Water Level Rise and Bank Erosion in the Case of Large Reservoirs

Abstract

The article presents an analysis of the complex mechanism of abrasion of shorelines built of non-lithified sediments as a result of rising water levels in the reservoir, along with its quantitative assessment. It allows forecasting the actual risks of coastal areas intendent for urbanization with similar morphology and geological structure. The task of the article is also to point out that for proper assessment of abrasion it is necessary to take into account the greater complexity of the mechanism in which abrasion is the result of co-occurring processes of erosion and landslides. During the analysis, the classic Kachugin method of abrasion assessment was combined with an analysis of the stability of the abraded slope, taking into account the circular slip surface (Bishop and Morgenster–Price methods) and the breaking slip surface (Sarma method). This approach required the assessment of the geotechnical properties of the soil using, among other things, advanced in situ methods such as static sounding. The results indicate that the cliff edge is in limit equilibrium or even in danger of immediate landslide. At the same time, it was possible to determine the horizontal extent of a single landslide at 1.2 to 5.8 m. In the specific cases of reservoir filling, the consideration of the simultaneous action of both failure mechanisms definitely worsens the prediction of shoreline sustainability and indicates the need to restrict construction development in the coastal zone.

1. Introduction

Mass movements are among the most catastrophic natural geological processes that occur in the world. Large-scale landslides threaten the existence of human habitats mainly in mountainous areas, but can also pose a danger to infrastructure in coastal areas, abrasion zones of high sea shores, and large bodies of water. Abrasive processes mainly affect sea coasts, which are affected by sea currents, tidal changes, and wave action induced by strong winds. In the case of natural lakes, the scale of abrasion is considerably smaller, due to, among other things, the stability of the water table and the lack of water currents carrying material away from the abraded zone [1]. However, the case is different with water reservoirs, increasingly constructed to ensure rational water management and a stable supply of fresh water for populated and agricultural areas. In their case, the method of operation of the reservoir assumes cyclical changes in the water level by several or even a dozen meters. Such a situation causes constant changes in the position of the abrasion platform and, at the same time, allows the formation of water currents that carry the eroded material deep into the reservoir. The scheduled cyclic operation of the reservoir is also associated with the threat of changes in groundwater levels in the reservoir. The complex geological structure of layers with different permeabilities means that the effect of water damming in the reservoir changes the pressures and properties of groundwater around the reservoir to varying degrees [2]. The effect of changes in groundwater flow as a result of changes in surface water levels and groundwater heterogeneity, can further influence increased ground erosion [3,4]. Reservation of safe and stable climatic conditions of a building object and protection from water is the basis of its proper maintenance [5]. In the case of sudden water hazards, it is important to perform diagnostics and take appropriate steps to get rid of moisture from structural elements [6]. Sudden moisture occurring in a building and structure is a threat to its durability [7]. Settlement of a building negatively affects both the technical condition of the structure and the comfort of use and, in the event of a sudden loss of stability through the building’s foundation, a building a building failure could occur.

At the same time, artificial inland reservoirs are often a very attractive landscape feature in areas without lakes, eagerly used for recreation. Progressive infrastructural development means that the coastal areas of such reservoirs are increasingly being considered as the location of resort complexes. Paradoxically, in such a situation, sections of high shore, often with a clearly formed cliff, offering investors and potential users charming views, become particularly attractive parts of the reservoir fringes.

In the case of landscaped park areas in Poland, it is prohibited to build new buildings within a 100 m wide strip of the shoreline of rivers, lakes, and other bodies of water, with the exception of objects serving water tourism, water management, or fishing [8]. Unfortunately, most artificial water reservoirs are not landscape parks, which suggests the possibility of erecting structures right on the shore. However, the lack of a criterion related to nature protection should not exempt from ensuring the construction safety of functioning and erected facilities.

In this situation, it becomes extremely important to define safety limits for erected infrastructure around the reservoir. Precise prediction of the effects and extent of abrasion over a certain period of time is extremely problematic with such a wide spectrum of time-varying factors. Exceptional impacts causing building disasters can be described as loads, acting on the building object caused by unlikely phenomena such as fire, explosion, or flooding [9]. Flood hazards are among the main causes causing moisture problems in buildings. In the literature, there is a term for flooding and waterlogging known as dirty water flooding of a building or structure. Dirty water flooding can be spoken of when the water is contaminated with substances hazardous to human health and life [10]. Rising water levels in reservoirs directly affect buildings located in the vicinity and can lead to building disasters.

