Influence of Calculation Parameters on the Slope Stability of the Historical Rasos Cemetery in Vilnius (Lithuania)

By inergency On Mar 30, 2024

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1. Introduction

Many objects of cultural (e.g., museums, theatres, statues) and religious importance (e.g., churches, cemeteries, religious houses) are located on naturally or artificially shaped hills or slopes. In the past, it had a tactical importance; the object located on the hill was difficult to attack due to the terrain. The other reason was the exaltation (glorification) of the place over the panorama of the area so as to further ennoble the object located there. In such cases, the stability, the potential consequences of insufficient fulfilment, and the minimum stability conditions are crucial. The consequences of exceeding the permissible stability conditions, based on the example of a geotechnical assessment of the effects of a landslide on an ancient monastery in central Italy, are presented in the paper [1]. The slope stability problem is not related to any specific area of the world. These issues exist in different countries, including the region of Western Macedonia in northern Greece [2], the mountainous areas of the Himalayas [3], Southwest China [4], or India [5,6]. Fatalities and other disastrous consequences caused by landslides have been described, i.e., in studies [7,8,9,10]. An important issue that must be taken into account in the analyses of the slope stability is the influence of the selection of mechanical parameters of the soil layers forming the slope [11]. An important issue at the stage of the slope stability analysis is the correct interpretation of the results of the geotechnical site investigations of the slopes [12,13,14]. Today, in order to identify places where a landslide may occur, probabilistic analyses of the stability of slopes in large areas are also carried out [15,16], also taking into account changes in groundwater pressure [17] and rainfall conditions [18].

This paper presents the assessment of the slope stability for the Rasos Cemetery in Vilnius (Lithuania). As a result of a part of the slope sliding, some of the cemetery objects were destroyed by being covered with soil. This study includes an analysis of the soil and water conditions of the slope as well as a list and description of the types of soil forming the individual layers. The paper points the results of incorrect repair attempts with the use of an anchored geotextile. The main part of this paper presents an original proposal of construction works that will ensure both the full stability of the slope and safety of all graves based on Polish standards [19] and European standards [20]. This is a very important value that determines the safety of slope stability. The output of the analysis is a factor of safety, defined as the ratio of the shear strength (or, alternatively, an equivalent measure of shear resistance or capacity) to the shear stress (or another equivalent measure) required for equilibrium. The article attempts to fill the research gap in determining the effects of adopting the calculation approach (characteristic values, DA2, DA3a, and DA3b in accordance with the geotechnical standard applicable in the European Union—Eurocode 7: Geotechnical design [20]) on the key calculation parameters describing slope stability—the factor of safety (FOS) and showing how the correct selection of calculation parameters is an important step in the design procedure with recommendations. The analysis was carried out using calculations: analytical (with the Fellenius method) and numerical in GEO5 software version 2023 (with the Bishop, Fellenius, Spencer, Janbu, and Morgenstern–Price methods).

2. The Description of the Terrain Conditions

An example of the slope stability analysis presented in this article concerns the actual terrain and soil conditions for the Rasos Cemetery in Vilnius. This necropolis and the people buried there are important for their historical significance for Poles, Lithuanians, and Germans. Many of the historic burial sites located in the cemetery are in a bad technical condition. This is mainly due to their location; the hill slides down as a result of geotechnical processes, covering the tombstones with soil. Therefore, it is necessary to properly stabilize the slope in order to protect these objects against complete destruction.

To stabilize the slope, the designer proposed a solution consisting of its surface reinforcement with the use of a geotextile anchored with steel bars. The anchor system was made of S400 steel bars with a diameter of ⌀16 mm and a length of about 1.5 m. The anchors were made of bars inserted perpendicular to the ground surface and bars embedded at an angle of 40° to the perpendicular bar up and down the slope. A 30 × 30 cm grating (made of the same steel bars as the anchors) was used as an anchoring system on the surface of the ground. The spacing between the elements of the anchoring system was approximately 3.0 m; Figure 1 shows a view of the top surface of the anchoring system.

In practice, the applied reinforcement solution turned out to be ineffective, the fertile soil slid over the surface of the geotextile and partially covered the graves located both on the slope and those at its foot with soil—Figure 2.

