood resources that could otherwise lead to disasters in some rainy regions, cannot excess a dam’s flood control risk. Therefore, research on the danger degree for flood control risk of earth dam reservoir staged operation is a key step for solidification or reconstruction for dangerous reservoirs, as well as an effective way to flood water resources utilization.

Dams are multipurpose structures that are constructed to improve human life. It is built for the production of hydroelectric power, economic improvement, providing water for irrigation and water supply and flood control (Hooshyaripor et al. 2014). Therefore, dams are essential element of infrastructure for any country (Wahl 2010; Razad et al. 2013). There are currently over 45,000 large dams being used throughout the world (DHI Water & Environment, 2009), and 800,000 dams have been constructed up to date (Zagonjolli 2007). Dams are usually classified under two different groups: earthen/rock and gravity. Figure 1 indicates the ratio of four dam types which are constructed in Europe and USA from 1900 to 1969. Most of the dams that are built during this period are earthfill and rockfill which is about 60% of the total number of dams. The second type is gravity dams that represent 25%, whereas the buttress and arch dams form the remaining 15%. Embankment (earthfill and rockfill) dams consist of compacted impermeable material (core) combined with coarse material (earth or rock) to return the water. The huge water volume that is retained in the reservoir can cause a serious flood to the properties and population in the downstream area if a sudden release from the stored water occurs (Razad et al. 2013). Dam failures are very rare, but they do occur. When dams do fail, usually it contributes to the catastrophic consequences. This is often because local communities are not sufficiently prepared. The amount of life or property loss that can occur from a dam breach has increased to a larger number during the past few decades. This is because there has been a lot of development in these areas that would be affected if a dam breach occurs (DHI Water & Environment 2009). Janson (1980) summarized some wellknown dam failures around the world. He found that about 2000 constructed dams were failed around the world since the twelfth century. There are approximately 200 dams that were failed during the last century which resulted in the death of more than 11,100 people. Johnstown dam in USA, Vajont dam in Italy and Machhu dam in India are the worst three dam failures which nearly caused 6800 of the deaths alone. Table 1 shows the examples of destructive dam failure throughout the world which collected from literature review. Dam breach analysis is an important element in the dam failure assessment. There are many existing approaches for estimation of dam breach parameters. But most of these approaches included many uncertainties which affect the accuracy of their predictions.

The asphalt core type embankment dam (ACED) with its many advantages has been applied worldwide since 1960s. Among the completed asphalt core dams, the Storglomvatn Dam in Norway and the Yele Dam in China were the highest until 2017, both with a dam height of 125 m [1,2]. In recent years, many investigations and applications for asphalt cores in embankment dams have been done. Wang and Höeg [3] proposed a simplified material model for analyzing asphalt cores in embankment dams based on extensive long-term creep triaxial test results. Wang and Höeg [4] as well as Akhtarpour and Khodaii [5] studied the cyclic behavior of asphalt concrete used as impervious cores in embankment dams for dam sites located in seismic regions. Zhang et al. [6] investigated the conditions that hydraulic fracturing would take place for asphalt cores in very high embankment dams and concluded that hydraulic fracturing would be of no concern. Asphalt concrete used as water barrier in dams provide watertightness, cracking resistance, and self-healing properties [7]. With the experience gained from research and field experience, the dam height of ACEDs has reached a level of more than 150 m. The 174 m high Quxue Dam was completed in February 2017 in China and other high ACEDs are under construction or under final design [8,9]. The 153 m high Zarema Dam is about to be completed in Ethiopia and the Moglicë Dam in Albania is in the early stages of construction and will be about 170 m high [9]. Asphalt core is placed and compacted layer by layer with transition zone on either side of the core with a compacted thickness of 20–25 cm to form a no-joint impervious wall protected by the transition zones in the embankment dam. The interface between asphalt core and transition zones play an important role to transfer stresses and deformations during the dam construction and reservoir impounding. The behavior of the interface of asphalt core-transition zone has not been investigated very much in the published literature. Tajdini et al. [10,11] studied the interface behavior between asphalt concrete and granular materials using direct shear tests. However, they used a small size 10 × 10 × 2.5 cm direct shear box with a cut smooth face of asphalt specimens for testing. The results and conclusions could have some limitations due the small sizes of the test box and the smooth face of asphalt specimens while the interface of the asphalt core-transition zone in a dam is rather rough and interlocked [12,13]. The authors have studied the interface behavior of asphalt core-transition zone in embankment dams using a large shear box with overlapping rectangular steel plates for an interlocking interface, and the results will be published in another paper [14]. In most of the ACEDs constructed so far, the asphalt core rests on a concrete plinth (sill), and the plinth is anchored to the rock foundation to serve as a cap for contact and curtain grouting. In cases where there is deep soil overburden, the plinth may rest on a concrete cut-off wall or jet-grouted wall. The asphalt core width is conventionally in the range of 0.5–1.2 m, and the core width is doubled toward the contact with the plinth on the foundation and against the abutments. The asphalt core-plinth connection (joint) is crucial and must remain watertight when the core and plinth undergo deformations (displacements) during construction and dam operation. For situations with gentle abutment slopes the connection is subjected to compressive and moderate shear strains that are unlikely to cause any leakage [2,12,13]. Kruntcheva et al.