Classical methods of assessing abrasion, such as Kachugin’s method described in [10], work well in situations where the water level in a reservoir is relatively stable, or in cases of short-term changes in the water level (e.g., high tide–low tide). This is because this model is taking into account only the abrasion process caused by waves and water. No soil mass processes such as landslides trigged by change of water level are considered in this solution. When water level variations of several meters take place on a seasonal (multi-month) cycle, it is presumed that classical methods of analysis may underestimate the threat. In order to test this hypothesis, analyses of various fragments of the cliff bank of the Jeziorsko reservoir were carried out, using a methodology that takes into account the periodic and alternating activity of water abrasion and mass movements in the form of coastal landslides.

A large artificial water reservoir—Jeziorsko Reservoir—was selected for such analysis, located on a lakeless plain in close proximity to the million-strong agglomeration of Lodz, where expectations of intensive recreational use are becoming increasingly common. However, the geological structure of the substrate and the morphology of the reservoir’s surroundings, as well as the peculiarities of water management, mean that long stretches of the shoreline are subject to severe erosion, posing a threat to potential infrastructure facilities in their vicinity. In consideration of shoreline development plans, the aspect of skillful forecasting of the rate and extent of abrasion and the scale of mass movements induced by it becomes extremely important.

It this paper, the combined model of Kachugin’s abrasion model and landslide of costal cliff was considered, in relation to some parts of Jeziorsko Reservoir. The results show the scale of final erosion of the cliff as dependent on combination of the water level uprise and geology of the site. The large range of coast abrasion in the case of a relatively short period of high water level occurring on the Jeziorsko Reservoir shows that great land abrasion may occur in the future.

2. Materials and Methods

2.1. Study Area: Jeziorsko Reservoir—General Description

An analysis of the impact of water level changes on bank abrasion was conducted in the area of the Jeziorsko Reservoir, located in central Poland on the Warta River (Figure 1).

The reservoir’s head dam is located at km 484 + 300 of the river and closes at the Warta river catchment area of 9012.6 km², of which the reservoir direct catchment area is 76.36 km². It is one of the largest lowland reservoirs in Poland: depending on the filling under normal operating conditions, its capacity is between 28.9 million m³ and 142.8 million m³, and its area is between 16.5 km² and 35.1 km². In the event of a flood and use of the entire complete flood reserve, the reservoir’s parameters can increase to 222.5 million m³ and 37.7 km², respectively. Normal operating conditions of the reservoir provide for its filling in the winter–spring period (February–April), maintenance of the obtained filling in the spring–summer period (April–September), and emptying in the autumn–winter period (September–December); maintenance of the minimum filling is planned and provided for in January. As a result, changes in the reservoir’s damming level occur cyclically and can reach up to 4 m: from 116.00 m above sea level (min. water level—MinPP) to 120.00 m above sea level (regular water level—NPP). If the flood capacity is utilized, the water level in the reservoir may rise by another 1.5 m to 121.50 m above sea level (max. water level—MaxPP), and in exceptional flood conditions by another 0.5 m to 122.00 m above sea level (extraordinary max. water level—NadPP).

This study covered the northern section of the eastern shore of the Jeziorsko Reservoir, with a length of about 900 m, located between the villages of Siedlątków and Popów (Figure 1). The distances in a straight line from the axis of the head dam to the extreme points of the analyzed shore section were, respectively, 1.4 km to the point at the northern end and 2.3 km to the point at the southern end. The latitudinal range of the analysis was limited to the zone located between the ordinate of the bottom of the reservoir 114 m above sea level and the line of the presumed extent of the abrasion impact zone from the land side, up to a maximum of about 200 m from the edge of the cliff.

Guided by morphological and geological data and observation of currently occurring abrasive processes, 4 design cross-sections were selected for analysis in the area of the eastern shore of the reservoir and the vicinity of the village of Popów (Figure 2).

