Keywords

1 Introduction

The hill on which the unique historical and architectural church is located, is special for Ukraine, as the birth of Christianity in Ukraine began from this place. According to the chronicle “The Tale of Bygone Years”. The first preacher of Christianity in the lands of Kievan Rus: called “Andrew the First”, erected, in the first century AD, a Cross on this site and foretold the emergence of a great city. Wooden and stone churches in the name of Andrew the First were built and destroyed as time passed on this site. In 1747, the construction of St. Andrew’s Church started with the project of Bartolomeo Rastrelli (Fig. 1).

Fig. 1
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Study area. Location of St. Andrew’s Church in Ukraine

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The historic building is constructed on a very complex geological landslide hill, which is washed by groundwater and spring waters.

At time of construction, complex engineering and geological studies of the area under construction were conducted and extensive work on the construction of strip stone foundation was carried out to create a massive foundation—church stylobate and its porch. During the construction works, the soil was removed, and groundwater and spring waters were drained. The foundations of the stylobate is made of natural stone and broken brick in lime-stone mortar, were laid at the depth of 3.5 m from the stylobate floor on the eastern side, 4.8 m on the western side. Given the problem area (such as the risk of landslides). Regular monitoring and fortification works are carried out. There are ravines on the slopes of the hill, where active displacements and erosion processes develop (Fig. 2). Around the development site there is a complex of unfavorable physical and geological phenomena such as landslides, considerable thickness of fill-up ground, significant ground heterogeneity, mechanical suffixation of clay particles into an existing inactive gallery, and external erosion of the hill massif. The base of the foundations of the southern, western and northern Church facades is eolian-deluvial loess-like loamy sands, which have sagging properties. The base of the foundations at the eastern part is morainic loam. Hydrogeological conditions are characterized by the presence of two groundwater levels.

Fig. 2
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An example of the active development of landslide processes with active developments and erosion processes on the slope of the Church

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Due to high landslide risk of the hill and great cultural value of the building, the historical and architectural site needs constant monitoring, strengthening and preservation for posterity [https://andriyivska-tserkva.kiev.ua/].

The World Heritage Convention of 1972 aimed at promoting and supporting the conservation of the world’s cultural and natural heritage. The basic principles of the convention states that the obligation of each participating state is to ensure the identification, protection, preservation, presentation and transmission of the cultural and natural heritage located in its territory to future generations (UNESCO 1972; The World Heritage Convention 1972).

The methodological issues and practical realization of these problems are analyzed in the in the publications of authors (Atzeni et al. 2015; Mainwaring and Olsen 2018; Miranda et al. 2020; Barla et al. 2014; Highland and Bobrowsky 2008; Carvalho et al. 2018; de Brito et al. 2018; Farenyuk et al. 2021; Kaliukh et al. 2018a, b; Lollino 2014; Mazzolani and Calado 2019; Zanakis et al. 2003; Papadopoulos and Vayas 2019 and others), building codes and documents EN 1992-1-1-2004, fib Bulletin 34, among others.

With respect to the usage of remote sensing of the earth from space, there are many works by scientists: Greben et al. (2020), Baum (2014), Trofymchuk (2020), Khyzhniak and Fedorovskyi (2020) and many others. A number of specialists worked on attracting information technologies to study landslide-hazardous areas, objects located on them, modeling and determining landslides, monitoring areas and to solve environmental and recreational and economic issues (Popov et al. 2020; Yue et al. 2021; Piestova et al. 2019).

GIS methods for creating landslide probability maps have been studied by several authors (Aleotti and Chowdhury 1999; Kanungo et al. 2009, Mersha and Meten 2020). The analysis in GIS can be numerical using actual data, or qualitative with a probability of occurrence of the event. Qualitative methods include geomorphological analysis and overlay and intersection inventory methods, with expert judgement, qualitative maps are created.

1.1 Surveyed Structural Damages and Previous Landslides

The visible superstructure of the church is based on a slightly wider underground two-story foundation. The base of the foundations of the eastern part is morainic loam.

During structural surveys, it was discovered that the superstructure had significant damages as follows:

  • Vertical and inclined cracks with a width of up to 2.0 cm in the walls of the superstructure.

  • Cracks width up to 2.0 cm (Fig. 3) in brick vaulted ceilings.

  • Walls and ceilings soaking and fungosity;

  • Deviation from the superstructure vertical wall.

Fig. 3
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Vertical crack with a width of up to 2.0 cm

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Whereas for the runway walls, the following damages were detected:

  • Diagonal cracks with a width of up to 3.0 cm;

  • Frost destruction of the brickwork and deviation from vertical of the reinforced concrete retaining wall,

  • Through cracks.

  • Local destruction of the outer layer and brickwork mortar.