Due to the intercultural nature of the Rasos Cemetery in Vilnius and its social importance, it was advisable to perform geotechnical construction works to ensure both the full stability of the slopes and the safety of users and graves. Proposed works were aimed to prevent further damage to both the graves located along the entire length of the slope.

Therefore, the following expert activities were proposed [21]:

(a)

Complementing geological and engineering research to the extent that allows for the full recognition of geotechnical groundwater conditions and the preparation of a geotechnical design in accordance with [20]. This geotechnical design should contain the elements provided in the standard, the following in particular:

–: The determination of computational geotechnical parameters;
–: The determination of partial safety factors for geotechnical calculations (including the required slope stability factor of safety);
–: The specification of the research necessary to ensure the required quality of earthworks and specialized geotechnical works;
–: The determination of the scope of the necessary monitoring of the slope stability, both during the execution of construction works (related to the slope stability) and after their completion;
–: The risk assessment of the occurrence of a hazard during these construction works.

(b)

After the recognition of the subsoil and adopting the method of slope stabilization, the detailed technology of construction works, including the methods and stages of their control, in particular the works to be covered, should be specified.

(c)

The applied method of the slope stabilization should ensure both their safety and the safety of users; moreover, it must not interfere with the existing burial sites.

(d)

After the stabilization of the slopes, their surface should be reinforced in accordance with their slope inclination.

The research was supplemented with an additional cone penetration test (CPT), heavy dynamic probing (DPH), and exploratory drillings. The cemetery is located in a hilly area of variable height. The difference in level between the foot and the top of the slope is up to 16 m. The slope is located at an altitude of 147.80–163.80 m above sea level, and the maximum slope angle is 35°. The geomorphological structure in the analyzed area is influenced by the geological phenomena of the Medininkai hill in Vilnius. The results of the subsoil research were obtained from geological documentation [22]; eleven types of soil in four geological groups were distinguished, as shown in Table 1.

New research points allowed for the development of five geological cross-sections in the places where areas with the greatest inclination occur. The slope stability assessment carried out by the designer showed a safety factor of 1.3. The geotechnical parameters that were adopted for the analysis (for example non-zero cohesion assumed for silty sands) raised concerns. Additionally, the assessment of the slope stability was performed on the basis of one pivot point, and the crowd load at the top of the slope was not taken into account. Therefore, in order to verify the design assumptions, our own analysis of the slope stability was carried out. This cross-section was also analyzed by the designer. Additionally, for detailed considerations, the geological cross-section with the greatest slope inclination was adopted. The locations of these cross-sections are shown in Figure 3; they are located near the tombstone “Black Angel” visible in Figure 2.

The cross-section of the slope from the geological documentation [22] is shown in Figure 4. There is a large thickness of anthropogenic soils, for which the designer assumed zero values of the angle of internal friction and cohesion. At the SZ-1 research point, CPT probing (Figure 4—red diagram) was carried out, while at the DZ-2 and DZ-3 points, DPH probing (Figure 4—blue diagram) was performed. The circled numbers in Figure 4 indicate the type of soil in accordance with Table 1.

The interpretation of the soil test results and the adoption of the computational parameters of the soil layers performed by the designer raised some doubts of the authors of this study. For example, in the analyzed cross-section, the following values were indicated in the description of the DZ-2 cross-section at the mid-research point:

–: Soil no. 11, number of strokes of the DPL probe N₁₀ = 22.5;
–: Soil no. 6, number of strokes of the DPL probe N₁₀ = 50.0.

The table [22] presents the following parameter values for determining the mechanical properties of individual soils:

–: Soil no. 11, number of strokes of the DPL probe N₁₀ = 35.5;
–: Soil no. 6, number of strokes of the DPL probe N₁₀ = 79.0.

3. The Analysis of the Slope Stability Factor of Safety

The factor of safety (FOS) is a measure of how stable a slope is against potential failure or a landslide. It is defined as the ratio of the available shear strength of the soil to the shear stress required to cause failure. The basic formula for calculating the FOS for a slope is in Equation (1):

$F O S = \frac{C + σ \cdot t a n φ}{τ}$

(1)

where:

$C$ —cohesion of the soil [kPa];
$σ$ —normal stress [kPa];
$φ$ —angle of internal friction [°];
$τ$ —shear stress [kPa].

