# Dynamic Inversion Method for Concrete Gravity Dam on Soft Rock Foundation
## 4 Engineering Examples  
### Overview of the Project  
A hydropower dam pivot project is located in Cambodia. The main structure consists of a 112 m high roller-compacted concrete gravity dam, a five-gate spillway at the top of the dam, a PH3 diversion structure, a PH3 powerhouse, and a switching station. According to the 500-year flood design and the calibration of the Probable Maximum Flood (PMF), the reservoir's key water levels are as follows: a calibration flood level of 151.88 m, a design flood level of 150.00 m, a normal storage level of 150.00 m, and a dead water level of 130.00 m. The reservoir has a total capacity of 717.3 million m\({}^{3}\), with a dead water capacity of 354.2 million m\({}^{3}\), and the capacity of the reservoir below the normal storage level of 681.3 million m\({}^{3}\). The dam has a crest elevation of 153.00 m and a base elevation of 41.00 m, with a maximum height of 112.00 m. The dam crest is 6.0 m wide. The upstream face is vertical above 84 m, while below this elevation, it has a slope of 1:0.3. The downstream face has a slope of 1:0.75, with a slope break at 145.00 m.  
To monitor horizontal displacement, a total of eight inverted plumb lines were installed at elevations of 153 m, 120 m, 88 m, 60 m, and 43 m on both the left and right banks of the dam. These instruments were designated as IP1-IP8, with displacement observations beginning on 21 March 2011. IP7 and IP8 were added in January 2014 and installed by July 2014, and their initial values were recorded. In 2018, additional plumb lines were installed in dam sections 4# and 7#, including IP9, PL1-1, PL1-2, and PL1-3 in section 4#, as well as IP10 and PL2 in section 7# (with IP6 as the reference point).  
The dam foundation's horizontal displacement is monitored using inverted plumb lines, which detect displacement in both the downstream and cross-river directions. The monitoring system consists of 10 inverted plumb line holes distributed across different elevations: IP7 in section 5 at the 43.00 m corridor, IP8 in section 6 at the 60.00 m corridor, IP5 and IP6 in sections 3 and 7 at the 88.00 m corridor, IP3 and IP4 in sections 2 and 9 at the 120.00 m corridor, and IP1 and IP2 at the 153.00 m elevation on the dam crest in sections 1 and 10.  
Additionally, in 2018, new inverted plumb lines were added to sections 4# (IP9) and 7# (IP10). The monitoring layout is illustrated in Figure 2. The foundation's inverted displacement was observed from baseline values recorded before reservoir impoundment. However, displacement data from the construction period are incomplete and not fully reflected. Since IP7 and IP8 were installed later as supplementary instruments, only post-2014 monitoring data are available. Initial values for IP9 and IP10 were recorded on 7 June 2018.  
In this paper, the measured data of IP6, IP10, and PL2 installed at dam section 7 are used for inversion analysis. The dam section 7# is equipped with three plumb lines for monitoring the displacement in the upstream-downstream direction. A normal plumb line (PL2) was installed at a 153 m elevation. Two inverted plumb lines (IP10 and IP6) were installed at 120 m and 88 m elevations. The plumb line allows for measuring relative displacement between the two ends of the plumb line. For a normal plumb line, the upper end of the wire is fixed at the top of the dam, while a heavy weight is damped at its lower end. For an inverted plumb line, the plumb wire is fixed at the lower end, and the upper end of the wire is linked to a float submerged in a water box in the observation area. Observations are recorded digitally.