Protecting highway bridges against debris flows using lateral berms: a case study of the 2008 and 2011 Cheyang debris flow events, China

ABSTRACT Lateral berms are often constructed to protect highway bridges against debris flows in mountainous regions. Currently, different solutions for lateral berm design are debated. The lack of standardization results in the improper design of lateral berms, limiting the mitigating effect. In this paper, a monitoring case of the mitigating effect of a lateral berm is introduced. The lateral berm was constructed through a bridge culvert at the alluvial fan of a debris-flow gully. In September 2008, a debris flow in this gully completely buried the lateral berm. The proposed numerical integral method was used to back analyse the flowing velocity and mud depth in berm. Results supported the speculation that abrupt decreases in mud depth and flow velocity in the lateral berm caused deposits that compressed the effective berm depth and resulted in overtopping flow. Therefore, we suggested reducing the berm width in order to increase the flow velocity in the berm. In June 2011, another debris flow with a smaller magnitude occurred in the gully, and the reconstructed lateral berm reportedly performed well to protect the bridge of Yalu highway. The case studies highlighted that berm width should be one of the main considerations in the berm design.


Introduction
Debris flows are major threats to the infrastructure of highways and high-speed railways. In China, for instance, 1036 potential debris flow gullies have been investigated along the well-known Sichuan-to-Tibet road, with nearly 400 debris flow events and 200 million RMB in economic losses recorded (Tang 1986;Yang 1993;Han et al. 2015b). These debris flow events often cause severe damage to the infrastructure of highways. As reported by Liu et al. (2014), the catastrophic Yingxiu debris flow event on 14 August 2010 in the Wenchuan area was responsible for damage to nine bridges and interrupting traffic for two months. Thus, the prevention and mitigation of debris flows are key to ensuring the safety of infrastructure in mountainous regions (Han et al. 2015a;Han et al. 2018).
To protect infrastructures against debris flows in mountainous regions, countermeasures must be used. Commonly used countermeasures include both passive and active measures (VanDine et al. 1997). Passive measures attempt to prevent debris flow by zoning or warnings and evacuation, e.g. early warning systems, proper land use strategies, and improvements to buildings (Han et al. 2017).

Background
Yalu highway is located in the mountainous region of southwestern Sichuan Province, China (as shown in Figure 1). It has been the focus of multi-year construction on the Chinese national highway network. The region along Yalu highway belongs to the southeastern margin of the Tibetan Plateau. High seismic activity in this region is dominated by the three major active faults distributed in the region, i.e. the Longmenshan, Anninghe, and Xiangshuihe faults (Chen et al. 2012). As a result of frequent tectonic activity and the complex geological and geographical conditions, strong earthquakes have occurred frequently, accompanied by large numbers of landslides and debris flows associated with serious damage (Wang et al. 2007;Chen et al. 2010). We investigated the geomorphologic conditions along Yalu highway, and divided the study region into two major segments: segment 1 from Ya'an to Shimian over hilly terrain and segment 2 from Shimian to Lugu over highlands and mountainous terrain. During the investigative work, 19 debris flow gullies were explored, with 6 gullies along segment 1 and 13 gullies along segment 2.
To protect the highway's infrastructure, structural countermeasures were planned to accompany the construction of Yalu highway, including check dams and lateral berms. These countermeasures were expected to obstruct the debris flow path or direct the debris flow to areas of low consequence. However, in the investigation work regarding the mitigation effect of these countermeasures, we found that some of them failed to protect the infrastructure of Yalu highway.
A typical case was reported by Han et al. (2013). As shown in the remote sensing image of Figure 1, a highway bridge crosses the alluvial fan of the Cheyang debris-flow gully (28 40 0 35.31 00 N, 102 15 0 21.24 00 E). The creek is a tributary of the Anning River, and it has a catchment area of 0.95 km 2 (95 ha) and high altitudes of ca. 2800-3400 m a.s.l. The gully is 1.6 km in length, with a headwater basin length of approximately 0.5 km. The basin is underlain primarily by quartz sandstone and slate of Triassic age. Because of strong tectonic movements, bedrock in the basin is highly fragmented. Scars are present on the upper slope, and the stability of the slope decreases under extreme conditions, such as earthquakes and heavy rainfall. Debris flow events are reported in this watershed every few years. To protect the highway bridge at the alluvial fan, a lateral berm was constructed through the bridge culvert. The original design is shown in Figure 2. The cement mortar berm had a depth of 3.65 m and an open berm width of 26.0 m. The berm had a 23.58% gradient along the path.
When constructing the lateral berm, the channel width was enlarged from its previous 10.0 m to 26.0 m. Based on the perspective that debris flow should decelerate in the berm to reduce abrasions to the concrete structure and to control the discharge of debris, this wide-berm design was expected to direct and reroute the debris flow through the bridge culvert effectively.
However, evidence showed that the enlarged-berm design failed to direct and transport debris flow as expected. On 17 September 2008, a debris flow event occurred after six hours of heavy rainfall. The involved debris mass was 36.6 £ 10 3 m 3 in volume as estimated by the in situ investigation. The bulk density of the debris flow mass was estimated as 17.30 kN m ¡1 . As shown in Figure 3(b), the lateral berm was completely buried by the debris flow, and overtopping occurred. This event also delayed highway bridge construction. For this reason, reconstructing the lateral berm with a more reliable design was of utmost importance.

