Solution of Inclinometer
Solution of Inclinometer
69–76
DOI: 10.2478/rgg-2023-0012
Received: 15 September 2023 / Accepted: 12 December 2023
Published online: 29 December 2023
ORIGINAL ARTICLE
1
Department of Geodesy and Geomatics Engineering, Hanoi University of Civil Engineering, 55 Giai Phong Road,
10000, Hanoi, Vietnam
2
Department of Planning and Urban Transport, University of Transport Technology, 54 Trieu Khuc Road, 10000,
Hanoi, Vietnam
* dungln@huce.edu.vn
Abstract
In the recent decade, Digitilt DataMate II and GK-604D inclinometer systems have commonly been used to evaluate horizontal
displacement as well as to test the calculation models of basement diaphragm walls in Vietnam. The difference in the equipment
constants as well as the calculation principle has confused the surveyors and even led to erroneous monitoring results.
Furthermore, the use of commercial programs DigiPro2 and SiteMater, which are expensive, in inclinometer data processing
requires a thorough understanding. Differences in calculation results between software occur due to the choice of the instrument
constant, the rounding principle, or the choice of the reference point at the bottom of the monitoring pipe. In this paper, we
summarize the calculation principles of Digitilt DataMate II and GK-604D inclinometer systems. To respond well to the data
processing of inclinometer systems for basement diaphragm walls in Vietnam, we have developed the ICTool program that can
efficiently calculate the observed data of the GK-604D system. The results of inclinometer data processing by the ICTool program
are homogeneous in comparison with DigiPro2 and SiteMater software. In addition, the ICTool program was established to
provide, free of charge, the communication of the monitoring of basement diaphragm wall displacement in Vietnam.
Key words: inclinometer data processing, DataMate II, GK-604D, basement diaphragm wall, inclinometer instrument constants
This work is available in Open Access model and licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
Publisher: De Gruyter
69
70 | Reports on Geodesy and Geoinformatics, 2023, Vol. 116, pp. 69–76
Inclinometer monitoring is based on the operating principle of the In which: d is the cumulative deviation from the bottom of the
accelerometer sensors located at the probe. When measuring hor- casing, and di is the deviation of each measurement interval.
izontal displacement, the probe has a system of two wheels run- The cumulative deviations of the casing compared to the vertical
ning along the grooves in the casing. The probe consists of two are used to determine the horizontal displacement value along the
force-balanced accelerometers: an accelerometer that measures depth of the observed object.
inclination in the plane of the probe wheels, which is called the A DigiPro2 and SiteMaster software are calculation tools provided
axis (commonly referred to as the direction of pressure); the other for data processing of Digitilt DataMate II and GK-604D instru-
accelerometer measures the inclination in the plane perpendicular ments respectively. The principles of these calculation are detailed
to the plane of the wheels, this plane is called the B-axis, Figure 1. in the following paragraphs.
In Figure 2 (a), the deviation (di ) at each monitoring position
of the casing is the relationship between the angle of inclination
(θi – determined by the accelerometer) and the reading interval 2.2 Calculation principle of Digipro2 software
(L) calculated by Eq. (1).
The readings displayed on the Digitilt DataMate II and imported
into Digipro2 software are not the angle or deviation of the casing,
di = L sin θi (1) Figure 3. These results are proportional to the tilt angle of the casing
and the instrument constant, which is represented by the following
In which: di is the deviation, L is the measurement interval (usually Eq. (3).
0.5 m or 2 feet), θi is the angle of tilt compared to the vertical at the
ith measurement point.
Dinh Trong et al, 2023 | 71
Figure 4. Raw data obtained from GeoKon GK-604D device (Deep Exca-
vation, 2021)
Figure 3. Observed data displayed in Digipro2 software
Di = IC sin θi (3)
SA = (A+) – (A–) /2
(6)
SB = (B+) – (B–) /2
In which: Di is the lateral deviation, and IC is the instrument con-
stant.
In which: A+, B+ are readings of A0 and B0 directions; A–, B– are
In a two-way measurement, the result of lateral deviation is
readings of A180 and B180 directions; SA , SB are the average values
the average value of two reversal measurements, Eq. (4). The first
of readings in two-way 0 and 180.
measurement has a conventional 0◦ direction and the second one
is 180◦ when the probe is reversed. This two-way measurement
allows the detection of systematic errors through check-sum value, CA = SA · M · RINT
which is the algebraic sum of the measured values in the two di- (7)
CB = SB · M · RINT
rections 0◦ and 180◦ for each reading interva; this value should
theoretically be zero. In which: M is the constant, equal to 0.05 corresponding to the
deviation value in millimeters and equal to 0.005 in centimeters;
RINT is the reading interval, this value is always 0.5 m; CA and CB
Di = (A0 – A180 ) /2 (4) are the values of local lateral deviation, regardless of directional
angle.