The main source of detected damages was the uneven foundation subsidence, caused by the presence of subsiding ground and sloping ground movements.

In the 1970s, a landslide occurred, after which, the slopes of the hill were fixed with semi-rings of Gambia piles up to 20 m deep, on which a reinforced concrete support pillow-block was mounted, and an observation deck was arranged on top of it. Another landslide was recorded in June 2012.

2 Methods

This research included data collection and analysis, use and processing of remote sensing data, data from geographic information systems, analysis in the Earth Observation (EO) Browser service using the java script programming method, mathematical calculation of the stability of the structures, modeling of the stress-deformed state of the object and adjacent territory and recommendations for consolidation (Fig. 4).

Fig. 4
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Structure scheme of the research work

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2.1 Data Collection and Organization

Data necessary for this study were collected from various sources. The study of relevant literature from published articles and monographs, data collection on the object of the study and the surrounding area, topographic map of 1: 50000, geological maps, radar-location images Sentinel-1A, B (spatial resolution 10 m) and images from Google Earth (spatial resolution up to 1 m). Ground studies and analysis of geological conditions of the study area were also conducted.

2.2 Use and Data Processing of Remote Sensing

Compared to traditional methods of studying the earth surface, remote sensing methods have significant advantages in terms of the scale of survey, obtaining global and local information about objects and their monitoring. The use of Persistent Scatterers (PS) of interferometric data allows the processing of a large number of different-time/radar-location images obtained by radar locators with synthesized aperture (PCA) from the satellite Sentinel-1 of European remote sensing system Copernicus, which enables the determination of vertical displacements with an accuracy of 4 mm/year, including the shear activity of research objects in large areas, while determining specific places of displacement.

The use of optoelectronic data from space surveys allows the detection landslide-hazardous areas, buildings located on them, active and temporarily stable landslides, and to monitor the dynamics of their movement, which enables a fast response to the findings, namely to collect material, select photos, maps, etc. on the object under study and take timely action to prevent emergencies.

Google Earth space images were used to further explore St. Andrew’s Church and the surrounding area. On the slope of the object under study on June 28 2012, there was a landslide. Figure 8 shows a map of time changes before and after the landslide, indicating the movement and area of the landslide. Therefore, the analysis of space images made it possible to assess the scale of the landslide hazard, calculate the area of the affected areas of the slope, and provided recommendations for specifying the location of ground research to further avoid negative consequences that could lead to emergencies.

2.3 Involvement of Geographic Information Systems

The geographic information system ArcGIS, was used to determine the area of the monitored object and its specific features (terrain, the presence of plantations, roads, water, buildings, etc.).

The spatial distribution and density of landslides mainly depend on topography, weather conditions, geology, land use/soil cover, and anthropogenic factors. Topographic factors include slope, aspect, and curvature based on digital elevation model data (DEM) as shown in (Fig. 5).

Fig. 5
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Slope, aspect, and curvature based on digital elevation model data

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Slope is a very important parameter for landslide studies because it has a direct relationship with landslide occurrence (Yalcin and Bulut 2007). Landslides are more likely to occur on higher slopes as a result of gravitational stress. The curvature map shows concave, convex, and flat surfaces (Fig. 3). After a rainfall event, a convex or concave slope contains more water and holds it for a longer period of time (Lee and Talib 2005). The more positive or negative it is, the more likely a landslide will occur. Aspect refers to the orientation of the slope, which is usually given in degrees from 0 to 360. It is widely viewed as an important factor in landslide studies because it controls slope exposure to sunlight, wind direction, precipitation (degree of saturation), and break conditions (Komac 2006).

Land use is the most important factor influencing the formation of landslides resulting from rainfall (Fig. 6). Changes in land use/cover due to anthropogenic activities such as deforestation, grazing, intensive farming and cultivation on a slope that is extremely steep can lead to slope instability. Vegetation contributes to resistance to slope movement. Vegetation reduces the effects of erosion and increases slope stability.

Fig. 6
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Land use

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Sentinel hub is open-source data. The EO Browser service provides access to space images of both visible and radar range. For monitoring, space images in resolution of 10 m per pixel are available (Fig. 7).

Fig. 7
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The maps of water saturation of the soil

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Fig. 8
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Identification of landslide-hazardous areas according to Google Earth

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The maps of water saturation of the soil were obtained using the EO Browser services. Combinations of images and selection by various criteria were used in the java scripts language. Soil moisture saturation maps were obtained.