2.2. Morphology of the Shore Zone of the Reservoir

In the shoreline of the Jeziorsko Reservoir, which is about 44 km long, there are distinguished sections of the following nature: abrasive, reinforced, neutral, accumulative, and erosive [11]. Natural shores, accounting for about 65% of the total length, clearly prevail over reinforced ones (35% of the shoreline). Among natural shores, those considered abrasive dominate, accounting for about 38% of the length of the natural shoreline of the Jeziorsko Reservoir [12]. They are characterized by a cliff, falling almost vertically (when developed in cohesive soils) or at an angle of about 60° when developed in non-cohesive soils. The height of the cliff depends on the shape of the adjacent land area and reaches the highest values in the Siedlątkow area (about 10 m). The lowest abraded shore slopes were found in the Brody area (0.6 m), where the abraded zones are punctuated by sections of predominantly accumulation [13]. The longest uninterrupted abraded section is found in the Siedlątków and Popów area and is about 800 m long with an average cliff height of 4.4 m [13]. The banks of an accumulation nature make up only slightly more than 5% of the length of the reservoir’s natural shoreline, are local in nature, and are mostly built of sands and gravels. In contrast, sections of shore along which no predominance of any of the morph-forming processes is observed, considered neutral, account for about 24% of the natural shoreline. The occurrence of erosion banks (less than 0.5%) should be considered marginal.

The formation of the Jeziorsko Reservoir bed in the study area indicates the existence of a pronounced slope—an abrasion platform, with an as-yet unformed dynamic slope [14]. It separates the relatively flat central part of the reservoir bed with an ordinate of about 114 m a.s.l., from the edge of the shore (mostly a cliff) with an ordinate of about 120.5 m a.s.l. The slope of the underwater part of the abrasion platform is about 2–3°, while the water level fluctuation zone increases to about 5–6°.

In the area of the conducted reconnaissance, the ordinates of the land area in a strip of about 100 m from the shore vary from about 122 m above sea level to about 136 m above sea level. The collected data allow us to adopt a generalized scheme of the morphology of the zones: bed, beach, and land (Figure 3 and Figure 4).

2.3. Geology and Geotechnical Properties

The described area is located in the western wing of the middle fragment of the Mogileń–Lodz Basin, in the Gniezno–Lask block section. This structural unit is built up by sub-Cenozoic sedimentary rocks with a total thickness of more than 4700 m, documented by the drilling of Uniejow 1. In the roof part of this profile, they are composed of gezy marls and Upper Cretaceous (mastrycht) limestones. Overlying them are sediments of the Cenozoic (Neogene and Quaternary). Their thickness generally does not exceed 40 m, and in places, these sediments have been completely eroded.

With regard to the shallow geological structure, in the analyzed northeastern region of the Jeziorsko Reservoir, fluvial sediments are separated of varied lithology (including partially humic sands of flood terraces, silts of depressions without drainage and valley bottoms, clays and silts locally admixed with sands), which fill the valleys of the Warta and Pichna rivers, which are cut into the chalk subsoil within a few to several meters. The profile of the analyzed eastern shore of the Jeziorsko Reservoir in the Popów area is composed of sediments of the Riss glaciation, more specifically, 2 levels of glacial till: the older phase (of the Oder River phase) and the younger (of the Warta River phase), separated by fluvioglacial sands and gravels. The total thickness of the clay deposits is about 10–12 m, and the sand and gravel deposits are about 6 m (Figure 5 [15]).

The selected computational cross-sections were located in 3 cases (J1, J2, and J3) in places where the cliff consists of glacial till developed as brown sandy loams with pebbles and boulders of crystalline rocks. In these places found locally, in the lower parts of the cliff, there was a small thickness cover of sediments from the flushing of the slope. These were mostly sand and silt deposits. The northernmost computational section (J4) was located in the zone of sand and gravel sediments.

Geotechnical properties of the area were described on the basis of laboratory tests of collected soil samples and by correlation with the results of advanced in situ tests—static soundings. The physical properties of soils were determined by [16]. On this basis, it can be concluded that in the cliff zone, fine-grained soils [17] are represented by a very wide range of sediments, from dust to compact sandy clays. The consistency of these soils is stiff (liquidity index between 0 and 0.25), and their specific density was predominantly in the range of 2.00–2.25 g/cm³ and corresponded to the values reported for similar soils in the literature [18]. The mechanical properties of the soil, necessary for the analysis of the cliff’s stability, were obtained by correlating with the results of static soundings performed in soils like those found in the cliff area. Due to the threat of a landslide, it was not possible to perform these tests directly in the cliff zone (Figure 6).

