Deviations’ analysis of the single-family buildings in the mining area

In this work changes of the inclinations values (in a horizontal plane) of a land surface and two buildings have been shown. They were induced by an operation of the 404 and the 405 coal beds located successively on the level of 490 m and 550 m, and realized on a south of the buildings (the South of Poland) by the use of five longwalls. Values of inclinations from the results of the geodesic measurements done in August 2019 have been determined. Subsidence and distances between neighbouring points (on a land surface and on the buildings’ walls) have been observed. Observations in two perpendicular directions, on 24 points (12 ground points and 12 wall points) have been conducted. Research results indicate that deviations are different for a ground and the buildings. It means that a process of deformation of the buildings and a terrain surface takes place differently. Moreover, the ground steps which occurred near the buildings (one in front of the first building, the other under the second building) cause anomalies in the inclinations values and changes in their directions and turns.


Introduction
The problem of correctly determining the deflections of buildings located in mining areas and the amount of compensation payments for this reason has been repeatedly raised at numerous symposia, seminars, conferences [1 -3], in professional literature [4 -6] and scientific articles [7 -13].After many discussions and consultations with representatives of various industries and institutions, at the Department of Surface and Building Protection of the Central Mining Institute in Katowice (Poland), it was possible to develop a uniform method for assessing the impact of buildings' inclination from the vertical on the loss of their value.Based on the research carried out, including test measurements of buildings' inclination from the vertical and theoretical analyses, including the costs of repairing mining damage, principles for measuring the buildings' inclination from the vertical and an algorithm for calculating the amount of compensation for the loss of value of inclined buildings were developed.
The main factor contributing to the deflection of buildings from the vertical is their location on the slopes (wings) of the subsidence trough [9].However, it should be noted that building deflections are occurring more and more often in areas affected by mechanical suffusion [14] and discontinuous linear deformations caused by underground mining [15], [16].
Article includes an analysis and comparison of the inclinations of two buildings situated in the area of discontinuous linear deformations induced by an operation of the 404/3, 404/5 and 405/1 coal beds.The single-story buildings were residential houses with the load-bearing wall structures and made using traditional technology.In the case of the first building, linear discontinuous deformation appeared under it, parallel to the front wall and perpendicular to its eastern wall.Discontinuous linear deformation also appeared in front of the second building, parallel to its front wall.The inclinations of the buildings were determined from the results of technical levelling, carried out at measurement points located on two perpendicular, external walls of the buildings (3 points on each wall) and in directions approximately parallel and perpendicular to the longitudinal axis of the discontinuous linear deformations.

Characteristics of buildings
The buildings are located in southern Poland, in the Rybnik Coal District.Both of them function as single-family residential houses with a utility part, constructed in traditional technology, with a loadbearing wall structure.They have one above-ground floor and are approximately 52 m apart in a straight line (building 2 is located north of building 1).

Building 1
Building 1 was constructed during 3 stages.
The western part was created in 1956.It includes a residential part (10 m x 10 m) and a vestibule (3.3 m x 2.4 m).The residential part had a basement, except for the south-west part.
In 1980, the eastern part was added, measuring 9.98 m x 5.60 m.
The vestibule was enlarged with additional utility rooms (including a boiler room) in 1981.
The horizontal projection of the house has the shape of a rectangle with dimensions of 18 m x 10 m.The height of the building is 7.8 m above ground level and it has a load-bearing wall structure.The thickness of the ground floor walls ranges from 0.38 m to 0.42 m and they are made of brick.The walls of the first floor are from 0.2 m to 0.4 m thick.The ceilings are steel girders with concrete slabs.The roof of the building was done as a flat roof without ventilation.Thermal isolation is blast furnace slag.The roof is built made of cladding covered with layers of bituminous felt.
Since its inception, the building has undergone numerous renovations.The roof structure over the western part of the building was changed to a wooden one covered with bituminous felt.Due to mining damage occurring in the facility, a reinforced concrete band was made at its foundation level in 2016.It runs all around entire building and the load-bearing walls.The outer band has a form of a rectangle with dimensions of 0.5 m x 1.0 m and consists of 22 rods (18 mm of diameter) in a longitudinal arrangement.Fragments of the band in the building are located along the load-bearing walls and have a form of a rectangle with dimensions of 0.4 m x 0.2 m.They were reinforced with 8 rods (18 mm of diameter).
The building has residential purposes at the present moment.There used to be a car repair shop and a grocery store in the eastern part of the building, but it was closed due to its poor technical condition.
Building 1 from the north is shown in Figure 1a.

Building 2
Building 2 has a form of a square (13 m x 13 m) with a little cutout with dimensions of 2.8 m x 2.6 m in the south-east part.The house has a basement on the entire horizontal plan and one above-ground floor.Its height reaches 9.5 m above ground level.
The house was made of brick, using traditional technology and has a load-bearing structure based on the walls.
There is an entrance to the building on the north side.In this part of the property there are also 3 garages, which are situated perpendicular to the house.
Figure 1b shows building 2 from the north-eastern side.

