DETECTION OF VERTICAL MOVEMENT OF MOKATTAM AREA USING PRECISE LEVELING TECHNIQUE

Abstract

There are many problems have been arisen in Mokattam since 1955 up till now. These problems appeared clearly in the retreat of the edge of upper Mokattam plateau, damage of Cornich street and some constructions there. For this, a strong recommendations are proposed to observe these problems to know the reasons of these occurrences which may be related to the movement of the upper plateau.

Full text

DETECTION OF VERTICAL MOVEMENT OF
MOKATTAM AREA USING PRECISE LEVELING
TECHNIQUE
BY
Dr. Eng. Khaled Mohamed Zaky Hassan
Dr. Eng. Ehab Salah Eldin Abdel Salam and Dr. Eng. Ashraf Abdel Moneim Ghoneim Lecturers of Surveying, Shoubra Faculty of Engineering Surveying Department, 108 Shoubra Street
ABSTRACT
There are many problems have been arisen in Mokattam since 1955 up till
now. These problems appeared clearly in the retreat of the edge of upper Mokattam
plateau, damage of Cornich street and some constructions there. For this, a strong
recommendations are proposed to observe these problems to know the reasons of
these occurrences which may be related to the movement of the upper plateau.
A geodetic network consists of 11 stations is designed and established at Mokattam
area for monitoring the horizontal and vertical movement at this area. The horizontal
movement is measured through the year of 1995. There is a strong recommendation to
observe and measure the vertical movement. For this purpose, two leveling lines
started from a fixed bench mark (lies outside the area under investigation) and passing
through all stations. Three successive remeasurements have been carried out using the
precise leveling technique. The measurements started at April 1997 to April 1998.
The time interval between remeasurements has taken to be six months as coventioned
for local areas. Each epoch of measurements has adjusted by least squares adjustment
technique. The elevations of all stations obtained from an epoch have been compared
with their corresponding values obtained from its next one to compute the vertical
movement. The results of these comparisons indicate that there is no vertical
movement at the lower and middle plateaus of Mokattam while there is a relatively
large downward vertical movement at the edge of upper plateau reached to 4
centimeters through a year. There is no vertical movement at the other places of the
upper plateau.
1. INTRODUCTION
There are several and different researches (geologic, geo-technical and
geodetic) covered the area of Mokattam [e. g. 1, 3, 9, 10] due to the appearance of
many problems. These problems have been arisen through the last decades at this
area. Examples from these problems are the retreat of the edge of the upper plateau of
Mokattam, damage of Cornich street and some constructions there such as the
international hotel of Mokattam. These problems may be due to the horizontal and
vertical movement of the upper plateau. strong recommendations are proposed by
geologists [1, 3] and geodesists [9, 10] to observe and monitor the horizontal and
vertical movement of Mokattam area (area includes the lower, middle and upper
plateaus of Mokattam). For this purpose, an optimal geodetic network (figure 1) is
designed and established at the upper, middle and lower plateaus of Mokattam using
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the specifications of networks used for deformation measurements [10]. This network
consists of 11 stations distributed as follows:
 2 have established at the middle plateau.
 7 have established at the upper plateau (4 at the edge near from faults or
areas of active movement and 3 at other places far from the edge).
 2 have established at the lower plateau.
The horizontal movement of the upper and lower plateaus of Mokattam has been
measured through the year of 1995. The measurements indicate that the middle
plateau is stable while the upper plateau moved horizontally by a relatively large
amount reached to 3.5 centimeters through the year of 1995 [10].
Figure (1) : The established geodetic network at Mokattam area
2. THE REPEATED MEASUREMENTS
For monitoring the vertical movement of Mokattam area, two leveling lines
passing through all network stations have proposed. These lines starting from a bench
mark fixed on a place outside of Mokattam area. The first leveling line started from
this bench mark passing through stations 1, 3, 6, 5, 10, 11, 9 and back to the same
bench mark i.e. complete loop. The second leveling line started from the bench mark
passing through stations 2, 4, 8, 7 and back to the same bench mark (see figure 2).
