# Variations of Fluvial Sediment Transport after Large Earthquakes: Field Study in Taiwan Catchments

## Abstract

**:**

## 1. Introduction

^{2}/year and the average chemical denudation rate is 65 mg/cm

^{2}/year. The results of Li [3] show that the average denudation rate in Taiwan is at least 1365 mg/cm

^{2}/year, corresponding to an erosion rate of 4 mm/year, which is one of the highest in the world. Hwang [4] found that the amount of sediment transported from the 49 catchments in Taiwan is related to the geological settings surrounding the catchments. Dadson et al. [5] estimated the suspended sediment discharge and inferred that 384 Mt/year of suspended sediments, which is equivalent to an erosion rate of 3–6 mm/year, is transported into the ocean from Taiwan. Dadson et al. [6] compared the variability of sediment discharges before and after the 1999 Chi-Chi earthquake and found that the central region of Taiwan was located near the epicenter, so the average sediment discharge after the earthquake increased by 4.4 times. Additionally, Lin et al. [7] and Chuang et al. [8] found that the amount of suspended sediment discharges from two major rivers in the central region of Taiwan increased more than four-fold after the 1999 earthquake.

## 2. Study Methods

#### 2.1. Calculation of Suspended Sediment Discharges

^{3}/s) through a power law, Cs = κQ

^{b}, where the exponent b is determined by the availability and mobilization of sediment and κ is the suspended sediment concentration at the unit water discharge [12]. The rating-curve method based on the Cs–Q power law relation is one of the most common estimation methods for suspended sediment discharge [14,15], especially in the case of insufficient hydrometric data. Kao et al. [15] collected water samples from rivers in eastern Taiwan and found that the Cs–Q power law relation still exists even under very low water discharge (<10 m

^{3}/s). This indicates that even at low water discharge, there is still suspended sediment transport in the river and that the transport characteristics of Taiwan’s rivers have transport-dominated conditions. In general, the rating-curve method is suitable for the calculation of suspended sediment in a river in a transport-dominated environment [16]. However, the shortcomings of a simple rating-cure method lie in the fact that the calculated suspended sediment discharge are expected values and there will be residual differences between the calculated and observed values. A modified rating-curve method is developed to reduce the residual difference.

^{3}/s) of the ith day. ${\mathsf{\epsilon}}_{\mathrm{i}}$ is the residual difference between the observed SSD at the ith day and estimated SSD at the ith day. By fitting the power laws to the data for selected time slices, while keeping the exponent, b, fixed at the pre-earthquake best-fit value to permit the direct comparison of sediment transport, the variation of the unit sediment concentration κ has been tracked to reveal the impact of the earthquake.

_{storm}for each typhoon is then determined. Sediment settled on the channel would be re-disturbed during subsequent rainstorm events [17]. The study attempts to examine the impact of earthquakes on sediment supply; therefore, it is assumed that the effects of re-disturbed sediment occurred constantly, and the variation of sediment discharge was mainly induced by periodical events (e.g., heavy typhoons and earthquakes). Although it is hard to examine that part of re-disturbed sediment, the effect of not doing so may mean that the impact of an extreme event (earthquake or heavy rainstorm) on sediment supply may not be examined in short-term observation. By enlarging the observation period, the impact of a single earthquake event on sediment supply can still be observed from sediment data. Further, unit suspended concentration is obtained from regression of one-year data, and it implies the suspended concentration under unit water discharge. The effect of water discharge during different rainfall events (e.g., typhoons) can be reduced.

#### 2.2. Measurements of Rock Strength and Joint Density

_{V}, was measured in the field. Based on the suggestions of ISRM [18], the joint density was calculated as follows:

_{n}is the investigated length of the nth set of joints along the direction perpendicular to the joint plane and N

_{n}is the joint number of the nth set of joints in the investigated length L

_{n}.

## 3. Earthquake Effects on Sediment Yields

#### 3.1. Changes in Observation Sediment Data

^{3}/s, the unit concentration after the earthquake was twice that before the earthquake. When the water discharge was more than 100 m

^{3}/s, the unit concentration after the earthquake was more than four times that before the earthquake (Figure 3). The results showed that the unit concentrations increased significantly as the water discharge increased.