2.4 Mathematical Calculation of Slope Stability, Modeling of Stress–strain State of the Object and the Surrounding Area and Recommendations for Strengthening

Calculations were performed taking into account the zones of weakness and gaps in the soil caused by the suffusion of soil into the drainage system of the building. This made it possible to obtain the values of the stress–strain state for the load-bearing civil structures of St. Andrew’s Church and to compare the numerical results and standard values of the strength of the main building structures. Software LIRA 9.6 (Ukraine) was used for the finite element method, the average size of the grid was 0.3 m. A model for the stabilization of the foundation using the method of “grounds jet grouting” was carried out on the basis of the calculation scheme, which took into account the detected cracks in the cross section of the masonry and the foundation in the wet state (Fig. 7).

The location of “jet”-columns under part of the object’s foundations was taken into account in the simulation model by changing the soil deformation modulus from the natural state to the weighted average deformation modulus and jet grouting jet-columns “jet grout”, which was determined by the formula (Farenyuk et al. 2021):

$$ \overline{E} = \frac{{(A_{bn} \cdot E_{bn} ) + (A_{jt} \cdot E_{jt} )}}{{A_{bn} +A_{jt} }} $$

where

\(\overline{E}\) :

is the weighted average module of stabilized ground deformation under foundations site.

\(A_{bn}\) :

is area of reinforced site under foundations without regard to “jet”-columns area.

\(E_{bn}\) :

module of ground deformation in natural state.

\(A_{jt}\) :

area of “jet”-columns on the site under foundations.

\(E_{jt}\) :

module of “jet”-columns material deformation.

A brief characteristic of the calculation options is given in the Table 1.

Table 1 “Building foundation” system calculations options
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To determine the effectiveness of the actions to strengthen the building of St. Andrew’s Church, several calculation were conducted, which also took into account the transverse existing cracks in the building. Different variants of water saturation of the base under the whole church building and its stylobate part were considered.

Modeling of soil water saturation in the calculations was performed by attributing values of soil properties corresponding to water saturation. The appearance of zones of weakening and voids in the soil due to suffusion into the drainage system located near the foundations was also taken into account. Modeling of base watering was carried out only on areas of foundations that were not stabilized by the “jet grouting” of the base.

3 Result and Discussion

The ArcGIS geographic information system was used to determine the boundaries of the monitoring area with the studied object, its features (terrain, presence of forest plantations, roads, water reservoirs, buildings). The particularity of the location required the implementation of space photography of ultra-high spatial diversity on the eastern side of St. Andrew’s Church. The selection of different-time space images for the period of 2012–2019 was carried out for a certain parts. All selected images underwent orthorectification procedure based on ground data, followed by determination of the landslide-prone area (Fig. 8).

In the first stage, a stability analysis was carried out regarding the landslide hazard slopes of the studied territory (Fig. 9). Based on the historical materials study, visual inspection of the slopes adjacent to the St. Andrew’s Church building and performed calculations, it was established that a significant part of the St. Andrew’s Church hill slopes were in a state close to ultimate equilibrium. At the second stage, the analysis of the stress–strain state of the building and foundation soil was carried out using the graphic model of the stylobate block (Fig. 10) and building constructions of the superstructure of the St. Andrew’s Church (Fig. 11).

Fig. 9
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Example of the results of calculation of SAC hill landslide hazard

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Fig. 10
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General view of the computational model of the SAC stylobate block installed above-stylobate slab

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Fig. 11
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General view of the computer model of the church building on the south-eastern side

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The calculations were carried out considering the results of visual inspections and foundation soil deformations calculations. In building numerical modelling, the following three groups of the “building—foundation” system stress–strain state calculations were performed:

  1. 1.

    Group 1—the stress–strain state calculation to determine the causes of the cracks’ occurrence in the building and its stylobate block walls in cases of the values of soil properties in a natural state, the water saturated foundation soils under the entire of St. Andrew’s Church building and its stylobate block, as well as in other unfavorable cases.

  2. 2.

    Group 2—the calculation to determine the actual stress–strain state of SAC structures considering the damage recorded during their visual inspection. The modeling was performed during several stages:

    • First stage: the calculations were performed to determine the causes of cracks in the walls of the church building and its stylobate part with the characteristics of the base soil in their natural state; modeling of a base soaking under the entire church building and its stylobate part; modeling of a foundations base soaking at the north-eastern part of the church building; modeling of a soaking of the stylobate foundations base and the south-western and central parts of the church building.

    • Second stage: the calculations were performed to determine the actual stress–strain state of the building structures, considering damages detected during the visual inspection.

    • The third stage: the calculations were performed to forecast the stress–strain state of the building structures under the possible conditions of the base operation.

