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RESULTS OF RECENT LEVELLINGS IN THE REGION OF MODENA
Paolo Russo Istituto di Topografia,Geodesia e Geofisica Mineraria Université di Bologna,Italy
Abstract The analysis of levellings carried out in the period 1950-1980 shows that a remarkable soil sinking hase taken place in the region of Modena. As data concern only a levelling line, the Municipality of Modena has set up a levelling network in 1981 in order to study the phenomenon. The layout of such network is described and the results of the first survey are discussed, with particular regard to accuracy attained in measurements. Finally new values about subsidence resulting from the first survey and from a partial survey carried out in 1982 are presented.
Introduction In 1979 remarkable sinkings of some levelling benchmarks located in Modena and in its suburbs, were discovered. This was pointed out by the comparison between the results of two levellings performed in 1950 and 1974 by I.G.M.I. (Istituto Geografico Militare Italians) and Cadastre along the line n.17 Bologna-Parma of the national levelling network.
Though it had not been measured the vertical movement of soil had already revealed itself. Several damages in fact had been noticed on hystorical buildings of the city for some time.
A research of all available levelling data regarding Modena area was carried out to get as many information as possible on subsidence. Unfortunately it resulted that the only line n.17 had been relevelled some times.
The graph of the variation of heights of the benchmarks of line n. 17 detected in various campaigns of measurements starting from 1950 is plotted on fig.1.
Although the heights of control points should be referred to a common origin, however stable linkage bench marks have not been found. An investigation about possible movements of various reference bench marks has suggested us to ascribe an indétermination of a few centimeters to data of levellings performed in 1972,1973,1979 and 1980.
Fig. 1 shows that the greatest sinkings have occurred in an area which extends for about 12 km from east to west; the maximum subsidence value is cm 81.8 from 1950 to 1979.
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^ ^ -
0
43
^ 47 / ^ ^ v t f ° MODENA ^ V
?km
LEV. LINE N. 17
^ \ 3 5
" ^ \ 25
^ ^ ^ M O D E N A
U ITALY ))
\ ° i00km
^ © ^ 21 ^ - ^ ° - ^ BOLOGNA
52 51 50 49 48 47 40 39 39 38 35 34 33 31 30 29 S5 24 23 22 21
80 cm
Fig.1 Displacement profiles concerning levelling line n. 17 Bologna-Parma of I.G.M.I.
With regard to the rate of soil sinking it is advisable to consider a long period as we do not know with accuracy the soil movements occurred between the two more recent sets of measurement (1979,1980) because of the different reference benchmarks assumed. The maximum sinking velocity has resulted about 4 cm/year between 1972 and 1980, in the linear hypothesis, as it showed by the diagram time/subsidence concerning bench mark n. 17/40 (fig.2). The new levelling network of Modena plane
In consideration of such remarkable soil vertical movements and of their possible consequences, the municipality of Modena
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_ 4 0
.BO
-60
.70
. 8 0
. 9 0
1972:1974
\ \
o
19791980
^ © - o
' "^^ f^" ' ' ' 0 M O D E N A K ' 7 - LINEN.17 m\j%jE.rtr\^** ^ ^ ^s
o 2
Fig.2 Diagram time/subsidence of the bench mark n. 17/40.
in 1981 decided to set up a levelling control network, with the following aims: detecting soil movements in detail in urban area and checking the extent of subsidence in the surrounding plane.
The territory which is object of study has a surface of about 350 km and includes the area in which the greatest soil sinking occurred and the most important industrial centres are located.
The course of levelling lines has been planned in order to comprise several old benchmarks whose heights are known at certain epochs. In this way new data on soil movements can be obtained since from the first survey. The new benchmarks have been placed in steady buildings on condition that they are not recent or susceptible of modification and far from rivers or reclaimed lands .
The levelling network itself is made by the city area network (fig.3) and by the esternal area network (fig.4) .
In the former the average length of sections is 0.25 km, while the length of loops is about 2.5 km, in the latter such lengths are respectively 1 km and 30km on average.The overall length of levelling lines is 160 km and 225 is the number of new benchmarks.
In the plane surrounding Modena soil is sinking also at considerable distance from the town. Therefore the reference benchmark (P/20) of the network has been placed in the slopes of the mountains (Appennino Modenese ) . The locality selected was considered stable, in relation to the subsidence of the plane, by geologists and it is nearer the area under control than other ones suitable to receive reference benchmarks. Moreover the levelling line which links the reference bench mark to the network runs for several kilometers over stable gravelly ground. A few control points were placed in emerging rocks near the reference bench mark.
In the first survey of the network, the levelling lines
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n.17 and n. 5 of I.G.M.I, have been levelled in order to connect the bench mark n.P/20 to the bench mark n.5/163 (fig.5). This point is situated in Appennines near Bologna city, it has been assumed as reference bench mark by Cadastre in 1974 and it is near the reference bench mark of I.G.M.I, levelling performed in 1980. By this way the heights of bench marks of Modena network can be used for any technical purpose being congruent with national levelling network heights.