Observational network
To monitor the slopes of buildings caused by an operation of the 1/II longwall located in the 405/1 bed and previous exploitation carried out in the 404/3 and 404/5 seams, an observational network was established, consisting of 24 measurement points (12 ground points and 12 wall points) stabilized in the ground and on the external walls of buildings, in 2 approximately perpendicular lines situated parallel and perpendicular to the longitudinal axes of the discontinuous linear deformations.
The observational network for building 1 consisted of 6 wall points (direction 1: s01, s02, s03, direction 2: s36, s37, s38) and 6 ground points (direction 1: z01p, z02p, z03p, direction 2: z34d, z35d, z36d).The wall points were metal pins mounted on the building's facade, and the ground points were metal rods -a diameter of 18 mm, a length of 30 cm (points z01p, z02p, z03p) and wooden pillars 25 cm long (points z34d, z35d, z36d).A medium length of sections was approximately 5.7 m and the distance between ground points and wall points was up to 3 m in a straight line.Under the building 1, approximately perpendicular to direction 1, between points s02 and s03, a 15 cm high ground step was created with a drop towards the south (Figure 2c).The location of the observational points for building 1 and the discontinuous linear deformation are shown in Figure 2a.
For building 2, a similar measurement network was established as for building 1, also consisting of 6 wall points (direction 1: s09, s10, s11, direction 2: s56, s57, s58) and 6 ground points (direction 1: z09p, z10d, z11d, direction 2: z56d, z57d, z58g).The wall points were metal pins located on the external walls of the building, and the ground points were a metal rod, wooden pillars and a metal nail with a diameter of 8 mm and a length of 20 cm.A medium distance between these points was approximately 3 m and the distance of the ground points from the building walls was up to 2 m in a straight line.In front of the northern wall of the building 2, approximately parallel to direction 2, a discontinuous linear deformation was formed in the form of a 20 cm high ground step with a drop directed to the south (Figure 2d).The location of measurement points around building 2 and the ground step is shown in Figure 2b.

Geodetic measurements
Inclinations of the buildings and the nearby ground in a horizontal plane were determined based on the results of distance measurements and height differences between neighboring observational points.Technical leveling was conducted from two different positions, using an instrument with an accuracy of ± 1.5 mm/km, which was the N32x Nivel System optical leveler on the SJJ1 aluminum tripod with a set of two TS-50 aluminum leveling patches.The first leveling measurements were performed before the start of operation in the 405/1 bed, in the 1/II longwall (04.03.2019).The frequency of measurements was from 2 to 4 weeks, depending on the position of an operation front in relation to the buildings.
As the front approached the objects, the frequency of observations increased.The last measurement has been taken at the end of the wall run (17.08.2019).
Simultaneously with the leveling measurements, distance measurements were done between neighboring ground and wall points.These measurements were made with the D510 Leica electronic distance meter with an error of ± 1 mm/m.

Results and discussion
Inclinations of buildings 1 and 2 and the ground near them were determined on August 17, 2019, after the completion of exploitation in the 405/1 bed, in the 1/II longwall, in two approximately perpendicular directions 1 and 2.
The I inclination between the i, i+1 neighboring observational points was determined from the quotient of the Δh relative height difference between these points and their mutual the l distance (formula 1): where:

Inclinations within the building 1
Table 1 shows the values of the building's inclinations observed between points s01 -s02, s02 -s03 (direction 1) and s36 -s37, s37 -s38 (direction 2) and the terrain surface around it between points z01p -z02p, z02p -z03p (direction 1 ) and z34d -z35d, z35d -z36d (direction 2).Research results juxtaposed in Table 1 show that values of ground inclinations observed along directions 1 and 2 are completely different (usually larger) than the values of building inclinations measured along analogous directions.This may be due to the fact that low buildings are stiff, which makes them less susceptible to dynamic loads than the ground.
These differences are especially visible in the case of direction 1 (perpendicular to the ground step with a drop value of 15 cm and located under the building).The inclination of the z02p -z03p ground section (-25.70 mm/m) is approximately 2.6 times greater than a slope of similar the s02 -s03 wall section (9.85 mm/m).Moreover, the direction of the terrain inclination (the south) is consistent with its theoretical inclination towards post-mining workings.However, the direction of the building's inclination (the north) was changed by a ground step running underneath it.Therefore, the inclination of an object is perpendicular to a longitudinal axis of the discontinuous linear deformation.The greatest inclination of almost -60 mm/m and towards the south was recorded in the z01p -z02p ground section and is more than 2.2 times greater than the inclination determined for adequate the s01 -s02 wall section (-26.81 mm/m).
For direction 2, parallel to a longitudinal axis of the discontinuous linear deformation, differences between inclinations of the ground and the building are smaller.For the terrain on the z34d -z35d section, inclination (18.47 mm/m) is approximately 1.3 times larger than the inclination for analogous the s36 -s37 section (-14.51 mm/m) located on the building's wall.The directions of inclinations of the ground (to the west) and the building (to the east) are opposite here.The inclination of the s37 -s38 wall section (-17.44 mm/m), located in the part of the building without a basement, is approximately 2.4 times greater than the inclination of the z35d -z36d ground section (-7.12 mm/m).In this case, the directions of inclinations of the terrain and the building are consistent (to the east).