^{3}/year, and the average annual sediment discharge was 57.77 Mt/year. During the period from 2004 to 2008, the average annual runoff was 2.92 km

^{3}/year and the average annual sediment discharge was 82.01 Mt/year. This exhibited that the annual sediment discharge increased by 1.4 times after the 2003 earthquake at a similar water discharge rate.

#### 3.2. Influence of Earthquake Frequency on Sediment Discharge

^{−1}) of earthquakes and the annual sediment discharge in the selected basin. Seed and Idriss [19] analyzed the relationship between the peak ground accelerations (PGAs) of earthquakes and epicentral distances and found that the PGAs generated by earthquakes of magnitude 5.0 to 6.0 fell to 0 g when the distance was more than 161 km from the epicenter. The PGAs generated by earthquakes with magnitudes greater than 6.0 were smaller than 0.1 g when the distance was more than 161 km from the epicenter. Therefore, I assumed the largest distant influence of an earthquake was 100 km. Ten different earthquake influence distances were employed to correspond to the annual sediment discharge in different catchments. The 10 earthquake influence distances ranged from 10 to 100 km with an interval of 10 km. When a catchment was located within the influence distance of an earthquake, it meant the catchment had been affected by the earthquake. By summating the number of earthquakes whose influence distances reached the catchment, the seismic influence frequency could be calculated by dividing the earthquake number by the length of time period from 1970 to 2009 in the year (Figure 5). The results showed that the seismic frequency in the Hualien catchment was the highest, and the lowest was in the Touchien catchment. In addition, the distribution of seismic frequency shows that the seismic influence frequency of the eastern region of Taiwan is higher than that of the western region, and that of the central region is higher than that of the northern and southern regions. By comparing the average annual sediment discharges with the seismic frequency at different influence distances, it was found that the squared correlation coefficient (R

^{2}) ranged from 0.21 to 0.62 (Figure 5a–c). The best correlation between the earthquake frequency and the average annual sediment discharges, R

^{2}of 0.62, was obtained when the earthquake influence distance was 50 km (Figure 5d). In accordance with the analysis of Seed and Idriss [19], the M-5.0 earthquake-induced horizontal ground acceleration was reduced from approximately 0.44 g to less than 0.05 g at a distance of 50 km from the epicenter, and even the M-7.6 earthquake-induced horizontal ground acceleration decreased to less than 0.2 g. The impact of these vibrations on geologic materials has been rather weak. The results are in agreement with the analyses of the landslide density induced by the 1999 Chi-Chi earthquake in the Chenyoulan and Tachia catchments [7,8]. When the PGA was less than 0.2 g, the coseismic landslide density begin to decrease rapidly, and the landslide density approached zero when the PGA was less than 0.1 g.

## 4. Recovery Periods of Fluvial Sediment Transport

^{3}and the annual runoff of the Chenyoulan River in 2000 was 0.54 km

^{3}, which were lower than their average values of 0.31 and 0.73 km

^{3}, respectively. Therefore, after the 1999 earthquake, the unit concentration in the two rivers did not increase immediately. In contrast, the annual runoff of the Peinan River in 2000 was 3.32 km

^{3}, which was greater than the average of 3.01 km

^{3}. Therefore, the unit concentration in 2000 was higher than the average before the earthquake. The results showed that the unit concentration of sediment transport did not necessarily exhibit an immediate increase in the subsequent year after an earthquake.