Survey of the network The first survey of Modena levelling network has been carried out in 1981. Equipment and procedures of special order levellings have been used. In particular the allowable discrepancy between indipendent forward and backward levellings between bench mark has been + 3 mm >/"ÏÏ, where D is the distance in km between bench. marks measured along the levelling route.
Measurements have been performed as quicKiy as possiuic to reduce the effects of soil movement on the results of levelling. Observed differences of heights have been corrected of rod graduation errors, even if they proved to be very little . No correction due to atmospheric refraction has been made, because of the negligible slope of levelling routes and
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'REFERENCE BENCH MARK
Fig.4 Modena plane levelling network.
*HS$
I.G.M.I. LEVELLING LINES MODENA NETWORK
© REFERENCE BENCH MARKS
Fig.5 Scheme of the junction of the levelling networks of Mode na and of I.G.M.I. ~"
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of the specified minimum sight ground clearence (0.5 m) and maximum sight lenght (40 m).
Some preliminary controls on accuracy attained in levelling have been kept before adjustment.
First of all the standard deviation S*(mm) of measured differences of heights along a unit distance (1 km) has been computed using the formula: I n ~ ~
/. 2 d./l.
2 y n
where: d.(mm) is the difference between forward and backward levelling of the ith section, 1.(km ) is its length and n is the number of sections. The values of S* obtained considering the network of the city area of the external area and the whole network separately are listed in tab.1.
TAB. 1 S*(mm) n
City area network | 0.31 i 102 | External area network| 0.51 I 156 | Whole network | 0.46 I 258 |
i 1 1
It is interesting to note that S* is remarkably lower in the city where the average length of the connection lines between two adiacent bench marks is 0.25 km, than in the external area where such distance is 1 km on average.
The second control has been made to verify if levelling loops misclosures exeeded acceptable limits.For this purpose wariable W/vL,where W(mm) is the misclosure of a levelling loop and L(km) is its perimeter,have been considered.The values of W have been computed from levelled height differences without gravity conections because the influence of earth's gravity field on loop misclosures is negligible in the area of Modena, owing to its limited surface and to the slight slope of terrain. In order to assume the observed values of such variable distributed according to a normal distribution,we have used the following procedure.First of all the mean x and the standard deviation S have been calculated from data,obtaining x = 0.15 mm and S = 0.94 mm;then the interval (-©o,+°o),has been divided into 4 class intervals,for each one of them the theoretical probability is p = 0.25.This means that beeing 22 the size of the sample, the theoretical frequency for each interval is f.=5.5.Finally the fitted frequencies f. have been compared with the correspon ding observed frequencies f . using the two-sided X test.As 1 is the number of the degrees of freedom,the value of 2 4 2 - 1
x = . 2' (f . - f. ) . f. is 1 .64- Stating a significance level 1 =1 Ol 1 1 a a
a = 0 .05 i s x\ n n = 0.001 and X2. 0 nr7C = 5.02 and t h i s means i .uu<o I , u . y / 5
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that the value of x2 is evidently not significantly large. Then assuming the normal distribution for W/ VT" it can be
reasonably fixed the confidence interval (x - 2S \/ï,x + 2S /T),i.e.(0.15 - 1.88/1, 0.15 + 1 .88 \fL )mm, for loop misclosures W. Only two values of W do not lie within such interval^ although they are comprised in the interval (x - 3S /T, x + 3S \7L"). In conclusion the hypothesis of the o o v J^ presence of blunders in measurements has been rejected, and all levelling data have been accepted for adjustment.
Finally it is interesting to make the following remark about the presence of systematic effects.Under the assumption of statistical independence of measured height differences 4H between the end points of individual segments.it is known
2 2 2 that variance of AE can be expressed by a = a 1,where a is
an 1 1 the variance evaluated for a distance of 1 km and 1 is the length of the segment.This means that the expected variance 2 2 2
o of W is <r„ - o L and if W's have a normal distribution N W p W 1
(0, cr) then the stadarized circuit misclosures W =w/ a /I" ¥ ' 1
have a standard normal distribution N(0,1 ). Now the standard deviation S of the values of W/ a VE", computed after having assumed a = 0.46 mm(see tab.1 ), results S = 2.14 mm. It is easy to proove that this value is significantly larger then 1. This fact is considered as a demonstration that the basic assumption of statistical independence of individual height differences between consecutive bench marks along a line is not satisfied (Vamcek, Krakywsky, 1982). This also explains the difference between the standard deviation S* evaluated by |1| and S computed from misclosures.
The outlined analysis points out that levelling data can be assumed in the adjustment of the network, even if they are affected by some systematic errors. By consequence the application to Modena network of adjustment methods (Vanicek, Krakiwsky,1982 ) in which observed differences of heights are considered as correlated quantities could give interesting results. For now measurements have been adjusted by least squares method under the statystical independence hypothesis. This is also justified by the probable slight exetent of systematic errors becau&e of the little values of standard deviation of observed height differences estimated using discrepancies and misclosures. Moreover we have got new data on soil vertical movement in a short time.
