# Application of Elastic Wave Velocity for Estimation of Soil Depth

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Testing Site

#### 2.1. Site Description

^{2}, respectively, and the latitude and longitude of the top of the mountain are N 36°29′15.7313′′ and E 127°18′40.5986′′. A drone aerial survey was performed to obtain a topographic map and digital elevation model. Figure 1 shows the topographic map: the area consists of one main stream and several branch streams. The vertical length and area of the main stream are approximately 206 m and 14,675 m

^{2}, respectively. Figure 1 also indicates the presence of the debris barrier and check dam at the site to prevent additional debris flow (N 36°29′04.3147′′, E 127°18′44.7017′′). The main stream was divided at four points, selected by considering slope characteristics: point A (N 36°29′10.8530′′, E 127°18′44.1891′′), point B (N 36°29′12.045′′, E 127°18′39.5912′′), point C (N 36°29′14.8329′′, E 127°18′30.7079′′), and point D (N 36°29′18.2046′′, E 127°18′23.6158′′). Point A, which is located at the bottom of the main stream, shows various fallen trees and weeds undergoing decay and rot, suggesting that considerable time has passed since the occurrence of the last debris flow. The slope of point A was measured to be approximately 10°, which is low compared to the slopes at points B and C. Thus, point A is covered with various flowed materials from the streams above due to debris flow. Point B shows a dramatically steeper slope of approximately 27° and the area mainly consists of sedimentary basin. Point C has the largest rapid slope (~32°) and width (maximum 105 m) among the selected points. Note that point C is located at a large catchment basin. Finally, point D indicates the initial zone where the debris flow occurred as ascertained by the presence of upright trees and a stable subsurface without collapsed conditions.

#### 2.2. Soil Classification

## 3. Methodology

#### 3.1. Seismic Survey

#### 3.2. Dynamic Cone Penetrometer Test

## 4. Results and Analysis

## 5. Discussion

_{1}and V

_{2}), and the time intercept (t

_{1}). However, the clear determination of V

_{1}, V

_{2}, and t

_{1}is not easy because wave velocity in a given layer is not constant, resulting from the natural soil deposits rarely being homogeneous and wave velocity slightly increasing with an increase in depth at a given layer. Note that seismic waves propagate in a medium through connected particles, and seismic wave velocity depends on soil structure and stress condition. Seismic wave propagation is primarily affected by the stiffness of the fabric in a particular material, and thus seismic wave velocity and effective stress (σ′) have a certain relationship with experimentally determined coefficients (α and β).

## 6. Conclusions

- The estimated soil depth using the soil classification based on the reference P-wave velocity shows high variation and high soil depth compared with that based on dynamic cone penetration test, reflecting the estimation of soil depth based on the reference wave velocity is not reliable.
- The seismic wave velocity slightly increases with depth even in one layer and it changes rapidly at layer boundaries. Because the graphical bilinear method newly suggested in this study is based on the change in the slope between wave velocity and depth, the estimated soil depths using the suggested method are comparable with the measured values by dynamic cone test, reflecting the enhanced reliability in estimating soil depth by seismic survey.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Aerial photography of the testing area. Points A and D denote the bottom and top streams, respectively. Points B and C indicate the middle stream. The field tests were performed from points A to D.

**Figure 2.**Sieve test results: (

**a**) bottom stream (point A in Figure 1); (

**b**) middle stream (point B); (

**c**) top stream (point C). D

_{10}, D

_{30}, and D

_{60}denote the diameters at passing percentages of 10, 30, and 60%, respectively. C

_{u}and C

_{g}are coefficients of uniformity and curvature, respectively.

**Figure 3.**Locations of the field investigations, including seismic survey and dynamic cone penetrometer (DCP). Note: the numbers with red circles denote the DCP testing sites (BS: 3 holes, MS: 3 holes, TS: 3 holes, and BTS: 10 holes); and the distance between each number in the figure is 10 m.

