Detailed analysis of the gravitational effects caused by the buildings in microgravity survey
 77 Downloads
Abstract
Gravity (microgravity) research is more frequently carried out in urban areas, in close proximity to various types of buildings. It is necessary to take into account the gravity impact of these buildings on the measurements by calculating and factoring in the appropriate correction. The easiest method to calculate the corrections is to base them on simplified models of the buildings, approximated mostly by a rectangular prism. This paper presents an analysis of correction based on simplified models of six different buildings. It has been clearly demonstrated that density of a simplified model of a building or an element of the building is different from the average density, especially for gravity measurements inside the buildings. The research demonstrates that it is better to approximate the building with two or three rectangular prisms than with only one treated as a whole. However, the difficulty lies in determining the density of the lowest storey, the value of which diverges from the average density the most. Nevertheless, it can be concluded that in calculating building corrections simplified models of the buildings can be used, even for observation stations that are located in a close proximity to the buildings, as long as the conditions described in this article are met.
Keywords
Building correction Microgravimetry Building density Urban areas Simplified building modelIntroduction
In recent decades, there has been a rapid expansion of urban areas, where the phenomena that may pose threat to urban infrastructure (and therefore the residents) have been appearing with increased frequency. Some of these phenomena are related to conditions of a nearsurface rock mass and can be examined by geophysical methods. An example of such phenomenon are continuous and discontinuous deformations of ground surface. They may have anthropogenic or natural origins. The most dangerous of them, are, obviously, sinkholes. The application of geophysical methods in these areas requires taking into account the urban factor, which is usually associated with the necessity to introduce appropriate corrections.
One of the geophysical methods that can be successfully applied in such conditions is microgravity method (Butler 1984; Gołębiowski et al. 2018; Loj 2014; Styles et al. 2005). An unquestionable advantage of this method lies in its simplicity, but unfortunately it has two basic limitations. One of them is an increased measurement error, resulting from increased ground vibrations, and the other is a gravity impact of a building on the measurements. As much as in the first case it is difficult or impossible to eliminate the error in the second case, but it can be reduced. One possibility is to ensure that the observation stations are not too close to the buildings. However, it reduces the scope of the method applications. The second option is to calculate a correction to eliminate the gravity effect of buildings (Śliz 1978; Panisoval et al. 2012; Dewu 2014; Dilalos et al. 2018). Building correction can also eliminate the impact of identified underground natural or anthropogenic objects (Golebiowski et al. 2016; Porzucek 2014).
Building correction calculation is connected with the determination of building geometry and mass. As it is commonly known, buildings are geometrically very complicated and for this reason in order to calculate the correction their geometry is frequently simplified. Most frequently, a building or its elements are approximated by rectangular prism or, sometimes, by polyhedron (Wójcicki 1993). It involves determining the density of the simplified objects, calculated on the basis of the building average density. This solution was submitted by Śliz in 1978. Analysing a typical fourstorey tenement house, he calculated the density for each storey and presented the distribution of the building correction only for this case. The question may therefore be posed whether the average density is indeed optimal, and this is the main subject of this article.
Building models
Urbanized areas are areas that have been inhabited, built on and extended over the centuries and are characterized by the presence of buildings of various ages. Building age determines the types of walls, their thickness as well as the material they are made of. There are two types of walls: external and internal walls ([N1]PNEN 199611+A1:201305/NA:201403 Eurokod6). Due to their function, external walls can be divided into loadbearing walls and stiffening walls, while internal walls can be divided into loadbearing walls, stiffening walls and partition walls. Loadbearing walls are used to carry vertical loads, as well as horizontal loads, limiting the displacements of the structure, while stiffening walls are used only to carry horizontal loads and maintain the stiffness of the structure. Partition walls do not carry any loads; they are only used to divide the internal space of the building. Regardless of the age, the function of the wall determines its thickness.
The analysis of a building correction distribution was carried out for three types of buildings, most frequently found in urban areas, i.e. a singlefamily detached house, tenement house and largepanel system building. The geometry was based on actual building plans, taking into account the type of materials to be used in construction (PNEN ISO 10456; PNEN ISO 6946:201710; Płuska 2009). For each case, we considered the variant of the building with cellar and without cellar.
The second building was the multifamily house of medium size—the tenement house. This building had four storeys (ground floor and three floors) with external wall length 45 and 24 m. Each floor was divided into five flats with an area of about 150 or 200 m^{2}. The building was designed in a longitudinal system, which means that the external walls and longitudinal internal wall, separating the flat from the corridor, were the loadbearing walls, while the walls dividing the area into flats were the stiffening wall. Internal area of the flat was divided by partition wall. Building with the tenement house size was chosen for one important reason, namely that objects of this size often dominate in city centres, because they were built from the earliest times. Taking into account this fact, three cases of tenement houses of the sizes described above were used for the analysis.
The third building was from the twentieth century, named Plattenbau or largepanel system building or LPS (Basista 2001). LPS were multistorey buildings founded on an identical segment repeated system built of two types of walls: loadbearing walls and partition walls. One segment, known as a tower block, size 72 × 24 m, consisting of 11 storeys (ground floor and ten floors) was selected for the analysis. Every storey was divided into 15 flats with an area of 62, 50 and 30 m^{2} and two staircases. This house was built in a mixed system. It means that the loadbearing walls were both perpendicular and parallel to the longitudinal axis of the building and together with floor slab were the stiffing elements of the building and divided the internal space into flats. The partition walls were used to divide the internal flat space.
Methodology of the building correction analysis
As described above, three types of buildings were selected for the analysis of building correction (Figs. 1, 2 and 3), which was called wall model. For the building correction analysis, it was assumed that the rectangular prism would be used to represent the shape of buildings. Therefore, in the wall model, each wall of the buildings was approximated with a single rectangular prism. The density of each prim was the same as the density of the material from which the wall was built. To calculate the building correction for wall model, the special program was created, using the Nagy algorithm (Nagy 1966). This is the algorithm used for calculating gravity effect from a rectangular prism, and before using the algorithm in the program, it was tested with Oasis Montaj and other programs for gravity modelling.