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3
The lengths of the first and second leveling lines reached to about 11.5 km. and 8.5
km. respectively.
Fixed bench mark
Fault
B. M.
Triangulation st.
Figure (2) : The distribution of network stations and leveling lines
Three repeated precise leveling measurements have been carried out started
from 1 of April, 1997 to 2 of April, 1998. The time interval between each epoch of
measurements and its successive one has taken to be six months as conventionally
proposed for local areas [6]. The following precautions have been taken into
consideration during measurements:

4
 The leveling lines started from a fixed bench mark and close it at the same bench
mark for checking up the accuracy of measurements by computing the closing error
of each line.
 The distance from the instrument to the foresight staff and backsight staff in each
position was approximately the same.
 The distance between the staff and the instrument did not exceed 150 meters.
 The three hair readings have taken at each leveling point and the difference between
them is checked to ensure that the staff was held vertically.
 The elevation of each station has measured twice.
 The leveling of the instrument has checked before took each observation.
 The level has calibrated before carried out each epoch of measurements.
 The staff has held vertically and carefully at each leveling point especially at turning
points.
 The heighest and lowest reading did not exceed 3 meters and 1 meter respectively
to
avoid the effect of refraction at lower and higher areas.
 The measurements have performed by a very skill and professional observer.
The following are the dates of repeated measurements which have been taken on the
established geodetic network with six months time interval:
 The first set of measurements has been carried out at 1 of April, 1997.
 The second set of measurements has been carried out at 1 of October, 1997.
 The third set of measurements has been carried out at 1 of April, 1998.
2.1. THE FIRST SET OF MEASUREMENTS
The first set of measurements consists of two leveling lines which have
proposed for determining the elevations of all geodetic stations from 1 to 11. The
measurements started at 1 of April, 1997 for two successive days. The elevation of
each station is measured twice. Table (1) includes the elevations obtained from the
first set of measurement.
Table (1)
The elevations of stations obtained from the first epoch of measurements
Dimension in meters
Station No.
Elevation 1
Elevation 2
Mean elevation
Remarks
1
2
3
4
5
6
7
8
9
10
11
B.M.
171.237
170.927
228.111
227.879
232.199
231.339
229.362
231.934
229.012
232.825
230.164
168.593
171.241
170.930
228.115
227.882
232.204
231.342
229.365
231.938
229.015
232.828
230.168
168.596
171.2390
170.9285
228.1130
227.8805
232.2015
231.3405
229.3635
231.9360
229.0135
232.8265
230.1660
Start and end point
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5
B.M.
168.593
168.595
of first leveling
line
Start and end point
of second leveling
line
* Elevation 1 : The elevation of station obtained from the first half loop.
* Elevation 2 : The elevation of station obtained from the second half of the loop.
The permissible closing error of each leveling line (complete loop) is determined
according to the following formula [2]:
e = 4 (k)½ ............................................................................ (1)
Where: e is the closing error in millimeters
k is the distance of leveling in kilometers
The permissible closing errors of the first and second leveling lines (e1 and e2
respectively) are given by:
e1 = 4 (11.5)½ = 13.56 mm.
e2 = 4 (8.5)½ = 11.66 mm.
The actual closing errors of the first and second leveling lines are determined from the
complete loops leveling lines. They are 4 mm. and 3 mm. respectively. The
corresponding values of their permissible (theoretical) closing errors are computed
using formula (1) and found to be 13.56 mm. and 11.66 mm. respectively. The
theoretical and actual values of closing errors are compared together to judge on the
accuracy of the leveling job. The comparison indicates that the actual closing errors
of both leveling lines are smaller than their corresponding theoretical values. That
means, the leveling job is accurate and there is no need to repeat the job or to
distribute this small actual error on the elevations of geodetic stations.