Parameter values obtained from the measurements [20] are characterized by variability within individual layers, resulting from both natural and measurement considerations [21]. In order to minimize the impact of inaccuracies in the estimation of soil properties and to guard against overestimation of cliff stability, the lower estimate of the 95% confidence interval, assuming a normal distribution within a given layer, was adopted as representative values of geotechnical parameters.

After analyzing the geological structure of the cliff exposures in the various survey sections, a simple single-layer geological structure and geotechnical parameters were finally adopted, as shown in

Table 1. Geotechnical parameters of soil adopted to slope stability analysis.

Cross-Section	Soil Type	Unit Weight γ [kN/m3]	Internal Friction Angle ϕ′ [°]	Cohesion c′ [kPa]	Wet Soil Unit Weigth γsat [kN/m3]
J1, J2, J3	sasiCl	20.00	25.00	12.00	20.50
J4	cSa	19.00	32.50	0.00	19.70

.

2.4. Previous Observations on the Dynamics of Shoreline Processes in the Jeziorsko Reservoir

The first analyses of the dynamics of the reservoir’s banks, particularly in the area of Popów and Siedlątków, were geomorphological studies, carried out against a certain geological background, but without the participation of strict geological engineering analyses. From this point of view, an important observation, found in later works as well (e.g., [12], is the fact that there is a post-glacial hilly upland in the study area [12,13]. This determines, to some extent, the predominance of clays among the sediments of the near-surface zone and at the same time indicates the existence of pronounced natural surface denivelations, sometimes reaching up to several tens of meters. These formations are also characterized by pronounced glacitectonic deformations in the form of folds, scales, and even faults [22].

The landslide potential of the hilly upland area, activated as a result of erosive water activity, was pointed out, among others, by [23], describing a landslide formed over the Warta River in Konopnica. These authors, following [24], classified the area of the entire northern part of the Jeziorsko Reservoir as an area threatened by intense landslides. The above statements unequivocally indicate that the analysis region, mainly due to its morphology and surface water activities, is an area of potential geohazards in the form of mass movements. At the same time, the study of [13] made it possible to include almost the entire currently analyzed section of the shoreline, in the category of abrasive shores; this was due to the coexistence of two key factors: the denudation of the terrain and the direct contact of the hills with the water stored in the reservoir. The lack of a natural beach during the period of the normal level of accumulation (NPP = 120.5 m above sea level) and the eastern exposure of the shore (with the dominance of westerly winds and about 3 km of water surface in this direction) can be considered the dominant factors affecting the observed abrasion of the shore. In this context, it is also worth noting that the NPP level was maintained in the analyzed period (1995–1999) for the 4th to 5th months of the year, which, due to the water management carried out, was a normal phenomenon until 2014, when the NPP value was lowered to the ordinate of 120.0 m above sea level [25].

The only parts of the shore in the section between Siedlątków and Popów, identified by [13] as a zone of accumulation character, are small parts of the shore that are a few dozen meters long: the natural bay near Popowo and the southwestern slope of the hill halfway between Popów and Siedlątków. A similar predominance of abraded zones was also indicated by [26]. According to [13], the height of the cliff in the area of the current study, at that time, was determined to be 2.3 to 10.1 m (average 5 m), the width of the shallows (the beach at the minimum water level in the reservoir) to be in between 23.4 and 53.9 m (average 40.0 m), and the angle of its slope to vary from 3°50′ to 12° (average 7°40′). Such values are also confirmed by the results of [26].

An important observation, also confirmed in later work, is that the observed shallows/beaches were formed as a result of shoreline destruction and are made of material first abraded and then transported towards the water body. The authors of [13] also noted that, although the rule in such cases is for beaches to move toward a state of equilibrium and lengthen, and for the abrasion process to die down slowly [27], in the case of the Jeziorsko Reservoir, due to cyclical and large changes in water level, this process can be significantly prolonged over time. This effect is due to the annual migration of accumulation, transport, and erosion by several tens of meters in a plan.

The dynamics of abrasion processes over many years was also the subject of research conducted using aerial photography [28]. The analysis included two time intervals: 1991–2004 and 2004–2009, as well as the year 2010. The obtained results indicate that in the Popów–Siedlątków region, the annual rate of abrasion decreased with the with the passage of years from 0.35–1.63 m/y in the first period to 0.26–1.28 m/y in the second period and 0.2–1.0 m/y in 2010. These observations correspond to some extent to the with the general trend of dying out of abrasive processes in the coastal zones of artificial water reservoirs, as described by [27], but they do not reflect the dynamics of this regression found at the time. Significantly, due to the peculiarities of the morphology of the Jeziorsko shore zone, the total retreat of the shore in the region of the coastal elevation of the Popów–Siedlątków area was estimated by [28] to be as much as 25 m in 13 years (Figure 7).

