**4. Experimental results**

#### **4.1. The behavior of cross section**

By using the method mentioned above, the behavior of the cross section is examined. **Figure 7** shows the final displacement vector distribution after experiment and the situation of cracks. The cracks occurred at the upper part of the dam body of which the situation is explained later. The downward displacement vector is large at the upper part while the displacement at the lower part is minimal.

The gauge points shown by the number in **Figure 8** are focused on highlighting the deformation pattern. The downward displacement at the vertical centerline of the dam body, of which

**Figure 7.** Displacement vector distribution after experiment.

**Figure 8.** Number of gauge points highlighted for observation.

**3.3. Calculation of strain**

28 Dam Engineering

**4. Experimental results**

the lower part is minimal.

**4.1. The behavior of cross section**

**Figure 7.** Displacement vector distribution after experiment.

As the gauge points are regarded as the nodes, the cross section is discretized with a triangular element. By using the plane strain condition, the shear and volume strains are calculated

**Figure 6.** Examples of image analysis process: (a) picture image; (b) binary image; and (c) noise reduction result.

By using the method mentioned above, the behavior of the cross section is examined. **Figure 7** shows the final displacement vector distribution after experiment and the situation of cracks. The cracks occurred at the upper part of the dam body of which the situation is explained later. The downward displacement vector is large at the upper part while the displacement at

The gauge points shown by the number in **Figure 8** are focused on highlighting the deformation pattern. The downward displacement at the vertical centerline of the dam body, of which

for each element with the theory of the finite element method.

the number is from 2 to 72, is shown in **Figure 9**. To observe the tendency of the settlement, the displacement is averaged with the period of 0.02 s which is the same as the period of shaking. The downward displacement becomes gradually large with the height of the gauge point. The deformation continues during the experiment at the upper part while the displacement at the lower part does not change so much during the experiment. It is found that the deformation of the upper part occupies the settlement of the dam.

Then, to observe the horizontal deformation, the change in the horizontal distance between two gauge points is investigated. For example, at the upper most part of the dam, the horizontal distance of gauge points 1 and 3 is presented (see **Figure 8**). **Figure 10** shows the change in the horizontal distances at various heights of the dam with time, in which the legend means the number of gauge points used for the distance calculation. While the horizontal distance becomes large at the height of the middle, the number of 29–31, at the early stage, the ones at the upper parts, the number of 1–3 and 5–7, gradually increase with time. The upper parts have a significant change in the horizontal distance finally. Entirely, the center part of the dam has the horizontal tension behavior except for the lowest part.

**Figure 9.** Downward displacement at the centerline of the dam.

means the corresponding actual one. The shear strain to upstream direction occupies the upstream lower part, while the downstream side of the dam shows the shear strain at the downstream direction. The shear strain in both directions becomes larger at the

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**Figure 12** indicates the volumetric strain distribution change. The positive value means the extension. It is found that the extension occurs at the upper part during the shaking. At the lower part, the extension and compression distribute apparently, and so the striped pattern can be seen. It is shown that the part showing the extension strain coincides with the part

The situation of the crest after the test is shown in **Figure 13**. The crack is marked with the red line. The crack in the dam-axis direction can be seen at the center of the crest as shown at the actual damage site. The sliding behavior cannot be found at the slope of the dam. In order to investigate the deformation situation at the crest, an additional experiment is carried out, at which the gauge points are set at the crest and slope as shown in **Figure 14**. As the situation was photographed from the top, the strain is estimated just for the horizontal plane (**Figure 15**). Therefore, the obtained strain is not the one on the slope but the apparent strain on the horizontal plane. Only the strain distribution at the crest is the accurate value

indicating the horizontal tension behavior explained (see **Figure 11**).

lower part than the upper part.

**Figure 12.** Change in volumetric strain distribution.

**4.2. Behavior of crest**

as a strain.