This formula assumes that the slope is homogeneous, isotropic, and has a constant slope angle. However, in reality, the value of the FOS for a slope is determined by several factors: soil type, slope angle and geometry, water content, vegetation, loading, and seismic activity. Taking into account these important factors, the general approach to the methodology for determining slope stability and determining the factor of safety value is presented in Equation (2):

$F O S = \frac{s u m o f m o m e n t o f m a x i m u m r e s i s t i n g f o r c e s}{s u m o f m o m e n t o f m o v i n g f o r c e s} = = \frac{s u m o f m a x i m u m r e s i s t i n g f o r c e s a r o u n d t h e a r c}{s u m o f m o m e n t o f m o v i n g f o r c e s a r o u n d t h e a r c} .$

(2)

In the first design approach, the slope stability analysis was performed based on the geological cross-section adopted by the designer. Because of the intention to present the results of the analysis to the designer of the slope protection, who did not use any numerical program, the calculations were carried out by the analytical method using Excel spreadsheets. The slope stability was tested for four pivot points to determine the most unfavorable position. The first of the pivot points (Figure 5a) was adopted using the slope geometry according to the Fellenius method, the second was adopted as calculated by the designer (Figure 5b), the third point was selected excluding a strong layer of soil no. 6 (Figure 5c), and the fourth one includes only layers of anthropogenic soils (Figure 5d). All schemes of the slope slip surface along with the division into calculation blocks are presented in Figure 5.

The calculations were carried out taking into account four different design approaches described in the standard [20]:

–: For the characteristic values of soil parameters and loads (such a situation does not appear in EC7 as a stability analysis);
–: DA3a design approach: A1 + M2 + R3—used to verify slope stability in Poland;
–: DA3b design approach: A2 + M2 + R3;
–: DA2 design approach: A1 + M1 + R2—used for calculations of the foundation in Poland.

The individual groups of parameters are listed in Table 2. The analysis included three groups of soil parameters:

[A]: The first group includes parameters read directly from the geological documentation [22];
[B]: The second are the parameters adopted by the designer;
[C]: The third are the parameters specified by the verifier—the co-author of this article.

The third group of parameters [C] was adopted by the verifier in accordance with the Polish standard [19]. This was due to doubts as to the correctness of the interpretation of the test results and zero parameter values determined for soil layers 1 and 2 (the zero values of these parameters may indicate that the results of the geotechnical tests have not been interpreted). This approach can be interpreted as an assumption that layers 1 and 2 will act as a load. However, their zero values adopted for the calculation for design scheme 4 always gave zero values of the stability factor of safety.

The parameters of the individual layers were determined, taking into account their physical characteristics, grain size composition, and the results of probing. New parameters were adopted for the test results in the analyzed geological cross-section. The parameters of anthropogenic soils were determined analogically; their zero values adopted for calculations (in the calculation scheme no. 4) always gave zero values of the stability factor.

Using the descriptions contained in the geological documentation, taking into account a possible reduction in shear strength [23], the following parameter values were assumed:

Additionally, the zero consistency was taken into account for non-cohesive soils, which were assumed to be non-zero for parameter groups [A] and [B] from incorrectly reading the test results. The calculated values of the slope stability (factor of safety) are presented in Table 3; values lower than the minimum value assumed by the designer 1.30 are marked in bold. The table shows the zero values of the stability (factor of safety) for scheme no. 4 (Figure 5d), which result from the assumption of zero strength parameters of anthropogenic soils.

It should be noted that the consideration of non-zero parameters for anthropogenic soils in the calculations resulted in the appearance of the slope stability factors for the fourth pivot point. Regardless of the adopted standard calculation approach [20], these factors (apart from the design approach based on characteristic factors) are lower than the required value of 1.3.

In the next design approach, the cross-section, marked in Figure 3 with the orange line, was adopted. The course of this cross-section was assumed to reach the area of the slope with the greatest inclination. The slope stability factor was determined for two positions of the pivot point. The first of them (Figure 6a) was adopted using the slope geometry according to the Fellenius method; in the case of the second point (Figure 6b), the “strong” layer of soil no. 6 was excluded. The schemes of the slope slip surface divided into calculation slices are presented in Figure 6.