During the period of the previous normal damming level (120.5 m above sea level), abrasion processes were not sufficiently counteracted by both the finer sediments (sand, gravel, and pebble fractions) accumulated in the zone of the beach and bed, as well as natural boulder beds of the nature of spurs, which formed in places of local occurrence of glacial water formations.

2.5. Methodology of Abrasion Analysis

The extent of the impact of the abrasion process inland depends on a number of factors, among which the most important are

−

change in the height of the water level;

−

the type of soil that builds the shore and the bottom including the beach zone;

−

the height of the wave depending on the speed and direction of the wind and the length of the wave run-up;

−

the duration of the impact of water on the shore.

In the case of the Jeziorsko Reservoir, however, these factors can be taken as established, resulting from the planned water management carried out on the reservoir and precise reconnaissance of the site.

The analysis of abrasion was carried out in two aspects: the total progress of the process as a result of shore erosion, and its destruction as a result of landslide processes triggered by the undercutting of the cliff by waves.

For the analysis of shore erosion, we used Kachugin’s graphical method, which is described by [10,29], among others, and whose scheme is shown in Figure 8. It basically consists in determining the point of intersection of the plane of inclination of the abrasion platform (α) with the level of water accumulation in the reservoir, raised by the wave height. From the point thus determined, a line sloping at an angle of β, i.e., at an angle that provides the boundary (dynamic) equilibrium for the slope in question, is run to the intersection with its surface. The distance of the point thus determined on the ground surface (labeled “A” in Figure 8) from the top edge of the cliff is the sought abrasion extent.

One of the most popular analytical methods, i.e., the Bishop and Morgenstern–Price and Sarma methods, was used to analyze landslide processes. The basic assumption of the Bishop and Morgenstern–Price method is that the slip surface is cylindrical [30,31]. On the other hand, the method of Sarma [32] assumes that the slip surface can have an arbitrary shape, and hence the broken slip surface was assumed in the analysis carried out. For each design case, stability analysis was carried out using an optimization process aimed at finding the critical slip surface.

The parameter that was used in the subsequent abrasion analysis was the horizontal extent of the landslide, denoted as x (Figure 9).

Abrasion analysis was carried out for four design cross-sections: J1–J4 (Figure 2), taking into account the normal level of water accumulation (NPP = 120.0 m above sea level) and the maximum level of water accumulation in the reservoir (MaxPP = 121.5 m above sea level).

In the individual design sections, the soil parameters were adopted in accordance with

Table 2. Geotechnical parameters of the soil adopted for slope stability analysis in the design section.

Cross-Section No.	Type of Soil	Bulk Weight γ [kN/m3]	Internal Friction Angle ϕ′ [°]	Soil Cohesion c′ [kPa]	Bulk Weight of Wet Soil γsat [kN/m3]
J1, J2, J3	Sandy loam	20.00	25.00	12.00	20.50
J4	Fine gravel, medium density	19.00	32.50	0.00	19.70

[33].

3. Results and Analysis

For abrasion analyses using Kachugin’s method, the averaged value of the angle of the abrasion platform was used, with this approach being of particular importance for the analysis of the J4 design section, where the variation in the angle of the α slope was significant and ranged from 2 to 110. In the other cases (J1–J3), the differences were at most 20.

Due to the lack of local data on wind directions and wind speeds, which have a direct impact on the height of the waves that form, archival data from the meteorological station in Kalisz (after [34]) were used to calculate the wave height (h_f), according to the Andreanov Formula (1) [12].

$${\mathrm{h}}_{\mathrm{f}}=0.0208 · {\mathrm{v}}_{\mathrm{w}}^{5/4} · {\mathrm{F}}^{1/3}$$

(1)

where

• h_f—wave height [m];
• v_w—wind speed [m/s];
• F—length of wave run-up [km] (width of body of water) taken as 3 km.

It was assumed that the wind in the analyzed area generally blows from the western sector (perpendicular to the analyzed shore of the reservoir), and its speed of significant morph-forming importance is 15 m/s. Although this is not the most common wind speed recorded in the area (it is generally lower here), nevertheless such a speed is much more important in the abrasion process than weaker winds, even with their higher frequency of occurrence.