In which: A0 is observed data in the 0◦ direction of axis A, and A180
is observed data in the 180◦ direction of axis A.
In two readings, we always have direction A0 and A180 readings DA = CA cos ZZ – CB sin ZZ
(8)
with opposite signs. Thus, the relationship between Eq. (1) and DB = CA sin ZZ + CB cos ZZ
the observed data shown in Eqs. (3, 4) give us the value of the
horizontal deviation in the depth of the casing in each interval, In which: ZZ is the directional angle; DA and DB are the horizontal
which is represented by Eq. (5). deviation values considering the directional angle.
In Figure 4 we can see an example of the raw observed data of a
GK-604D inclinometer up to a depth of 30 m.
D
di = L sin θi = L = L (A0 – A180 ) / (2IC) (5) With readings at a depth of 30 m that is noted in the red rectangle,
IC
we have readings of direction A+ = 1013, B+ = –380, and direction
A– = –1052, B– = 320. The rounding calculation using Eq. (6),
For example, to calculate the red oval in Figure 3 with observed
SA = 1033, SB = –350, continuing to apply Eq. (7) to calculate the
data at a depth of 3.5 m, and according to the calculation instructions
horizontal deviation value at this position in centimeters, regardless
of the Digitilt DataMate II device (Slope Indicator, 2011), with the
of the directional angle ZZ, we have CA = 1033 · 0.005 · 0.5 = 2.58
device constant IC = 25000 (in metric units) and the probe length
cm, CB = –350 · 0.005 · 0.5 = –0.88 cm. The result of the A direction
L = 500 mm, we can calculate the lateral deviation of the A axis
is illustrated in the red rectangle of Figure 5, the B direction result
with reading A0 = –299 and A180 = 154 which is di = –4.53 mm in
is not shown here.
applying Eq. (5).
When observing a local object, regardless of the spatial orienta-
The horizontal displacement value is calculated by subtracting
tion angle, we can assume that pressure is directed perpendicular
the initial lateral deviation from the current deviation. Since this
to the diaphragm wall, so the directional angle is ZZ = 0◦ . Then
value is the horizontal movement of the casing, this value is also
we can see that the value of DA , DB in formula (8) equals the value
the horizontal displacement of the observed object.
CA , CB . In Vietnam, displacement monitoring is mostly applied
to observe the diaphragm wall in the basement. This is a locally
2.3 Calculation principle of SiteMaster software observed object and therefore, during monitoring, it is always put
the ZZ value to zero. Thus we can easily identify the displacement
The probe of GK-604D, including two Micro-Electro-Mechanical of the diaphragm wall following the direction of the excavation. In
Sensor accelerometers, directly gives A+, and A- readings at each this case, applying formulas (7) and (8) provides the same results.
monitor depth when the wheels of the probe run in the groove of Similar to calculating with data at the depth of 29.5 m, we get the
plane A. At the same time, the remaining accelerometer gives us the value of the A-axis deviation of CA = 2.41 cm. In conformity with the
interpolation reading B+, B- of the B axis, Figure 1. These readings principle of horizontal displacement calculated from the bottom of
are the output voltage which is proportional to the sine of the angle the monitoring pipe, we have the horizontal displacement value at
72 | Reports on Geodesy and Geoinformatics, 2023, Vol. 116, pp. 69–76