whole aboveground part of building (called ad whole building),

cellar (two cases),

ground floor,

for each floors separately,

together from the first floor upwards.
For each building, a grid of observation points was created, both outside and inside the building. Inside the building, the observation stations were located in two variants: for the building without cellar the station was on the ground floor, but for the building with cellar on the cellar floor. The value of density was calculated separately for outside and inside the building.

inside the building, observation stations must be at least 20 cm from any wall,

outside the building observation stations must be at least 50 cm from any wall,

the observation was made on tripod and the gravity measurement system was at the height of 30 cm from the surface,

only these stations were used for calculation in which the correction value for wall model was greater than 20 nm/s2, which was about half of the measurement error of CG5 gravimeter.
W_{i}—wall model density value, S_{i}—simplified model density value, n—number of stations.
Results
Optimal bulk densities for the simplified model of the old singlefamily detached home
ρin+0^{a} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρout^{b} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρin1^{c} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρavg^{d} (g/cm^{3})  

Whole house  0.61  30  0.52  50  0.57  
Ground floor  0.76  20  0.58  40  0.65  
I floor  0.40  20  0.51  10  0.42  10  0.49 
Cellar^{f}  − 1.31  20  − 1.54  
Cellar^{g}  − 1.84  10  − 1.82 
Optimal bulk densities for the simplified model of the new singlefamily detached home
ρin+0^{a} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρout^{b} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρin1^{c} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρavg^{d} (g/cm^{3})  

Whole house  0.44  20  0.39  30  0.43  
Ground floor  0.49  10  0.42  20  0.46  
I floor  0.32  20  0.41  10  0.33  10  0.40 
Cellar^{f}  − 1.59  10  − 1.74  
Cellar^{g}  − 1.93  10  − 1.91 
Optimal bulk densities for the simplified model of the mediaeval tenement house
ρin+0^{a} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρout^{b} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρin1^{c} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρavg^{d} (g/cm^{3})  

Whole house  0.65  140  0.60  240  0.62  
I–III floor  0.53  90  0.60  60  0.54  50  0.58 
Ground floor  0.91  70  0.69  190  0.75  
I floor  0.52  60  0.63  40  0.53  30  0.58 
II floor  0.53  20  0.59  20  0.54  20  0.58 
III floor  0.54  10  0.58  10  0.54  10  0.58 
Cellar^{f}  − 1.06  60  − 1.44  
Cellar^{g}  − 1.73  30  − 1.63 
Optimal bulk densities for the simplified model of the eighteenthcentury tenement house
ρin+0^{a} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρout^{b} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρin1^{c} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρavg^{d} (g/cm^{3})  