As in the case of the cross-section adopted by the designer, the first calculations were carried out using the calculation parameters for individual groups of soil parameters. The results of the calculations are presented in Table 4, while the values lower than the minimum value assumed by the designer 1.30 are marked in bold.

4. Discussion

An analytical analysis of the slope stability factor was performed for two cross-sections using six calculation schemes. In each of them, calculations were carried out for three groups of soil parameters and for four design approaches. The analysis showed that, regardless of the adopted calculation approach, the required slope stability factor was not obtained. If the value of the factor of safety is less than 1.0, the slope is unstable. In the range of values 1.0–1.3, there is a serious risk of slope instability, and only when the factor of safety value reaches above 1.3 is the slope classified as stable.

If the characteristic parameters [A] were taken into account in accordance with the geological documentation [22], the slope was not stable for schemes 3, 4, 5, and 6. Moreover, it should be emphasized that the analyzed slope was not stable for all the schemes in the case of the DA3a design approach. Similar results were obtained for the analysis of the slope stability for the group of soil calculation parameters that were assumed by the designer [B]. The analysis carried out on the basis of the non-zero cohesion value of soils no. 4 and 6 (sands with silt addition and fine sands) showed only a slight increase in the stability factor, averaging 5.5%. The assumption of zero anthropogenic soils parameters resulted in an increase in the slope stability in the section analyzed by the designer. Nevertheless, it does not reflect the actual parameters of these soils, which did not slide down the slope, which would have happened with these parameters.

The adoption of soil parameters in accordance with Polish standards [19], including parameters for anthropogenic soils, resulted in a decrease in the value of the slope stability factors for computational schemes 1, 2, and 5 and their increase for schemes 3 and 6. It is clear that the required value of the slope stability factor should be ensured regardless of the adopted pivot point, and it should be analyzed in the most dangerous cross-section. Analyses based on the cross-section adopted by the designer give much higher values of the slope stability factor than those obtained in the cross-section with the greatest inclination. In this cross-section, regardless of the adopted soil parameters, for any of the design approaches, the value of the slope stability factor assumed by the designer was not obtained.

For the additional validation of the analytical calculations, the slope stability was checked using the GEO5 software version 2023. The obtained values of the slope stability factor were lower than the results obtained analytically. In the cross-section with the highest slope inclination, the minimum value of the factor was 0.87 for the DA3a calculation approach—Figure 7—and analytically—0.96.

The comparison of the slope stability factors obtained with different design approaches (in relation to the DA3a—approach adopted in Poland) shows that the most unfavorable stability factor is as follows:

–: Approximately 43% lower than the result obtained from the characteristic values;
–: Approximately 21% lower than the result obtained using the DA2 design approach;
–: Approximately 24% lower than the result obtained using the DA3b design approach.

The comparison of both methods of determining the slope stability factor (analytical calculations with the Fellenius method and using the GEO5 software) indicates that the calculated values are lower than those obtained with the GEO5 software. This difference is on average 15%, which is less than 0.16 of the value of this factor. The calculations using the GEO5 software are more accurate than analytical calculations; they result from a greater number of checked pivot points. After the implementation of the geological cross-section and soil parameters, the software automatically calculates the stability factor, reducing human work to a minimum. Additionally, the software used in the analyses makes it possible to test the slope stability in a greater number of cases by using interpolation. However, having some experience and taking into account the arrangement of layers in the slope cross-section, it is possible to determine the value of the slope stability factor with sufficient accuracy by means of analytical (engineering) calculations. Another issue is the assumption of the required value of the slope stability factor. The designer had assumed the value of 1.30, which in the literature is recommended for the full identification of the subsoil and precise determination of the parameters of geotechnical layers [24,25]. In the case of basic identification of the subsoil, the factor value is assumed as 1.4 ÷ 2.0 depending on the risk to the safety of this earth structure [24,25,26]. The influence of uncertainty in the value of geotechnical parameters on the estimated value of the slope stability factor has been described many times [27,28,29,30,31,32,33,34]. According to the authors of this manuscript, in the analyzed case (the absence of full recognition of geotechnical parameters and low risk to human life, which results from the type of object), the recommended value of the slope stability factor should be at least 1.50.