The calculated wave height was exactly 0.84 m, with its value rounded to 1 m used to estimate the extent of abrasion, which creates a certain margin of safety for the predictions presented.

For the purpose of the analyses, it was assumed that bottom scouring occurs to the ordinate of about 115 m above sea level, i.e., 1 m (the assumed wave height) lower than the minimum level of damming, which is 116 m above sea level in the Jeziorsko Reservoir. The last assumption made was the value of the angle β, i.e., the angle of slope of the surface of the newly created slope, which remains in boundary equilibrium. This value was adopted after Kachugin as 420 for the design sections: J1, J2, and J3, where the cliff is made of sandy clays, and 400 in cross-section J4, where the shore is sand and gravel deposits.

The obtained forecasts of the extent of abrasion in the designated computational cross-sections are summarized in

Table 3. Forecasted total extent of abrasion of the eastern shore of the Jeziorsko Reservoir in the places of the adopted calculation cross-sections, taking into account the amount of water damming in the reservoir.

Cross-Section No.	Extent of Abrasion (from the Top Edge of the Cliff to Point A in Figure 8) [m]			Angle of Inclination of the Abrasion Platform α [°]	Angle of the Stable Slope β [°]
	Water Accumulation Level [m a.s.l.]
	120.0 (NPP)	121.5 (MaxPP)	122.0 (NadPP)
J1	0.0	12.3	19.7	4	42
J2	4.6	30.5	39.3
J3	0.0	23.1	29.2
J4	0.0	9.9	14.7	6	40

, taking into account the different ranges of water accumulation in the reservoir, which, if the other parameters assumed in the forecast are kept constant, are of decisive importance. The maximum range of possible abrasion at normal water accumulation in the reservoir up to the ordinate of 120 m above sea level, and at maximum accumulation up to 121.5 m above sea level, as well as at extraordinary accumulation up to the ordinate of 122 m above sea level, were evaluated.

As can be seen in Figure 10, the normal level of damming can locally trigger the abrasion process. To this end, simultaneously with the maintained water damming, relatively strong winds (v_min = 15 m/s) would have to occur, causing significant, nearly meter-high waves, which, hitting the shore, would lead to its erosion. The analysis shows that only in one of the four selected transects (at J2) would the above conditions cause (adopting the concept of abrasion prediction according to Kachugin) a retreat of the shore by nearly 3 m, while in the remaining analyzed sites at NPP, no abrasion would occur.

In the case of higher water levels in the reservoir (Max PP and NadPP), abrasion, although varied, was predicted throughout the analyzed section at the locations of the design cross-sections, ranging from 10 to 30 m at MaxPP and 15–40 m at water accumulation up to 122 m above sea level.

The results of the cliff stability analyses are presented in the form of the value of utilization of slope bearing capacity V_u, which is determined as the ratio of sliding moments (M_a) to holding moments (M_p) (2) and the extent of the potential landslide niche (x) (Table 3).

$${\mathrm{V}}_{\mathrm{u}}={\displaystyle \frac{{\mathrm{M}}_{\mathrm{a}}}{{\mathrm{M}}_{\mathrm{p}}}}100\%<100\%$$

(2)

The stability analysis carried out showed the possibility of loss of bearing capacity of the analyzed slopes in almost every design section (

Table 4. Results of stability analysis in design section J1.

Method	Parameter	Computational Situation
		NPP	MaxPP
Bishop	x [m]	1.2	2.4
	% use of stability	106	92
Morgenstern–Price	x [m]	1.8	1.9
	% use of stability	98	86
Sarma	x [m]	2.5	2.8
	% use of stability	132	160

,

Table 5. Results of stability analysis in design section J2.

Method	Parameter	Computational Situation
		NPP	MaxPP
Bishop	x [m]	1.5	1.4
	% use of stability	118	118
Morgenstern–Price	x [m]	2.4	2.0
	% use of stability	109	106
Sarma	x [m]	3.1	3.0
	% use of stability	146	143

,

Table 6. Results of stability analysis in design section J3.

Method	Parameter	Computational Situation
		NPP	MaxPP
Bishop	x [m]	2.3	2.5
	% use of stability	213	212
Morgenstern–Price	x [m]	4.6	3.4
	% use of stability	184	190
Sarma	x [m]	5.8	5.5
	% use of stability	240	238

and

Table 7. Results of stability analysis in design section J4.