A fortran computer program is designed and prepared for adjusting the elevations of
network stations those obtained from each epoch of measurements using the least
squares adjustment technique [4, 5]. The input data of the program are the difference
in elevations between stations, the horizontal distance along the leveling lines
between stations to determine the weight of each difference. Table (2) includes the
adjusted elevations of all stations obtained from the adjustment of first epoch of
measurements and the standard deviations of all elevations. The results of adjustment
stage contain the residuals of height difference between stations and the adjusted
height difference.
Table (2)
The adjusted elevations of stations obtained from the adjustment
of first set of measurements
Dimension in meters
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6
Station no.
Adjusted elevation
St. deviation
1
2
3
4
5
6
7
8
9
10
11
171.2395
170.9282
228.1135
227.8807
232.2025
231.3402
229.3647
231.9355
229.0132
232.6265
230.1653
0.004
0.003
0.003
0.004
0.004
0.003
0.002
0.003
0.003
0.003
0.003
2.2. THE SECOND SET OF MEASUREMENTS
The second set of measurements started at 1 of October, 1997 for two
successive days. It consists of the measurements of the same two leveling lines. Table
(3) includes the elevation of all stations from 1 to 11.
Table (3)
The elevations of stations obtained from the second epoch of measurements
Dimension in meters
Station No.
Elevation 1
Elevation 2
Mean elevation
Remarks
1
2
3
4
5
6
7
8
9
10
11
B.M.
B.M.
171.236
170.925
228.110
227.877
232.178
231.357
229.366
231.916
229.009
232.804
230.166
168.593
168.593
171.239
170.929
228.112
227.881
232.181
231.361
229.369
231.918
229.012
232.808
230.169
168.597
168.597
171.2375
170.9270
228.1110
227.8790
232.1795
231.3590
229.3675
231.9170
229.0105
232.8060
230.1675
Start and end point
of the first
leveling line
Start and end point
of the second
leveling line
The theoretical or permissible closing errors of the first and second leveling
lines obtained from equation (1) are 13.56 mm. and 11.66 mm. respectively. Their
corresponding actual closing errors obtained from the second epoch of measurements
are 4 mm. and 4 mm. respectively. The comparison of theoretical and actual values
of closing errors indicates that the actual closing errors of both leveling lines are less
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7
than their corresponding permissible errors. That is mean, the measurements of
second epoch are relatively accurate and there is no need to distribute these errors on
the elevation of stations.
Table (4) contains the adjusted elevations of all stations from 1 to 11 and their
standard deviations. These values of elevations and standard deviations obtained
from the application of the designed computer program for adjusting leveling nets on
the second epoch of measurements.
Table (4)
The adjusted elevations of stations obtained from the adjustment
of second set of measurements
Dimension in meters
Station no.
Adjusted elevation
St. deviation
1
2
3
4
5
6
7
8
9
10
11
171.2380
170.9275
228.1112
227.8797
232.1800
231.3582
229.3667
231.9171
229.0107
232.8063
230.1673
0.003
0.004
0.002
0.004
0.003
0.004
0.003
0.002
0.003
0.004
0.003
2.3. THE THIRD SET OF MEASUREMENTS
The third set of measurements started at 1 of April, 1998 for two successive
days. The measurements includes the same two leveling lines those have been
observed through the first and second epoch of measurements. The elevations of all
stations from 1 to 11 are determined. Table (5) includes these elevations obtained
from the completed two loops.
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8
Table (5)
The elevations of stations obtained from the third epoch of measurements
Dimension in meters
Station No.
Elevation 1
Elevation 2
Mean elevation
Remarks
1
2
3
4
5
6
7
8
9
10
11
B.M.
B.M.
171.237
170.926
228.109
227.879
232.161
231.380
229.367
231.898
229.010
232.785
230.169
168.593
168.593
171.239
170.930
228.113
227.882
232.165
231.383
229.370
231.900
229.012
232.788
230.172
168.596
168.596
171.2380
170.9280
228.1110
227.8805
232.1630
231.3815
229.3685
231.8990
229.0110
232.7865
230.1705
Start and end point
of the first
leveling line
Start and end point
of the second
leveling line
As mentioned in sections 2-1, 2-2, the theoretical errors of the two leveling
lines are 13.56 mm., 11.66 mm. respectively. The actual closing errors of these
leveling lines are 3 mm. for both lines (see table 5). The comparison of actual and
permissible closing errors of both leveling lines indicate that the observations of third
epoch are relatively accurate.