**Figure 4.**Travel time-distance curves through seismic survey: (

**a**) BTS; (

**b**) BS; (

**c**) MS; and (

**d**) TS. Note 10, 20, 30, and 100 m distances indicate points 1, 2, 3, and 10, respectively, in Figure 3.

**Figure 6.**Measured DPI values of each stream: (

**a**) BTS; (

**b**) BS; (

**c**) MS; and (

**d**) TS. Note the numbers in each figure indicate the location of dynamic cone penetration test described in Figure 3.

**Figure 7.**Method for selecting soil depth through measured elastic wave velocity. Line “a” denotes the first slope between wave velocity and depth. Lines “b”, “c”, and “d” represent the second, third and fourth slopes, respectively. Point “e” is the intersection point between lines “a” and “b”. Note the figure is the relation between wave velocity and depth of point 1 (or 10 m distance) in the BTS line (Figure 3).

**Figure 8.**Estimated soil depth profile based on graphical bilinear method: (

**a**) 30 m of BTS; (

**b**) 80 m of BTS; (

**c**) 100 m of BTS; (

**d**) 20 m of BS; (

**e**) 30 m of MS; and (

**f**) 20 m of TS.

**Figure 9.**Soil depth based on dynamic cone penetration test: (

**a**) 30 m of BTS; (

**b**) 80 m of BTS; (

**c**) 100 m of BTS; (

**d**) 20 m of BS; (

**e**) 30 m of MS; and (

**f**) 20 m of TS.

**Figure 10.**Comparison of soil depths estimated by seismic wave velocity and measured by dynamic cone penetration test.

Position | Soil Depth (m) | Error Ratio (%) | ||||
---|---|---|---|---|---|---|

Measured | Estimated | |||||

Dynamic Cone Test | Reference P-Wave Velocity | Graphical Bilinear Method | Reference P-Wave Velocity | Graphical Bilinear Method | ||

BTS | 1 | 1.1 | 2.3 | 1.1 | 109.1 | 0.0 |

2 | 0.8 | 2.0 | 0.8 | 150.0 | 0.0 | |

3 | 1.0 | 1.8 | 1.0 | 80.0 | 0.0 | |

4 | 0.4 | 1.9 | 0.5 | 375.0 | 25.0 | |

5 | 0.5 | 1.4 | 0.6 | 180.0 | 20.0 | |

6 | 0.2 | 1.8 | 0.5 | 800.0 | 150.0 | |

7 | 0.6 | 1.4 | 0.5 | 133.3 | 16.7 | |

8 | 0.7 | 2.4 | 1.0 | 242.9 | 42.9 | |

9 | 1.9 | 5.6 | 1.9 | 194.7 | 0.0 | |

10 | Over 2.0 | 3.5 | 3.0 | - | - | |

Average | 251.7 | 28.2 | ||||

BS | 1 | 0.2 | 1.7 | 0.2 | 750.0 | 0.0 |

2 | 0.9 | 1.4 | 0.9 | 55.6 | 0.0 | |

3 | 1.0 | 3.4 | 1.2 | 240.0 | 20.0 | |

Average | 348.5 | 6.6 | ||||

MS | 1 | 1.1 | 2.4 | 1.0 | 118.2 | 9.1 |

2 | 0.8 | 2.6 | 0.9 | 225.0 | 12.5 | |

3 | 1.0 | 2.4 | 1.1 | 140.0 | 10.0 | |

Average | 161.1 | 10.5 | ||||

TS | 1 | 0.4 | 4.4 | 0.6 | 1000.0 | 50.0 |

2 | 1.9 | 5.2 | 2.2 | 173.7 | 15.8 | |

3 | 0.9 | 4.2 | 0.9 | 366.7 | 0.0 | |

Average | 513.5 | 21.9 |

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**MDPI and ACS Style**

Choo, H.; Jun, H.; Yoon, H.-K. Application of Elastic Wave Velocity for Estimation of Soil Depth. *Appl. Sci.* **2018**, *8*, 600.
https://doi.org/10.3390/app8040600

**AMA Style**

Choo H, Jun H, Yoon H-K. Application of Elastic Wave Velocity for Estimation of Soil Depth. *Applied Sciences*. 2018; 8(4):600.
https://doi.org/10.3390/app8040600

**Chicago/Turabian Style**

Choo, Hyunwook, Hwandon Jun, and Hyung-Koo Yoon. 2018. "Application of Elastic Wave Velocity for Estimation of Soil Depth" *Applied Sciences* 8, no. 4: 600.
https://doi.org/10.3390/app8040600