The standard deviations for a distance of 1 km which results from adjustment is s = 0.943 mm while the standard deviations of the heights of the bench marks have been computed with regard to two different points: the bench mark P/20 (S.
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(a) Cb)
±(0
±13-
- l )
-SL -31 41
Fig.6 Standard deviation S of heights resulting from adjustment; (a) reference bench mark: P/20, (b) reference bench mark: C/1 .
Michèle M.) which will be assumed as reference bench mark in next relevellings of the network, and the bench mark C/1, ( Mo-dena, Civic Tower) which is located just in the center of the city area. This procedure allows us to evaluate the significance level of soil sinkings in the whole territory and of relative soil vertical movements in the urban area, where damages of buildings produced by differential movements of foundations are frequent. Fig.6 shows that least squares estimated standard deviations does not exceed 4 mm, and 1 mm in the first (a) and in the second (b) case respectively.
Recent soil vertical movements (1981-1982) The municipality of Modena set up a levelling network in
1962 for technical purposes. Several bench marks of that network have been relevelled in 1981. Therefore it has been possible to determine contour lines of equal subsidence for the period 1962-1981 (fig.7). The soil sinkings rappresented by such lines may be affected by a systematic error, whose value should not exceed a few centimeters, due to possible little movements of the reference bench marks assumed in the levelling carried out in 1962. In any case the graph of fig.7 indicates that the more remarkable vertical movements (55-85 cm) took place in the northern part of the town and they are distributed in an area which stretches from east to west for
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Fig. 7 Contour lines (in cm)of equal subsidence in the period 1962-1981.
2 4 km at least and has a surface not inferior then 12 km .
New data about subsidence are also given by the displacement profile along levelling line n.17 Bologna-Parma (fig.8). The levelling performed by Cadastre in 1974 has been assumed as reference in order to use a greater number of bench marks to describe the phenomenon and to point out only recent movements. Fig.8 shows that subsidence involves the whole urban area of Modena and in particular the hystorical centre where soil sinking comes to 17-9 cm: soil appears stable out of the town, in north-west and south-east areas. In the same figure the profiles resulting from 1979 and 1980 levellings are also plotted. Although results of the recent surveys are congruent however a significant variation of movements from 1979 to 1981 does not appear , while we have seen that phenomenon rate is about 2-2.5 cm/year in the city area.
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CENTRE 1 9 7 4
.20 cm
Fig.8 Displacement profiles along levelling line n. 17 in the period 1974-1981.
_,_ ,__ 'so
Fig.9 Diagram of P.,accumulated discrepancies.concerning levelling line n.5 and n.17; line (a) represents the computed mean of P. and line (b) its standard deviation.
This can be explained if we consider that heights of fig.8 are referred to the stable bench mark n.5/163 which is about 60 km far from Modena and which is linked to the levelling network by a branch line. By consequence the influence of possible unmodelled systematic errors,above all, may be noticeable enough. To prove this the graph of P. = v p. is reported in fig.9, where @ is the discrepancy i=1 of the I section and i is the number of adiacent sections starting from the first one of the levelling lines n.5 and n. 17 of I.G.M.I.
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Fig.10 Variation of heights of some bench marks of Modena Network in the period 1981-1982.
indicated in the same figure. The average slant of the line a(estimated mean of P.) indicates the presence of systematic effects in measurements (Fieri,Chiarini 1967).
This problem fortunately regards only old data because the new reference bench mark which will be used in next relevelling is close to Modena network.
Anyhow waiting for a new survey of the whole network, some levelling lines located in the city area have been relevelled in 1982 in order to get some recent data about relative soil vertical movements. Measurements have been carried out under the same technical specifications used in 1981. Variation of heights reported in fig.10 are referred to the bench mark 19/5 which is supposed to be the most stable within the surveyed area. Movements appear to increase northwards; the maximum value is 2.5 cm (bench mark n.N/15).
Conclusions The survey of Modena levelling network outlined in the
present communication is a zero-measurement. Therefore we have to wait for a relevelling to know soil movements.
For now it can be pointed out that a good accuracy has been
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attained in the first levelling, even if the analysis of data has showed the presence of some systematic effects in measurements . Then it will be necessary to reduce the influence of such errors in next field operations and to consider them in adjustment of the network.
With regard to subsidence, the results of new levellings performed in 1981 and 1982 give us an idea of areal distribution of soil sinkings and indicate that their actual values are not less then 2.5 cm/year in the city area.
Acknowledgements I have to thank the municipality of Modena, Dr. M. Barbarel-
la of the Istituto di Topografia,Geodesia e Geofisica Minera-ria of Bologna University who elaborated the computer program for the adjustment of the network and the Land Surveyor P. Barbieri , who gave me a great deal of help in this study.
References Chiarini A., Pieri L.,1967^ Analisi statistica degli errori
della livellazione di alta precisione.Atti dell'Accademia delle Scienze.dell'Ist.di Bologna,A.255,série XII.TomoIV, Bologna, 20 p.
Vanicek P., Krakiwski E.,1982: Geodesy: The concepts.North Holland Publishing Company.Amsterdam,Netherlands,691 p.
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