Method	Parameter	Computational Situation
		NPP	MaxPP
Bishop	x [m]	1.6	0.5
	% use of stability	451	1000
Morgenstern–Price	x [m]	1.5	1.9
	% use of stability	547	581
Sarma	x [m]	3.3	1.1
	% use of stability	258	530

).

In the case of the first design section, at the normal level of damming (NPP), without additional loading, only the Morgenstern–Price method indicated no loss of slope stability. On the other hand, at maximum damming level (Max NPP), potential loss of stability was indicated only by the Sarma method (Table 3). In the other three computational cross-sections (J2, J3, and J4), all the methods used indicated a potential loss of slope stability, but with a different range of impact (x).

Since, naturally, each of the adopted calculation methods gives different results, in order to better illustrate the horizontal extent of the landslide “x”, the average values obtained from the various methods, calculated for each situation, were summarized (Figure 11).

The measurements and calculations made it possible to quantify the predicted abrasion and compare the application of the Kachugin method and the methodology including slope slides due to sudden loss of stability. This analysis was carried out in the damming range between 120.0 and 121.5 m above sea level, the most typical hydrological situation of the reservoir. Since Kachugin’s method does not provide an answer to the question of the duration of abrasion, its effect in a given cross-section was converted to a 0.1 m increase in water level. In the case of stability analysis, on the other hand, the results of the various methods were first averaged over the given computational cross-sections. Since the calculation results indicated that even the maintenance of the minimum water level (120.0 m above sea level) is associated with a loss of stability of the cliff, it was assumed that potentially every 0.1 m increase in water level could be the cause of a landslide. As a result, a comparison of average maximum abrasion ranges for the Kachugin method of 17.8 m and for the landslide method of 37.1 m in the range of accumulation up to 121.5 m above sea level was obtained (

Table 8. The extent of abrasion in individual sections and the average value for the study area, determined by the Kachugin method and on the basis of stability analysis.

Cross-Section No.	Abrasion According to the Kachugin Method		Abrasion Due to Cliff Slide
	Average Abrasion per 0.1 m Rise in Water Level [-]	Maximum Abrasion Range [m]	Average Abrasion per 0.1 m Rise in Water Level [-]	Maximum Abrasion Range [m]
J1	0.82	12.30	1.30	19.50
J2	1.73	25.90	2.30	34.50
J3	1.54	23.10	4.20	63.00
J4	0.66	9.90	2.10	31.50
Average value	1.19	17.80	2.48	37.13

).

4. Discussion

Comparing the results obtained by the classical Kachugin method and by analyzing cliff stability, it is worth noting that, unlike the graphical evaluation of abrasion, the extent of the landslide determined by analytical methods was increased in only one case as a result of an increase in damming. In the case of the other cross-sections, rising water levels even reduced the extent of the landslide. At the same time, it is worth noting that the extent of the cliff landslide calculated in this way relates to only one episode, which can be revived in subsequent years, as a result of the progress of abrasion.

The plausibility of the predictions may be indirectly strengthened by slightly more detailed observations and analyses of the J4 design cross-section.

This cross-section recorded the relatively smallest width of the beach, which was 17 m at an elevation of 117.25 m above sea level, while in the other cross-sections, it was about two times greater. Thus, it would be expected that the proximity of the cliff in this area should cause, already at the damming up of the water in the reservoir to NPP, the activation of abrasion, while this is indicated neither by the developed forecasts nor by observations of the current state. In the described fragment of the shore, the largest beach slope angle (about 110) among those measured during the site visit was registered, which in turn, combined with the distinctly rocky nature of its surface, probably causes the dissipation of waves and lowering of water energy before its contact with the cliff. This would explain the current behavior of this section of the cliff, which, in the form of a “promontory”, deviates in a westerly direction, indicating a slower rate of abrasion at this location compared to adjacent zones.

At the same time, it is worth noting that regardless of the destructive impact of the reservoir’s water on the shore, due to its geological structure and morphology, it is prone to landslides. The activity of mass processes in the study area has already been indicated by [22], who observed in the Siedlątków area, in the abraded shore zone, a landslide of about 300 m² and a colluvium volume of about 700 m³. The high dynamics of shoreline processes and the interaction of erosion due to wave action with mass movements and can be evidenced by the fact that only 5 years later, only modest remnants of the landslide remained; almost all of the colluvium was boarded up [13,21]. The current survey work no longer showed visible traces of the aforementioned landslide, so all the landslide material has been removed deep into the reservoir.