Table 1. Raw data of the first cycle (December 30, 2016) and the second cycle (January 20,
2017) of the ICL2 borehole
*** ***
GK 604M(v1.3.0.8,02/17);2.0;FORMAT II GK 604M(v1.3.0.8,02/17);2.0;FORMAT II
PROJECT :165xd PROJECT :165xd
HOLE NO. :ICL2 HOLE NO. :ICL2
DATE :12/30/16 DATE :1/20/17
TIME :9:19:53 TIME :10:29:53
PROBE NO.:1609783 PROBE NO.:1609783
FILE NAME:i2_001.gkn FILE NAME:i2_002.gkn
#READINGS:57 #READINGS:57
FLEVEL, A+, A-, B+, B- FLEVEL, A+, A-, B+, B-
27.5, 677, -733, 758, -742 27.5, 681, -734, 769, -753
27.0, 651, -705, 739, -744 27.0, 655, -709, 749, -722
26.5, 635, -689, 721, -680 26.5, 639, -693, 731, -690
26.0, 631, -691, 729, -687 26.0, 633, -693, 739, -696
25.5, 611, -672, 727, -690 25.5, 615, -677, 737, -700
25.0, 522, -644, 722, -688 25.0, 521, -642, 732, -698
24.5, 582, -635, 775, -734 24.5, 586, -639, 785, -744
24.0, 564, -620, 734, -689 24.0, 567, -623, 744, -689
23.5, 550, -602, 625, -579 23.5, 554, -606, 633, -589
23.0, 515, -578, 437, -426 23.0, 512, -575, 447, -436
22.5, 472, -530, 191, -202 22.5, 475, -533, 201, -212
22.0, 426, -498, -102, 63 22.0, 432, -504, -92, 53
21.5, 403, -460, -514, 534 21.5, 402, -459, -504, 514
21.0, 370, -428, -749, 782 21.0, 374, -432, -739, 772
20.5, 332, -382, -930, 941 20.5, 332, -383, -920, 961
20.0, 287, -333, -1026, 1060 20.0, 291, -337, -1016, 1049
19.5, 258, -309, -1027, 1039 19.5, 255, -306, -1017, 1039
19.0, 216, -292, -920, 955 19.0, 221, -297, -910, 950
18.5, 214, -271, -701, 732 18.5, 219, -276, -691, 729
18.0, 165, -221, -541, 581 18.0, 166, -222, -532, 572
17.5, 87, -149, -368, 408 17.5, 93, -155, -358, 398
17.0, 37, -92, -211, 248 17.0, 30, -85, -201, 238
16.5, -32, -17, -74, 114 16.5, -25, -24, -64, 104
16.0, -67, 18, 31, -5 16.0, -71, 22, 41, -15
15.5, -110, 57, 122, -88 15.5, -115, 62, 98, -73
15.0, -116, 63, 98, -61 15.0, -116, 62, 98, -61
14.5, -115, 57, 122, -88 14.5, -113, 55, 132, -98
14.0, -90, 32, 162, -129 14.0, -92, 34, 172, -139
13.5, -52, 1, 193, -169 13.5, -56, 4, 203, -179
13.0, -19, -25, 194, -174 13.0, -17, -27, 207, -184
12.5, 29, -74, 179, -148 12.5, 33, -78, 189, -158
12.0, 80, -136, 164, -109 12.0, 84, -140, 174, -119
11.5, 160, -217, 128, -63 11.5, 163, -220, 138, -73
11.0, 229, -289, 83, -26 11.0, 237, -297, 94, -36
10.5, 301, -346, 46, 18 10.5, 308, -353, 56, 8
10.0, 319, -374, 33, 32 10.0, 328, -383, 43, 22
9.5, 330, -384, 36, -8 9.5, 337, -391, 46, -18
9.0, 331, -383, 102, -60 9.0, 334, -386, 112, -70
8.5, 320, -377, 163, -131 8.5, 323, -380, 173, -141
8.0, 321, -374, 223, -193 8.0, 323, -376, 233, -207
7.5, 346, -402, 287, -258 7.5, 340, -396, 297, -268
7.0, 320, -367, 332, -308 7.0, 336, -383, 342, -318
6.5, 295, -351, 388, -339 6.5, 293, -349, 398, -349
6.0, 312, -371, 399, -353 6.0, 317, -376, 409, -363
5.5, 329, -385, 416, -363 5.5, 330, -386, 426, -373
5.0, 319, -372, 422, -379 5.0, 327, -380, 432, -389
4.5, 311, -369, 411, -354 4.5, 329, -387, 421, -364
4.0, 280, -325, 415, -368 4.0, 305, -350, 425, -378
3.5, 231, -300, 334, -286 3.5, 255, -324, 344, -296
3.0, 232, -290, 144, -101 3.0, 254, -312, 154, -111
2.5, 211, -263, -54, 41 2.5, 233, -285, -44, 31
2.0, 189, -248, -243, 240 2.0, 214, -273, -233, 230
1.5, 156, -215, -358, 393 1.5, 177, -235, -348, 383
1.0, 121, -192, -446, 508 1.0, 134, -205, -436, 498
0.5, 115, -174, -490, 559 0.5, 124, -183, -480, 549
0.0, -734, NaN, -753, NaN 0.0, -734, NaN, -753, NaN
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