**5.2. Results**

**Figure 17** shows the shear strain distribution and **Figure 18** indicates the volumetric strain distribution at the time when the model locates the center of shaking from downstream to upstream. It is found that the large shear strain occurs at the lower part for both cases while the direction is different for the case. Although Case 1 shows that the shear strain to the same direction occurs, the shear strain to the different direction is distributed for Case 2. For the volumetric strain, the maximum value is shown at the top and both ends of the bottom, and the upstream side has the compression strain, and the downstream side has the extension strain for Case 1. On the other hand, Case 2 shows that the extension and compression strain distribute alternatively. This stripe pattern can be seen in the centrifugal loading test as shown in **Figure 12**. However, the large extension strain cannot be seen in the numerical simulation. As a result of the numerical simulation, the analysis results are different from the experimental results. In particular, the large extension strain at the upper part cannot be realized by the

**Figure 16.** Model size of the numerical simulation. (a) Case 1 and (b) Case 2.

**Table 1.** Material parameters used for numerical analysis.

Unit weight (kN/m3

**Parameters Dam body Base (Case 2)**

) 18 18

Seismic Crack Investigation in an Earth Dam by Centrifugal Loading Test

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Cohesion (kPa) 15 15

Elastic modulus (kPa) 3000 2850 Internal friction angle (°) 35 35 Poisson's ratio 0.3 0.3

**Figure 17.** Shear strain distribution of the numerical simulation. (a) Case 1 and (b) Case 2.

Seismic Crack Investigation in an Earth Dam by Centrifugal Loading Test http://dx.doi.org/10.5772/intechopen.78788 35

**Figure 16.** Model size of the numerical simulation. (a) Case 1 and (b) Case 2.


**Table 1.** Material parameters used for numerical analysis.

**4.3. Summary of the experiment**

**5. Numerical examination**

intensified at the upper part.

reflected wave depending on the location.

not observed.

34 Dam Engineering

**5.1. Conditions**

**5.2. Results**

It can be concluded from the experimental results as follows:

**1.** The cracks in the dam-axis direction can be realized by the experiment. Such a crack shown at the earthquake damage is caused by the extension strain. Therefore, the extension stress is caused by the parts of the crest. While the extension failure is not examined in the design

**2.** The shear strain at the cross section developed to the slope direction. While the shear strain distribution coincided with the sliding failure of the slope, the failure form by sliding was

To investigate the reproducibility of the extension strain distribution by numerical simulation, the dam model of which size is the same as the 1-G shaking test [2] is simulated. In this study, two cases are examined. The first one is the case in which the dam body is directly shaken at the bottom of the dam. The second one is the case in which the thin base is added under the dam. The objective of the second case is to input the inhomogeneous wave into the dam body. When a given wave is subjected to the bottom of the base, the shaking of the bottom of the dam body becomes a little inhomogeneous, while the amplitude is not so different. The dam body has a height of 150 mm and upstream and downstream gradients of 1:0.545. As the slope gradient is steep, the shaking would be

To examine the strain distributions, the elasto-plastic finite element method (FEM) using Mohr-Coulomb's criteria as the yield function is applied in this study. The bottoms of the

**Figure 16** shows the schematic view of the models and **Table 1** indicates the material properties. By setting the elastic modulus of the base a little smaller than that of the dam, the shaking situation at the bottom of dam body becomes inhomogeneous by the different behavior of

**Figure 17** shows the shear strain distribution and **Figure 18** indicates the volumetric strain distribution at the time when the model locates the center of shaking from downstream to upstream. It is found that the large shear strain occurs at the lower part for both cases while the direction is different for the case. Although Case 1 shows that the shear strain to the same direction occurs, the shear strain to the different direction is distributed for Case 2. For the volumetric strain, the maximum value is shown at the top and both ends of the bottom, and

models are subjected to 2.4 Hz of a horizontal sine wave. The amplitude is 280 gal.

process, the counterplan may be necessary as the earthquake resistance.

**Figure 17.** Shear strain distribution of the numerical simulation. (a) Case 1 and (b) Case 2.

the upstream side has the compression strain, and the downstream side has the extension strain for Case 1. On the other hand, Case 2 shows that the extension and compression strain distribute alternatively. This stripe pattern can be seen in the centrifugal loading test as shown in **Figure 12**. However, the large extension strain cannot be seen in the numerical simulation.

As a result of the numerical simulation, the analysis results are different from the experimental results. In particular, the large extension strain at the upper part cannot be realized by the

**Acknowledgements**

support.

**Author details**

Akira Kobayashi1

Osaka, Japan

**References**

(in Japanese)

(in Japanese)

2011;**31**:1579-1593

2 Kyoto University, Kyoto, Japan

AGSSEA. 2015;**44**(2):27-34

Engineering Geology. 2006;**86**:118-133

Engineering; 2004; Vancouver Canada. Paper No. 2359

dam. Tsuchi to Kiso. JGS. 1975;**23**(5):11-20 (in Japanese)

\* and Akira Murakami2 \*Address all correspondence to: koba5963@kansai-u.ac.jp

This study was carried out with the support of the grant in aid for scientific research (A) and (B) of JSPS. The experiments were assisted by Mr. Tsurui and Mr. Sugano who were the graduate students of Kyoto University at that time. We appreciate the financial and technical

Seismic Crack Investigation in an Earth Dam by Centrifugal Loading Test

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1 Department of Civil, Environmental and Applied systems Engineering, Kansai University,

[1] Kato T. Flood mitigation function and its stochastic evaluation of irrigation ponds. Bulletin of the National Research Institute of Agricultural Engineering. 2005;(44):1-22

[2] Miyanaga Y, Kobayashi A, Murakami A. 1-G model test with digital image analysis for seismic behavior of earth dam. Geotechnical Engineering Journal of the SEAGS &

[3] Lin ML, Wang KL. Seismic slope behavior in a large-scale shaking table model test.

[4] Masukawa S, Yasunaka M, Kohgo Y. Dynamic failure and deformations of dam-models on shaking table tests. In: Proceedings of 13th World Conference on Earthquake

[5] Tsutumi H, Watanabe H, Ogata N, Shiomi S. Dynamic test for seismic design of fill-type

[6] Masukawa S, Yasunaka M, Hayashida Y. Shaking table tests by silicone rubber dam model with different ratio of crest length to dam height. Tsuchi to Kiso. JGS. 2008;**56**(10):16-19

[7] Kim MK, Lee SH, Choo YW, Kim DS. Seismic behaviors of earth-core and concrete-faced rock-fill dams by dynamic centrifuge test. Soil Dynamics and Earthquake Engineering.

**Figure 18.** Volumetric strain distribution of the numerical simulation. (a) Case 1 and (b) Case 2.

analyses. The distribution of the shear strain is also quite different from the observed one. As a present conclusion, the ordinary elasto-plastic model is not suitable for the dynamic analysis of the dam.