Table 5 shows the results of slope stability calculations for the determined most dangerous section of the slope and for different calculation methods using the GEO5 program. The parameters of soil group [C] were used for the calculations; for the parameters of groups [A] and [B], the program calculated the zero slope stability factor in anthropogenic soils. In the table, the results determined by the Fellenius method, which was also used for analytical calculations are indicated in bold.

The calculations of the slope reinforcement were performed assuming the minimum factor value of 1.50. After analysing the geotechnical conditions of the slope, a design solution involving the use of steel elements to stabilize this object was proposed. The proposed solution and works should be designed so as to prevent covering, damaging, or destroying the tombstones during construction works. Therefore, the proposed method of ensuring the slopes’ stability is their stitching with steel sections or pipes placed perpendicular to the surface of the slip or landslide plane. The length of these elements should ensure their proper anchoring in the ground by ensuring the bearing capacity of soils on the side surface of the sections. It was proposed to use steel pipes with a diameter of 508 mm and a wall thickness of 10 mm, which have proved successful in stabilizing the slope at the St. Anne’s church in Warsaw [35].

It has been calculated that the anchoring should be made at four points of the slope cross-section with sections 10.0 m, 12.0 m, and 15.0 m long [21,36]. The length of the sections was determined based on the necessary anchoring length in the substrate and taking into account the height of the landslide body. The methodology for determining the anchorage length was presented in the study [37]; in the analyzed case, for the parameters of soils forming slopes, the anchoring depth is 5.0 m below the expected slip line. The lateral spacing between the rows of pipes should be about 5.0 m, but ultimately, the pipe layout should take into account the location of burial sites. The proposed design solution was developed to ensure a slope stability factor (in the cross-section of the greatest inclination) of at least 1.50. The proposed solution will ensure both their stability and the safety of users and will not interfere with the existing burial sites. Below, the proposal of the steel pipe arrangement in the analyzed area of the cemetery, where the inclination of the slope has the highest value, is presented—Figure 8.

5. Conclusions

The article shows that in order to properly determine the slope factor, it is extremely important to appropriately adopt the soil parameters for the calculations and to select the geological cross-section. The soil parameters should be carefully determined based on the interpretation of the results of field research, taking into account their statistical treatment. The parameters assumed for calculations should ensure a minimum of a 95% confidence level. The soil parameters in the analyzed slope, adopted in accordance with Polish recommendations, meet this condition.

Based on the recognition of the subsoil, the designer had assumed the geotechnical parameters of the slope cross-section layers. In order to ensure the slope stability, the designer had assumed zero values of mechanical parameters for anthropogenic soils. This assumption is correct only for the selected pivot point, but it is not valid for the slope stability analysis for other point locations. In our opinion, greater incorrectness is the assumption of the slope cross-section not in the line of the maximum slope inclination but along the research points. By adopting the cross-section in this way, the value of the slope stability factor was overestimated by 0.23 in comparison to the section with the highest slope using the analytical analysis. In the case of the analysis using the GEO5 program, the difference was even greater, ranging from 0.23 to 0.42 depending on the design approach, with an average of 0.31. Regardless of the terrain conditions of the analyzed area and difficulties with the use of field research equipment, it is necessary to analyse the stability of slopes in the steepest (unfavorable) geological cross-section of the slope.

Regardless of the method of calculation, the value of the slope stability factor for the values of the characteristic parameters calculated numerically oscillates around 1.0. This indicates the need to undertake protective works, especially in the sections with the steepest slope. In the analyzed case of the stability of the slope, where the historic Rasos Cemetery in Vilnius is located, the calculation results indicate the need and justification for carrying out specialized earthworks in order to increase the stability of this slope (achieving the required factor of safety value—a minimum value 1.3 and, even better, a value of 1.5).

The analyses carried out on the discussed issue allow for the development of general conclusions for various historical places located in the area affected by earth slopes. The main recommendation is the need for special care in determining geotechnical parameters, taking into account local water and ground conditions and the correct selection of the slope cross-section for analysis (which will ensure the ability to properly determine the critical slope slip surface). Only a careful and thorough analysis of these factors (as an element of the measuring and monitoring the sustainability process) allows us to confidently determine the safety of the slope in a given location.

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