Following the impoundment of an embankment dam, the seepage field of the dam body is seen to gradually stabilize. At this point, seepage within the dam body is primarily influenced by environmental variables, such as the upstream level, which demonstrate a certain lag effect. As one of the main problems encountered in data analysis of embankment dam monitoring, lag-effect analysis of dam-body seepage plays an important and central role in health diagnosis and safety monitoring of embankment dams. For example, the lag time recorded at each measurement point must be known when using monitoring data to determine the saturation line, thereby determining the relationship between seepage pressure and upstream level. Lag-effect analysis is also required in selecting preset factors when establishing seepage models. The causes and mechanism of the seepage lag effect of embankment dams are complicated. Gu et al. (2005) summarized the mechanism as follows. Variations in the upstream level alter the dam seepage field from one stable condition to another, and the transition process occurs over a certain time period. This transition is the main cause of the seepage lag effect. Delayed transmission of water pressure in the dam body is another factor contributing to the lag effect. Further, response times of seepage monitoring sensors, such as piezometric tubes and osmometers, with regards to variations occurring in the seepage state could also contribute to the lag effect. At present, only a few specialized studies are being conducted with focus on the seepage lag effect in embankment dams. The basic method used in these studies involves comparison of the process line of the measured water pressure with those of the corresponding upstream water level. This technique serves to qualitatively determine the lag time of the seepage in terms of the appearance time of “peaks” and “valleys” in the process line. Gu et al. (2005) utilized the mean value of the upstream water level over several time periods as the precession factor for the hydraulic-pressure component in their seepage monitoring statistic model, thereby considering the hysteresis effect of seepage. In addition, several scholars have investigated seepage characteristics of embankment dams while also inadvertently studying aging characteristics of seepage. Ozer and Bromwell (2012) used the finite element method and measured seepage data to simulate seepage and aging characteristics of embankment dams. Simeoni (2012) investigated the relationship between the lag time and pore-water pressure using the piezometer experimental method. Wang et al. (2013) studied the influence of the crack self-healing phenomenon on the permeability of dams via 12 simulation tests. Lee et al. (2007) explored the tracer experiment method combined with specific engineering to study the concentrated seepage path of embankment dams. However, a common drawback of the studies mentioned above concerning determination of the seepage lag time is the exclusive utilization of qualitative estimations without quantitative measurements. It is, therefore, necessary to apply new ideas and methods to accurately quantify the seepage lag effect.

According to the ICOLD (International Commission on Large Dams), the majority of failed dams either did not have any monitoring system or had a system that was out of order [1]. This finding therefore demonstrates the importance of inspection and an appropriate monitoring system for regular observation of dam performance. The objective of dam monitoring, which plays a significant role in the concept of dam safety, is to provide data in order to evaluate dam performances throughout its whole life cycle. The typical safety control variables could be classified into 3 categories: mechanical effects (deformation, displacement), hydraulic effects (seepage flow rate and pore water pressure) and environmental effects (reservoir water levels, precipitation and temperature) [2]. Such variables are quantified by means of monitoring instruments installed in dams. Once the monitoring data is collected, it is necessary to analyze it inside and in the vicinity of the dam for the purpose of determining and understanding the dam’s behaviour. Changes in the behaviour of dams in response to thermal or seasonal effects and to variations in the reservoir water level are mostly reversible. By separating the hydrostatic effect induced by the impounding variations and the thermal effects induced by the temperature variation, some aspects can be better understood. It should be noted that the thermal effects are negligible for embankment dams, and thus can be neglected for analyzing the measurements collected in such dams. Multiple correlation methods are used to draw up models for the following-up and surveillance of monitoring measurements. Over the last fifty years, the increase of knowledge in the field of data analysis has led to the development of analytical methods which can exploit these databases, yielding excellent results [3]. The first physical-statistical model which statistically determines the effects of hydrostatic and thermal loads was formulated in 1967 [4,5]. This HST model accounts for mechanical behaviour, by using a statistical regression technique to find out correlations between causes and quantified effects. It is based on a mean seasonal thermal reference curve for the phenomena observed on dams and it enables one-year periodic variations to be identified according to the reservoir level and time. After many years using this model, its limitation was revealed by the phenomena which are sensitive to variations of temperature because it cannot take real temperature into account. In 2004, a new model named HST-T (-T for thermal) [6] was developed after the heatwave of 2003 to better consider the influences of harsh thermal conditions. Concerning embankment dams, the monitoring of pore water pressure is crucial because it is the main indicator of internal erosion and seepage problems and has a significant role in the stability of geotechnical works [7–9]. Pagano [10] focused on these pore water pressure measurements at different stages of the dam lifetime. The authors collected measurements, particularly during the consolidation process within the dam, in order to detect the effectiveness of measurements, in revealing watertightness problems. These problems are influenced by various external factors due to the fact that the effects of variations in reservoir water levels are not instantaneous since the flow inside the dams are delayed by the low hydraulic conductivity of the materials constituting the embankment.