Methodology
We observed the redesign work on the lateral berm of the Cheyang gully. Over-enlargement of the channel while constructing the lateral berm was speculated to be the reason for the countermeasure failure. The abrupt drop in flow velocity in the berm significantly reduced the transport capacity and caused a blockage in the berm. In this case, therefore, the concentration and acceleration of debris flow using a narrowed berm appeared to be a more rational solution.
To support our speculation, the mud depth and flow velocity in the berm were first analysed. Numerical integral methods perform well with the irregular domain of integration. We used the Riemann integral method as demonstrated in our previous studies to solve the issue of the complex bed surface in natural river channels.
(1) Estimating peak discharge of debris flow The first step of this method is to estimate the peak discharge, Q. We used the method illustrated by Chen and Chuang (2014). The peak discharge of debris flow is proportional to the water flow peak discharge, Q w , fed by rainfall in the watershed catchment.
where c V is the volumetric sediment concentration of debris flow mass and is commonly no more than 0.65, according to Wrachien and Mambretti (2011), and often ranges from 0.48 to 0.55, according to Chen and Chuang (2014). The water flow peak discharge Q w can be estimated as follows: where C is the runoff coefficient, which ranges from 0.7 to 0.9, as recommended by SWCB (2005); I denotes the maximum hourly rainfall intensity (mm h ¡1 ); A is the watershed area (ha); and t c is the so-called concentration time as a function of watershed characteristics. According to Tropeano et al. (1996) and Berti et al. (1999), where L is the headwater basin length, H m is the average basin elevation, A is the watershed area (km 2 ), and H 0 is the basin outlet elevation. Equations (1)-(3) indicate that debris flow peak discharge is regarded as the amplification of water flow discharge due to the involvement of a large amount of solid debris.
(2) Mathematically reproducing the cross-section of lateral berm The second step is to describe the cross-section of the lateral berm from a mathematical perspective. We used the numerical integral method in previous studies (Han et al. 2015c). An inclined polyline defined by a series of vertices replicates the concrete bottom, and an interpolation is made between two neighbouring vertices ( Figure 4). To obtain solutions as close to the desired integral solution as possible, the reproduced bed surface between two vertices is partitioned using linear interpolation with a small increment of Dx ( Figure 4). In this way, the cross-section is partitioned into m segments.
(3) Iterative solution of mud depth in berm and velocity distribution Assuming a horizontal flow surface H dummy , the mud depth h at the segment i can be expressed as The mud depth is also partitioned with an increment of Dy. In this way, Equation (4) can be rewritten in the following discretized form: Equation (5) implies that the peak discharge Q equates the summation of the discharge in each sub-cross-section. For simplification, we assume that the velocity profile through depth follows a uniform law: where v i ð Þ is the mean velocity at the segment i. The Manning-Strickler equation can be used to determine that In this way, Equation (5) can be reduced to To estimate the unknown flow surface, an iteration algorithm is proposed. Generally, we initially assume a flow surface H dummy and increase the flow surface gradually with a small increment of Dh in each iterative step. Given this flow surface, a dummy peak discharge, Q dummy , can be obtained by using the numerical integral method. When the obtained dummy peak discharge Q dummy satisfies the following terminate condition (Equation (9)), the preliminary flow surface H is determined as H dummy .
In Equation (9), e is a manipulated parameter used to control the accuracy of the calculation; here, a value of 0.01 is adopted. The iteration algorithm stops only when Equation (9) is satisfied. Otherwise, the H dummy will increase by a small increment of Dh in the next step, and the iteration algorithm continues. The iterative solution of flow surface H is subsequently used to analyse the velocity distribution across the berm. The lateral distribution is estimated by Equation (7), and the vertical distribution is estimated by the profile law proposed by Johnson et al. (2012) because of its best fit to laboratory experiments (Han et al. 2015c): where a is a parameter controlling the amount of shear within the bulk of the flow; here, a = 0.5 is suggested (Iverson 2012). j denotes the vertical location through flow depth. Equations (4-10) are used to estimate the flow depth h and flow velocity v in the berm. The design of the lateral berm follows these two principles: The berm should not over-decelerate flow velocity because deposition can cause blockage. The flow depth in the berm should not exceed the height of sidewalls because of the potential for overflowing.
The proposed approach was implemented in code. We programmed the core function of the approach in a MATLAB environment. MATLAB was chosen because of its powerful capacity for matrix operations and visualization features. Prior to starting the program, the controlling parameters and the shape of the cross-section must be input into separate text files in ASCII format. The program reads these files, reproduces the concrete bottom of the berm, and then iteratively searches for an approximation of the flow surface. The final determined flow surface is used to calculate the flow depth across the cross-section and can be subsequently displayed with the help of the visualization function embedded in the MATLAB environment.