These observations indicate that abrasion of cliff edges should be considered as a complex, interacting process resulting from wave action: erosion and transport of material toward the reservoir, as well as mass movements in the form of landslides in the cliff zone. Interestingly, a greater extent of the area at risk of loss of stability is carried by the maintenance of the normal level of damming than by the maximum level of damming, which is the opposite of the Kachugin method assessment. This indicates an important piece of information that, contrary to appearances, cyclic, even small (0.1 m) increases in the water level in the reservoir may be more dangerous from the point of view of rapid threats than its rapid rise (as in the case of a storm).

If the magnitude of the water level rise just by 0.1 m is taken as a reference level, then a simple division of the abrasion extent obtained by the Kachugin method by the value of the water level change in Jeziorsko Reservoir shows that the abrasion rate will be about 1 m per 0.1 m water level rise. However, if we also take into account the impact of cliff landslides, which can be determined from observations as occurring once every 10–15 years, the total abrasion rate increases to over 3 m/0.1 m of water level rise (as an average over the considered period of 15 years).

The results of the calculations correspond well with previous observations of the abrasion rate of the banks of the Jeziorsko Reservoir, which allow us to assume that when the high water level (NPP) is maintained for one-third of the year, it is about 1.3 m/year. Dividing this value by the 1.5 m difference in water levels in the reservoir and multiplying by 10 years and 3 (hypothetically assuming that damming persists throughout the year), we obtain a value of 3.9 m/0.1 m of water level rise, which is slightly higher than the sum effect of erosion and cliff landslides (3.7 m/0.1 of water level rise) (Table 8 and Figure 12). At the same time, this value is considerably higher than that implied by classical analyses using the Kachugin method.

To a certain extent, observations of the actual rate of abrasion confirm the hypothesis about the need to take into account other factors in assessing the rate and extent of abrasion than only those considered in the Kachugin method. However, there is still a noticeable underestimation of this process in the predictions made. This fact is probably influenced by factors related to measurement imperfections (e.g., the lack of a cast-iron information on the geotechnical properties of the soil exactly in the cliff zone), as well as the variability of ambient conditions over the multi-year period of analysis resulting from the operation of the reservoir (e.g., duration of damming, episodes of emergency damming above the MaxPP level, changes in the condition of water flow in the reservoir area affecting the change in the state of stress in the ground).

The obvious question is whether the adopted analysis methodology can be applied to other reservoirs. It seems so, although we are of the opinion that the key factor in this case is not so much the type of soil that builds the cliff, but the arrangement of geological layers in its area and the height of water damming in the reservoir. Such an observation is due, among other things, to the observation of the different response of the cliff to damming when calculating the stability of the bank slope. Also, the simple geological structure of the bank within the escarpment creates quite specific conditions for abrasion in the case of the Jeziorsko Reservoir. However, including all these variables in the analysis is extremely difficult, if only because of the long and variable period of their impact (differences in reservoir water levels).

5. Conclusions

The analyses carried out allow us to present the following conclusions:

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Kachugin’s classical geometric method does not take into account the dynamics of water level fluctuations and the impossibility of forming an abrasion platform and local loss of stability by the cliff. It seems that predicting the rate of coastal abrasion based on only Kachugin’s method may be underestimated, even more than twice.

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Observations of the processes and rates of shoreline retreat indicate the co-occurrence of shoreline erosion and landslide processes.

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Including cliff stability calculations in the abrasion analysis also allows better prediction of its rate and extent. Comparison of the results of the analysis and the actual abrasion processes observed over a period of 15 years, in the case of the Jeziorsko Reservoir, gives satisfactory results, although it indicates that still not all environmental factors conducive to abrasion are taken into account in the analysis.

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The adopted analysis methodology can be applied to other reservoirs whose regular height of seasonal damming causes active abrasive processes to occur in the zone below about 1 m from the maximum damming. The presence of a homogeneous soil layer in the abraded zone is also an important factor.

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The general conclusion is also that despite the fact that the law allows the construction of buildings in the abraded zone, such investments are exposed to destruction even located tens of meters from the edge of the water body. Thus, regulations for the erection of engineering structures in the coastal zone should not only address environmental-ecological aspects but also those related to geohazards.