The prepared computer program of adjustment is applied on the measurements
of the third epoch. The results of adjustment included the adjusted elevations of all
network stations and their standard deviations are recorded in table (6).
Table (6)
The adjusted elevations of stations obtained from the adjustment
of the third set of measurements
Dimension in meters
Station no.
Adjusted elevation
St. deviation
1
2
3
4
5
6
171.2379
170.9272
228.1110
227.8793
232.1629
231.3812
0.002
0.004
0.004
0.003
0.004
0.003
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9
7
8
9
10
11
229.3682
231.8991
229.0107
232.7868
230.1698
0.003
0.002
0.002
0.003
0.003
3. DETERMINATION OF VERTICAL MOVEMENT AT MOKATTAM AREA
All the repeated measurements of the leveling lines are the base for
determination of the vertical movement at Mokattam area through a certain time
interval. For local areas, the difference of elevations or vertical movement (dv) can be
determined from the adjusted elevations obtained from two successive measurements
as follows [6]:
dv = Vi+1 - Vi
Where Vi is the adjusted elevation obtained from an epoch i
Vi+1 is the adjusted elevations obtained from the next epoch i+1
The difference in elevations at all network stations from 1 to 11 of each time interval
(six months) are considered as the vertical movement at these stations.
3.1. THE VERTICAL MOVEMENT THROUGH FIRST AND SECOND
TIME INTERVALS
The first time interval is the time from April, 1997 to October, 1997 (interval
between the first and second epoch of measurements). The second time interval is the
time interval between the second and third epoch of measurements from October,
1997 to April, 1998. The difference in elevations (vertical displacement) of network
stations through the first and second time intervals are recorded in table (7).
Table (7) : The vertical movement at Mokattam area through the
time interval of a year
Station No.
dv1
dv2
dv
remarks
1
2
3
4
5
6
7
8
0.0015
0.0008
0.0023
0.0010
0.0225
0.0180
0.0020
0.0184
0.0001
0.0003
0.0002
0.0004
0.0171
0.0230
0.0015
0.0180
0.0016
0.0011
0.0025
0.0014
0.0396
0.0410
0.0035
0.0364
* Station at lower plateau
* Station at lower plateau
* Station at middle plateau
* Station at middle plateau
* Station at the edge of
upper plateau near from a
fault
* Station at the edge of
upper plateau near from a
fault
* Station at upper plateau
* Station at the edge of
upper plateau near from a
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01
9
10
11
0.0025
0.0202
0.0020
0.0000
0.0195
0.0025
0.0025
0.0397
0.0045
fault
* Station at upper plateau
* Station at the edge of
upper plateau near from a
fault
* Station at upper plateau
* dv1 is the vertical movement through the first time interval.
* dv2 is the vertical movement through the second time interval.
* dv is the vertical movement through the time interval from April, 1997 to
October,
1998.
3.2. ANALYSIS OF VERTICAL MOVEMENT THROUGH A YEAR
From the results of vertical movement at Mokattam area through a year (time
interval from April, 1997 to April, 1998) which are recorded in table (7), we can
notice that:
-The difference in elevations at stations 1 and 2 (stations established at lower plateau
of Mokattam) are 1.6 mm. and 1.1 mm. respectively. These amounts of differences at
these stations are less than the standard deviations of elevations of them obtained
from any epoch of measurements (see tables 2, 4, 6). So that, these amounts can not
be considered as vertical movements.
- The difference in elevations at stations 3 and 4 (stations established at middle
plateau of Mokattam) are 2.5 mm. and 1.4 mm. respectively. These amounts of
differences are small compared with the standard deviations of elevations of these
stations. So that, we can not considered these values as vertical movement at stations
3 and 4.