Whole house  0.52  120  0.49  180  0.53  
I–III floor  0.42  60  0.47  50  0.42  50  0.46 
Ground floor  0.74  60  0.58  150  0.62  
I floor  0.41  50  0.49  30  0.41  30  0.46 
II floor  0.42  20  0.47  20  0.42  10  0.46 
III floor  0.42  10  0.46  10  0.43  10  0.46 
Cellar^{f}  − 1.25  50  − 1.58  
Cellar^{g}  − 1.78  30  − 1.72 
Optimal bulk densities for the simplified model of the new tenement house
ρin+0^{a} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρout^{b} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρin1^{c} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρavg^{d} (g/cm^{3})  

Whole house  0.39  80  0.38  130  0.39  
I–III floor  0.31  50  0.36  50  0.32  30  0.35 
ground floor  0.57  40  0.47  110  0.50  
I floor  0.31  30  0.37  30  0.31  20  0.35 
II floor  0.31  20  0.35  10  0.32  10  0.35 
III floor  0.32  10  0.34  10  0.32  10  0.35 
Cellar^{f}  − 1.47  30  − 1.73  
Cellar^{g}  − 1.88  30  − 1.84 
Optimal bulk densities for the simplified model of the LPS
ρin+0^{a} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρout^{b} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρin1^{c} (g/cm^{3})  Δmax^{e} (nm/s^{2})  ρavg^{d} (g/cm^{3})  

Whole house  0.47  70  0.42  70  0.47  
I–X floor  0.43  70  0.46  50  0.38  70  0.46 
II–X floor  0.43  50  0.45  30  0.38  60  0.46 
Ground floor  0.62  30  0.57  60  0.59  
I floor  0.42  30  0.49  20  0.35  30  0.46 
II floor  0.43  10  0.47  20  0.36  20  0.46 
III floor  0.43  10  0.46  10  0.37  10  0.46 
IV floor  0.43  10  0.45  10  0.38  10  0.46 
V floor  0.44  0  0.45  0  0.39  10  0.46 
VI floor  0.44  0  0.45  0  0.39  0  0.46 
VII floor  0.44  0  0.45  0  0.40  0  0.46 
VIII floor  0.44  0  0.45  0  0.40  0  0.46 
IX floor  0.44  0  0.45  0  0.41  0  0.46 
X floor  0.44  0  0.45  0  0.41  0  0.46 
Cellar^{f}  − 1.50  30  − 1.67  
Cellar^{g}  − 1.87  30  − 1.85 
These tables do not include the density for three cases: the cellar simplified model for observation stations on the ground floor; the cellar simplified model for observation station in cellar and ground floor simplified model; and whole building for observation stations on the ground floor. For two of them, it was necessary to calculate the building correction from the wall model because observation stations were affected not only by external but also by internal walls, so that the distribution of the correction was too complicated to use the simplified model to approximate a single object. In the third case, it was illogical to take measurement on the ground floor in the building with cellar.
 1.
The optimal densities calculated for external station were generally higher than the average density, whereas for internal stations they were lower. While for external station the optimal densities for successive storey approached to the average density, for the internal stations they were always lower.
 2.
The biggest differences between the average and optimal densities for the simplified model were for cellar, ground floor and first floor, that is, for building elements laying closest to the observation station.
 3.
The biggest differences in density between the simplified model and average density (ρavg) were obtained for the ground floor for external station. This difference clearly increased for massive buildings with thick wall, that is, for old buildings. For mediaeval tenement house, the simplified ground floor model density for ground floor calculated from external stations was as much as 0.16 g/cm^{3} higher than the average density but from internal stations in cellar by 0.07 g/cm^{3} lower.
 4.
Of course, the higher the floor the closer the calculated density was to the average density and the difference between correction values of both models was smaller.
 5.
It is worth to note that the calculated optimal density for simplified whole building model was usually very close to the average, but the correction differences (Δmax) were the highest. It follows that it was more correct to calculate the building correction from simplified model of the building consisting separately of the ground floor (eventually separately of the ground floor and first floor) and the rest part of building than to calculate correction from simplified whole building model.
 6.
The density calculated for light buildings (new singlefamily detached home, tower block) was very close to the average density, for external observation station.
 7.
In Tables 1, 2, 3, 4, 5 and 6, there are two variants of density calculations for cellar. In the first, the optimal density was calculated using the volume calculated similarly to the aboveground parts, i.e. the approximating rectangular prism had a base with the building outline. For this model, a large discrepancy between the average (ρavg) and calculated density was obtained. After a thorough analysis, a second simplified cellar model was created, based on internal contours of the foundations, and for this model, the average density was calculated. It is important to realize that foundations real density was similar to density of cellar surrounding rocks and their gravity influence was very small. For this new simplified cellar model, the calculated optimal density was close to the average density.
Detailed results of building correction for the eighteenthcentury tenement house for outside observation stations
From (m)  To (m)  ρ (g/cm^{3})  %  Δmax (nm/s^{2})  