**Figure 10.** Change in the horizontal distance at the centerline of the dam.

**Figure 11** shows the change in shear strain distribution. The situation starts from the left end of shaking, moves to the center and right end, and then reverses to the center and finally returns to the left end. The positive value means the shear strain at downstream shown in **Figure 4(a)**, which coincides with the right-hand side. The time

**Figure 11.** Change in shear strain distribution.

means the corresponding actual one. The shear strain to upstream direction occupies the upstream lower part, while the downstream side of the dam shows the shear strain at the downstream direction. The shear strain in both directions becomes larger at the lower part than the upper part.

**Figure 12** indicates the volumetric strain distribution change. The positive value means the extension. It is found that the extension occurs at the upper part during the shaking. At the lower part, the extension and compression distribute apparently, and so the striped pattern can be seen. It is shown that the part showing the extension strain coincides with the part indicating the horizontal tension behavior explained (see **Figure 11**).

#### **4.2. Behavior of crest**

The situation of the crest after the test is shown in **Figure 13**. The crack is marked with the red line. The crack in the dam-axis direction can be seen at the center of the crest as shown at the actual damage site. The sliding behavior cannot be found at the slope of the dam. In order to investigate the deformation situation at the crest, an additional experiment is carried out, at which the gauge points are set at the crest and slope as shown in **Figure 14**. As the situation was photographed from the top, the strain is estimated just for the horizontal plane (**Figure 15**). Therefore, the obtained strain is not the one on the slope but the apparent strain on the horizontal plane. Only the strain distribution at the crest is the accurate value as a strain.

**Figure 12.** Change in volumetric strain distribution.

**Figure 11.** Change in shear strain distribution.

**Figure 11** shows the change in shear strain distribution. The situation starts from the left end of shaking, moves to the center and right end, and then reverses to the center and finally returns to the left end. The positive value means the shear strain at downstream shown in **Figure 4(a)**, which coincides with the right-hand side. The time

**Figure 10.** Change in the horizontal distance at the centerline of the dam.

30 Dam Engineering

**Figure 13.** Cracks at the crest after the experiment.

**Figure 14.** The gauge points on the crest and the slope. (a-1) Left end: shear strain; (a-2) left end: volumetric strain; (b-1) center: shear strain; (b-2) center: volumetric strain; (c-1) right end; shear strain; (c-2) right end: volumetric strain; (d-1) center: shear strain; (d-2) center: volumetric strain.

The shear strain is shown to develop to the upstream and downstream direction near the wall of the sand box. These results may be caused by the friction between wall and dam model. The direction of shear strain distributes alternatively, and the large shear strain develops in the upstream and downstream direction.

On the other hand, while the volumetric strain also shows the stripe pattern, the direction of the strain development is dam-axis one, which coincides with the crack situation shown in **Figure 13**. It can be found that the crack shown in **Figure 13** is caused by the extension

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strain at the crest.

**Figure 15.** Shear and volumetric strain at the crest and slope.

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**Figure 15.** Shear and volumetric strain at the crest and slope.

The shear strain is shown to develop to the upstream and downstream direction near the wall of the sand box. These results may be caused by the friction between wall and dam model. The direction of shear strain distributes alternatively, and the large shear strain develops in

**Figure 14.** The gauge points on the crest and the slope. (a-1) Left end: shear strain; (a-2) left end: volumetric strain; (b-1) center: shear strain; (b-2) center: volumetric strain; (c-1) right end; shear strain; (c-2) right end: volumetric strain; (d-1)

the upstream and downstream direction.

center: shear strain; (d-2) center: volumetric strain.

**Figure 13.** Cracks at the crest after the experiment.

32 Dam Engineering

On the other hand, while the volumetric strain also shows the stripe pattern, the direction of the strain development is dam-axis one, which coincides with the crack situation shown in **Figure 13**. It can be found that the crack shown in **Figure 13** is caused by the extension strain at the crest.