      The design scheme of the building considered the through cracks detected during the visual inspection. The occurrence of loosening zones and voids in the soils due to suffusion from the adit systems located in the immediate vicinity of the church foundations was also considered. The first stage of calculations was designed to model the stress–strain state of structures under various possible operating conditions of the base, and to determine the causes of cracks. For the second and third stages of calculations, the detected through cracks in the brickwork were considered in the building analytical scheme. In addition, cracks in the overstressed sections of the foundations obtained by the first stage of calculations were modeled. The results of the second stage of calculations allowed to estimate the actual stress–strain state of the structures. The results of the third stage calculations allowed to assess the changes in the structures stress–strain state if the base was soaked.

  3. 3.

    Group 3—mathematical modelling of the of St. Andrew’s Church structures stress–strain state in case of possible degradation of the physical and mechanical characteristics of the foundation soils. In the calculations, the base soils soaking was modeled by assigning to the soils underlying the foundations, parameters that corresponded to water saturation state (based on the engineering geological survey data). Accordingly, to model most unfavorable conditions, reduced stiffness coefficients were assigned for some base areas or for the entire foundation.

Based on the results of calculations, we may conclude that the main cause of cracks in the masonry of the load-bearing elements of the church and stylobate are the excessive values of relative deformations in the foundation, along with the unstable loads resulting from the structural system of the building.

Modeling of the soaking of the base showed significant overstressed zones, which indicates a probable additional expansion of cracks and the possible emergence of new ones, with an exception of the soaking base of the foundations at the north-eastern part of the stylobate, where the building is somewhat leveled, relative deformations are reduced and, in turn, zones of overstressed areas are reduced (Farenyuk et al. 2021; Slyusarenko et al. 2022).

The actual stress–strain state of structures for the period of inspection is characterized by the presence of extremely tense zones in which the values of the effective tensile and compressive stresses are at the limit of the strength of the masonry as follows:

  1. (a)

    Maximum tensile stresses:

    • Foundation areas lying below the wall of the main facade of the stylobate at its intersection with the foundations under the transverse walls;

    • Areas of masonry wall of the main facade of the stylobate below the window openings, and in places adjacent to the transverse walls of the stylobate;

    • Sections of walls and ceilings on the second floor of the stylobate in the area of the main entrance to the church;

    • Areas of the church ceiling at the places adjacent to the brick cylinder of the dome;

  2. (b)

    Maximum compressive stresses:

    • Local areas of destruction of masonry (crumpling) in places where the change of marks of the intersecting foundations’ sole comes in contact with the stylobate walls (Fig. 12).

Fig. 12
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Scheme of the foundations of the church building and the stylobate part with the indication of the marks of their pedestal

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The values of the main stresses in the walls of the church building do not exceed the strength of the brickwork, except for local areas on the floor at the junction with the brick dome. At the same time, the brickwork of the church floor (ceiling of the 2nd floor of the stylobate) in the area of the main entrance and the iconostasis is within maximum allowable stresses. Overstressed areas are identified in the masonry of the stylobate foundations and in the wall of its main facade.

To predict the change in the stress–strain state of the load-bearing structures of the church building and stylobate when changing the operating conditions of the foundation, another numerical simulation for stresses was made to simulate the soaking of the foundations of stylobate, including its cracks. The results of the calculation shows an establishment of the structural system of the church building and stylobate that is extremely sensitive to additional deformations at the base due to soaking. Such sensitivity is manifested in the appearance of additional areas of overstrained sections of brickwork, where the values of tensile stresses is increased by 50–200%. Such changes are also applicable to stylobate structures, where the calculation shows the largest changes in the stress–strain state. (The values of the main tensile stresses in the roof of the church building are increased by 50–60%). These tensions will inevitably provoke the appearance of new cracks in the load-bearing structures of the stylobate, the church building and the opening of existing ones.

Given the current technical condition of the building, the process of cracks opening may lead to the destruction of individual structural elements and might be critical to the stability of the building.

4 Conclusions

Effective methods of monitoring changes of archeological buildings should include the use of radar-location and optoelectronic data of remote sensing, as the use of such techniques provide opportunities to search for objects and areas that are prone to be destroyed by landslide processes, to provide an opportunity to assess the scale of potential problem(s) and trends in future development of displacements. This allows to remotely identify a list of objects at risk of destruction, and provide a tool for making management decisions.

Based on the results of mathematical modeling of the actual stress–strain state of the building structure, recommendations for consolidation/restoration/strengthening were given, and geotechnical works of St. Andrew’s Church and the surrounding area were performed:

  • Restoration and strengthening of damaged building structure.

  • Strengthening the church foundation by “jet”-columns, restoration of facades and interiors.

  • Improvement of technical condition of the adjacent landslide and restoration of integrity of church buildings by reinforcing damaged areas were made.

Techniques of information technology, remote sensing of the earth from space and geotechnical protection are proved to provide historical monuments with reliable protection from adverse geological processes and ensure long-term reliable operation.