Inclinations within the building 2
In Table 2 the values of the inclinations of building measured on the s09 -s10, s10 -s11 (direction 1) and the s56 -s57, s57 -s58 wall sections (direction 2) and terrain on the z09p -z10d, z10d -z11d (direction 1) and the z56d -z57d, z57d -z58g ground sections (direction 2) have been juxtaposed.Results of measurements juxtaposed in Table 2 show that values of terrain inclinations are generally greater than values of building inclinations in both directions.
The greatest difference (4.2 times) was observed along direction 1, approximately perpendicular to the ground step with a height of 20 cm and a drop towards the south, on the z10d -z11d ground section (-54.41 mm/m) and analogous the s10 -s11 wall section (-12.94mm/m).The direction of inclination of all sections, both ground and wall, is southern and consistent with the site of exploitation, south of the building.
Along direction 2, approximately parallel to the linear discontinuous deformation of the terrain, smaller discrepancies were noted (max.by approximately 2.6 times) between the inclinations of the ground (the z56d -z57d section: 20.90 mm/m) and the building (the s56 -s57 section: 8.05 mm/m).The directions of inclination of the ground and the building are consistent, to the east.
Taking into account the values and directions of the building inclinations along directions 1 and 2, it can be said that its resultant inclination is in the SSE direction, i.e. approximately perpendicular to the discontinuous deformation of a linear type.

Conclusions
Taking into account the values of inclinations of buildings No. 1 (the ground step with a drop of 15 cm towards the south and under the building) and No. 2 (the ground step with a drop of 20 cm also towards the south and in front of the building) and the land surface near them, observed after the end of exploitation of the 1/II longwall located in the 405/1 coal bed, along directions 1 and 2, respectively, approximately perpendicular and parallel to the longer axis of a discontinuous deformation of a linear type of the ground, the following conclusions can be drawn: − the values of building inclinations are several times smaller than the values of terrain inclinations, which may be due to the fact that low buildings are characterized by significant stiffness compared to 'loose' subsurface soil layers, which makes them less susceptible to the deformation process; − regardless of the location of the discontinuous deformation of a linear type of the land in relation to the building (under or in front of it), the building inclinations have a direction approximately perpendicular to the longer axis of a ground step; − the occurrence of discontinuous linear deformation under the building may cause change its inclination to the opposite direction than indicated by the location of post-mining workings (here from south to north); − an appearance of the discontinuous deformation of a linear type in front of building does not basically change the direction of its inclination; − the lack of a basement in part of the building may result in the greater values of inclinations in this part compared to the ground inclinations located near the part of the building without a basement.The weaker connection of this part of the building with the ground results in its greater susceptibility to the deformation process.

Figure 1 .
Inclined buildings: a) building 1 on the north side, b) building 2 on the north-east side 3. Characteristics of completed exploitation In 02.2019, an operation of the 405/1 coal bed began at an average depth of 550 m and a height of approximately 1.7 m.Exploitation in the 1/II longwall was carried out with a cave-in of roof rocks and with a slope of 18° towards the north, on the south of the buildings, towards the south.Operation in this longwall ended in 09.2019.Before an extraction from the 405/1 seam has been started, the coal seams (404/3 and 404/5) were exploited.Exploitation of the 404 seam had place in the years 2013-2018, using the longwalls and a roof rock caving.Extraction of a hard coal from the 404/3 seam took place by use of 2 longwalls (the 1/II and the 2/II longwalls).The walls respectively were 4.0 m and 3.4 m high and the mining levels were 410 m (in the east) and 575 m (in the west).The slope of the seams was 17° towards the north.Extraction was carried out in the 1/II longwall from 05.2013 to 12.2013 and in the 2/II longwall from 08.2016 to 02.2017.Operation of the 404/5 bed began in 11.2015 with the 1/II longwall.It was carried out to 3.3 m high and at the level of 470 m.Operation of this longwall ended in 06.2016.Exploitation in the 2/II longwall was conducted from 10.2017 to 04.2018.Mine working was 3.5 m high and was localized at the level of 550 m.The slope of the bed towards the north was 18.5°.

Figure 2 .
Observational network and ground steps close to: a) the 1 buildingtop view, b) the 2 buildingtop view, c) the 1 buildinga ground step with a 15 cm drop, d) the 2 buildinga ground step with a 20 cm drop

Table 1 .
Inclinations values of the building 1 and a terrain surface around it

Table 2 .
Inclinations values of the building 2 and a terrain surface around it