Whole house  0.5  1  0.54  83.8  70 
1  2  0.53  72.3  60  
2  3  0.52  56.3  40  
3  4  0.51  43.4  30  
4  6  0.51  19.6  30  
Ground floor  0.5  1  0.76  46.3  40 
1  2  0.74  13.5  30  
I–III floor  0.5  1  0.46  43.9  30 
1  2  0.46  45.5  30  
2  3  0.47  14.9  30  
3  4  0.47  6.6  20  
4  6  0.48  2.4  20  
Cellar  0.5  1  − 1.80  5.7  30 
1  2  − 1.80  0.7  20 
As it could be expected, the most stations with the Δmax value above 20 nm/s^{2} were observed in zone closest to the building. The analysis for all buildings shows that above 6 m from the building Δmax for all stations was smaller than assumed 20 nm/s^{2}.
Value of Δmax for density different than optimal in ± 0.1 g/cm^{3} for the mediaeval tenement house
Density range (g/cm^{3})  − 0.1  − 0.08  − 0.06  − 0.04  − 0.02  0  0.02  0.04  0.06  0.08  0.1 

ρin+0^{a} I–III floor  280  220  190  160  120  90  100  150  190  240  290 
ρin+0^{a} I floor  140  120  110  90  80  60  50  70  100  120  140 
ρin+0^{a} II floor  80  70  50  40  30  20  20  40  60  70  90 
ρout^{b} whole house  330  290  250  220  180  140  110  110  150  190  230 
ρout^{b} ground floor  120  110  100  90  80  70  60  50  60  70  80 
ρout^{b} I–III floor  150  120  90  70  40  60  90  120  150  180  210 
ρout^{b} I floor  60  50  40  30  30  40  50  60  70  80  100 
ρin1^{c} whole house  480  430  380  330  290  240  190  260  330  410  480 
ρin1^{c} ground floor  290  270  250  230  210  190  180  160  170  190  220 
ρin1^{c} I–III floor  210  160  130  100  80  50  80  130  170  210  260 
ρin1 I floor  480  430  380  330  290  240  190  260  330  410  480 
The analysis of calculated Δmax showed that the greatest influence on correctness of calculated correction from building had incorrect density estimation for simplified model: ground floor, jointly higher floor and whole building. This is due to the fact that for these cases the Δmax was significantly increased during the determination of the optimum density values. The observation station distance was also affected, which was confirmed by the small, absolute variation of the correction for floors above the first floor. After analysing all data, it can be assumed that deviation in density from optimal ± 0.04 g/cm^{3} can be accepted.
Conclusion
The approximation of building with simplified model, usually rectangular prism, to calculate building corrections has been used for many years. Densities for these prisms have usually been taken as average densities resulting from mass of building’s parts and its volume. However, the question may be asked whether densities calculated in this way are optimal for calculating the correction. In this paper, density analysis was performed for six different buildings. The research was carried out for observation stations outside and inside the building. Inside the building, observation stations were on the ground floor and in the cellar.
The obtained results clearly confirmed that it is impossible to use the average density for simplified models of ground floor or cellar for internal station—the differences between the correction values from the wall model and the simplified model Δmax are too big. It also turned out that the calculated optimal density from external and internal stations was different. The first one was greater than the average density and the second smaller.
The analysis of the results also shows that the better results of correction value were obtained when the building was divided into the ground floor and rest of aboveground parts than when whole building was approximated by one rectangular prism. Nevertheless, problem with density of the ground floor still remains. This density was significantly different from the average value, and the differences were greater for building with thick and massive walls.
During the research, it also turned out that in case of simplified cellar model created it should be remembered that the average density should be calculated using its volume calculated on the inside the foundations and not calculated on the outside the building.