- The difference in elevations at stations 5, 6, 8 and 10 (stations established at the
edge of upper plateau and near from the borders of some faults) are 3.96 cm, 4.1 cm,
3.64 cm, and 3.97 cm respectively. These amounts of elevation differences occurred
through the time interval from April, 1997 to April, 1998. The amounts of these
differences are considered relatively too large with respect to the values of standard
deviations of elevations at these stations which did not exceed 4 mm. The vertical
movement at these stations directed downward. These amounts of vertical movement
at the border of faults lie near to the edge of the upper plateau of Mokattam indicate
that the blocks of rocks at the edge will be damaged suddenly as occurred since 1955
up till now.
- The difference in elevations at stations 7, 9, and 11 (stations established at other
places on the upper plateau and far from the edge and faults) are 3.5 mm, 2.5 mm and
4.5 mm respectively. These amounts of differences are approximately equal to the
standard deviations of elevations at these stations. So that, we can not consider these
differences in elevations as vertical movements.
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00
- The results indicate that, the parts at faults near to the edge of the upper plateau will
damage at any time and the dewelling buildings will become more nearly from the
edge. That is reflect the dangerous on the human life at these areas.
4. CONCLUSIONS
 A geodetic network is designed and established at Mokattam area for monitoring
the vertical and horizontal movement at this area.
 The running program for monitoring the vertical movement at Mokattam area
included two local leveling lines crossing some faults there. Three successive
measurements on these leveling lines have been carried out using the precise
leveling technique and instruments. The adjusted elevations of all stations
obtained from each epoch of measurements have been determined. The vertical
movement through two time intervals (complete one year) is determined at each
station.
 The results of vertical movement indicate that the lower and middle plateaus of
Mokattam are stable and does not move vertically. The parts near to the edge and
at the borders of some faults in the upper plateau of Mokattm moved downward
by a relatively large amount reached to 4 cm through a year (time interval from
April, 1997 to April, 1998). The other parts far from the edge of upper plateau are
stable.
 The results are very dangerous and give a red light toward the dewelling buildings
near to the edge and building new constructions near to that edge.
REFERENCES
[1] Abdel Tawab, S. and Moustafa, A. R. , (1985), " Morphostructure and Non-
Tectonic Structures of Gebel Mokattam ", Middle East Research Center, Ain
Shams University, Science research series, vol. 5, 1985, pp. 65 - 78.
[2] David Clark, (1966), " Plane and Geodetic Surveying ", Published by Constable
and Company Ltd., 10 - 12 orange Street W. C.
[3] Elleboudy, A. M., (1990), " Analysis of Mokattam Rockfall ", A paper presented
to Civil Engineering Department, Shoubra Faculty of Engineering, 1990.
[4] Mikhail, E. M. and Gracie, G., (1980), " Survey Computations and Adjustment " ,
Van Nostrand Fleinnold Company, New York, 1980.
[5] Mikhail, E. , M, (1976), " Observations and Least Squares " , Harper & Row
Publisher, New York, 1976.
[6] Vyskocil, P., (1984), " Procedures for Monitoring Recent Crustal Movements -
Part 1 " , ICRCM, 25066 ZDIBY , No. 98, Prage, Chekoslovakia.
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[7] Vyskocil, P., (1984), " Procedures for Monitoring Recent Crustal Movements -
Part 2 " , ICRCM, 25066 ZDIBY , No. 98, Prage, Chekoslovakia.
[8] Wassef, A. M., (1974), " On the Search for Reliable Criteria of the accuracy of
Precise Leveling Based on Statistical Considerations of the Discrepancies ",
Bulletin Geodesique No. 112.
[9] Zaky, Kh. M., (1993), " Design of basic Network For Monitoring Crustal
Movement of Mokattam Hills " , M. Sc. thesis, Shoubra faculty of Engineering,
Surveying Department, Zagazig University, Benha Branch, 1993.
[10] Zaky, Kh. M., (1997), " De Measurements of the Upper Mokattam hill " , Ph. D.
thesis, Shoubra faculty of Engineering, Surveying Department, Zagazig
University, Benha Branch, 1993.
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