## 5. Influence Factors for Sediment Supply

^{−3}), average annual runoff (Q, km

^{3}/year), and seismic frequency (Eq, year

^{−1}) were independent variables. The seismic frequency was the average annual number of earthquakes with a magnitude of more than 5 and influence distance of 50 km. Through the analysis, the best-fit relationship could be obtained (Figure 9):

^{1.359}∙UCS

^{−0.787}∙Jv

^{1.502}∙Eq,

^{2}for the regression analysis was 0.838, which meant that the efficiency of the regression relation (Equation (5)) was 83.8%. In other words, the four influence factors contributed around 84% of influence on sediment yields. This equation implies a long-term relationship between sediment discharge and influence factors. Therefore, it cannot be used to predict annual sediment discharge. The equation also reveals a positive relationship between sediment discharge and runoff, joint density of rocks, and earthquake frequency, and a negative relationship between sediment discharge and rock strength. Furthermore, each influence factor was pulled out separately, and then the regression analysis was conducted. The value of R

^{2}was obtained in the absence of one of the influence factors. Furthermore, the efficiency of the influence factor could be calculated as the difference between the R

^{2}before and after the influence factor was pulled out.

^{2}remained at 0.276 only (Table 1). This meant that the efficiency from annual runoff was 56.2%, which is the highest among the four influence factors. The efficiency of the UCS factor was the second highest at 18.5%. The efficiencies of the Jv and Eq factors regarding the annual sediment supply were 3.4% and 5.7%, respectively. It can be seen that the influence of geomaterial properties (including rock strength and fragmentation) on the sediment yield was 21.9%, and the influence of extrinsic factors (including runoff and earthquake) was 61.9%. The difference of long-term average annual sediment discharges between catchments was mainly determined by the extrinsic factors. The rest of the efficiency (16%), which was not contained in the multiple regression analysis, can be attributed to other factors, such as human activity, temperature, and experimental errors, which were not discussed in the study.

## 6. Conclusions

## Supplementary Materials

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Distribution of river catchments and hydrometric stations. The star symbols represent the epicenters of the 1999 Chi-Chi earthquake and 2003 Chengkung earthquake.

**Figure 2.**(

**a**) The Cs–Q relationships before and after the 1999 Chi-Chi earthquake in the Chenyoulan River. (

**b**) Variation of suspended sediment discharges in the Chenyoulan River. The thick black line represents the lower boundary of suspended sediment discharges.

**Figure 3.**(

**a**) The Cs–Q relationships before and after the 1999 Chi-Chi earthquake in the Tachia River. (

**b**) The ratios of unit sediment concentrations after and before the 1999 Chi-Chi earthquake in the Tachia River.

**Figure 5.**Distribution of seismic frequencies, and relationships between seismic frequencies and the averagely annual SSD under different influence distances: (

**a**) 10 km, (

**b**) 50 km, and (

**c**) 100 km. (

**d**) Variation of determination coefficients at different influence distances.

**Figure 6.**Time series of unit sediment concentrations in (

**a**) Touchien River, (

**b**) Choshui River, and (

**c**) Peinan River.

**Figure 7.**Variations of the ratio, ∆κ, of unit concentration in (

**a**) Touchien River, (

**b**) Chenyoulan River, and (

**c**) Peinan River.

Influence Factor | R^{2} * | Efficiency (%) |
---|---|---|

average annual runoff (Q, km^{3}/year) | 0.276 | 56.2 |

average uniaxial compressive strength (UCS, MPa) | 0.815 | 18.5 |

average joint density (Jv, m^{−3}) | 0.966 | 3.4 |

seismic frequency (Eq, year^{−1}) | 0.943 | 5.7 |

others | 0.838 | 16.2 |

^{2}was obtained in the absence of one of the influence factors. Furthermore, the efficiency of the influence factor could be calculated as the difference between the R

^{2}before and after the influence factor was pulled out.

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**MDPI and ACS Style**

Lin, G.-W.
Variations of Fluvial Sediment Transport after Large Earthquakes: Field Study in Taiwan Catchments. *Water* **2018**, *10*, 1836.
https://doi.org/10.3390/w10121836

**AMA Style**

Lin G-W.
Variations of Fluvial Sediment Transport after Large Earthquakes: Field Study in Taiwan Catchments. *Water*. 2018; 10(12):1836.
https://doi.org/10.3390/w10121836

**Chicago/Turabian Style**

Lin, Guan-Wei.
2018. "Variations of Fluvial Sediment Transport after Large Earthquakes: Field Study in Taiwan Catchments" *Water* 10, no. 12: 1836.
https://doi.org/10.3390/w10121836