The research results clearly show that the closer building the station was the greater calculated error for simplified model was. Incorrect estimation of simplified model density increased of course building correction error calculated in stations. It is not possible to estimate what is the acceptable deviation from the optimal density but it can be assumed that if it does not exceed ± 0.04 g/cm^{3} the accuracy of the calculated correction is satisfactory.
It is also worth to note that the calculated error at any station for floor above the first floor was small, so that the range of the optimal density deviation was also larger.
It can be concluded that simplified model can be successfully used to calculate building correction, even for the stations within short distance to the building. However, it is important to remember about conditions specified in the article.
Notes
Acknowledgements
This paper was financially supported from the research subsidy No. 16.16.140.315 at the Faculty of Geology Geophysics and Environmental Protection of the AGH University of Science and Technology, Krakow, Poland, 2019. This paper was presented at the CAGG 2019 Conference “Challenges in Applied Geology and Geophysics” organized at the AGH University of Science and Technology, Krakow, Poland, 10–13 September 2019.
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
References
 Basista A (2001) Betonowe dziedzictwo: architektura w Polsce czasów komunizmu. Wydawnictwa Naukowe PW (in Polish)Google Scholar
 Butler DK (1984) Microgravimetric and gravity gradient techniques for detection of subsurface cavities. Geophysics 49:1084–1096CrossRefGoogle Scholar
 Dewu Yu (2014) The influence of buildings on urban gravity surveys. J Environ Eng Geophys 19(3):157–164CrossRefGoogle Scholar
 Dilalos S, Alexopoulos JD, Tsatsaris A (2018) Calculation of building correction for urban gravity surveys. A case study of Athens metropolis (Greece). J Appl Geophys 159:540–552CrossRefGoogle Scholar
 Golebiowski T, Porzucek S, Pasierb B (2016) Ambiguities in geophysical interpretation during fracture detection—case study from a limestone quarry (Lower Silesia Region, Poland). Near Surf Geophys 14(4):371–384Google Scholar
 Gołębiowski T, Pasierb B, Porzucek S, Łój M (2018) Complex prospection of medieval underground salt chambers in the village of Wiślica, Poland. Archaeol Prospect 25:243–254CrossRefGoogle Scholar
 Loj M (2014) Microgravity monitoring discontinuous terrain deformation in a selected area of shallow coal extraction. SGEM 14th international multidisciplinary scientific geoconference, 17–26 June 2014, Albena, Bulgaria, vol 1, pp 521–528Google Scholar
 Nagy D (1966) The gravitational attraction of a right rectangular prism. Geophysics 31:362–371CrossRefGoogle Scholar
 Norm [N1] PNEN 199611+A1:201305/NA:201410 Eurocode 6: Design of masonry structuresGoogle Scholar
 Norm PNEN ISO 10456 Building materials and products—hygrothermal properties—tabulated design values and procedures for determining declared and design thermal valuesGoogle Scholar
 Norm PNEN ISO 6946:201710 Building components and building elements—thermal resistance and heat transfer coefficient—calculation methodsGoogle Scholar
 Panisoval J, Pasteka R, Papco J, Frastia M (2012) The calculation of building corrections in microgravity surveys using close range photogrammetry. Near Surf Geophys 10(5):391–399CrossRefGoogle Scholar
 Płuska I (2009) 800 years of brickmaking in Poland—historic development in its technological and aesthetic aspects. Conserv News 26:26–54Google Scholar
 Porzucek S (2014) Underground gravity survey for exploration unknown galleries. SGEM 14th international multidisciplinary scientific geoconference, 17–26 June 2014, Albena, Bulgaria, vol 1, pp 637–644Google Scholar
 Śliz J (1978) Wykrywanie pustek skalnych metodą gradientu pionowego siły ciężkości w rejonach zwartej zabudowy miejskiej. Polska Akademia Nauk Odział Kraków, Komisja Nauk Geologicznych, Prace geologiczne 110:1–54 in Polish Google Scholar
 Styles P, McGrath R, Thomas E, Cassidy NJ (2005) The use of microgravity for cavity characterization in karstic terrains. Q J Eng Geol Hydrogeol 38:155–169CrossRefGoogle Scholar
 Wójcicki A (1993) Gravity attraction due to buildings for the calculation of gravity urban correction. Acta Geophys 41:385–396Google Scholar
Copyright information
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.