Solution and effect
(1) Determination of peak discharge The peak discharge of the 2008 Cheyang debris flow event was back-analysed, and detailed data used in the calculations are listed in Table 1. The calculated peak discharge of that event was 57.16 m 3 s ¡1 . In checking the calculation results, we also investigated the residual evidence of the event in situ. The residual mud line on the bank was approximately 3.0 m in height, which indicated that the area of the debris flow cross-section was 12.0-18.0 m 2 . The flow velocity was witnessed by local residents as approximately walking speed, i.e. 3.0-5.0 m s ¡1 . Consequently, the peak discharge was estimated to range from 36.0 m 3 s ¡1 to 90.0 m 3 s ¡1 , which is consistent with the theoretical calculation based on geomorphological and precipitation conditions. In a comprehensive consideration, an approximation of 60.0 m 3 s ¡1 is used to back-analyse the event.
(2) Estimating in-berm velocity For the performance of the lateral berm, the slope of the berm was designed to be 23.58%. Because the berm's bottom was constructed of sleek concrete, the roughness, n c , could be small; thus, n c = 0.18 in the berm was used. Guideline for determining the roughness could be found in Li et al. (2016). The numerical integral method described above was used to determine the mud depth and velocity in the concrete berm ( Figure 5). The results revealed that flow depth decreased to 1.16 m and that the mean velocity abruptly decreased to 2.97 m s ¡1 when the debris flow mass entered the concrete berm. The greatly decreased velocity therefore limited the mass transport capacity, thus causing the boulders and debris to deposit gradually. The deposits accumulated, compressing the effective depth of the berm and subsequently resulting in overtopping flow. This theoretical analysis supports the speculation that the inappropriate deceleration solution resulted in overtopping during the 2008 Cheyang debris flow event.  To address the overtopping issue, we optimized this lateral berm design for the local administration. The optimization was based on the acceleration solution. We tested the performance of a narrowed cross-section 6.5-m wide. The results in Figure 5 show that the flow depth and mean flow velocity both increased. The narrowed lateral berm is supposed to keep debris travelling, thereby preventing depositing and overtopping flow. For this reason, we suggested reducing the width of the lateral berm from 26.0 m to 6.5 m. (

3) Evaluating surface abrasion of concrete structures
Highly concentrated debris flow transports large boulders at high velocity. It is extremely erosive to the bottoms and sides of the berm (Banihabib and Iranpoor 2015). Two types of abrasions to the concrete bottom can be categorized, i.e. friction abrasion (Horszczaruk 2004;Liu et al. 2006;Banihabib and Elahi 2009;Zou et al. 2016) and impact abrasion (Liu et al. 2012;Banihabib and Iranpoor 2015) as shown in Figure 6. Both types of concrete abrasion were found in the lateral berm during the 2008 event ( Figure 7). As such, it is important to check the surface abrasions of the concrete bottom. To evaluate the surface abrasion of concrete structures, an index of E R is often used. It represents the abrasion ratio, and is defined as the unit weight loss after abrasion.
where m 1 and m 2 denote the concrete weights before and after abrasion, t denotes the abrasion duration, and B is the abrasion area. E R is given in kg/(h¢m 2 ), and a higher value signifies weaker tested  concrete abrasion erosion resistance. Previous studies focused on measuring E R via laboratory experiments, and in Table 2, we summarize the measurements obtained in some of these studies. However, most previous studies explored the concrete abrasion ratio by sand-water or water flows, which are understood to be much less abrasive and erosive than debris flows. Chen et al. (2004) suggested that the concrete bottom erosion rate by debris flows is approximately 4.5 £ 10 ¡5 cm s ¡1 , which equates to 4.35 kg/(h¢m 2 ). Abrasion by debris flows may be 5-10 times larger than that by sand-water flows (Liu et al. 2006;Liu et al. 2012).
Owing to the small amount of knowledge on concrete abrasions by debris flows, we must compromise and assume that the Cheyang debris flow had the same abrasive capacity as the debris flow presented by Chen et al. (2004). This means that the 0.35-m thick concrete bottom in the original design permits 212-h abrasion by debris flow. We also suggest increasing the stiffness of the berm bottom via some enhancement, such as using a metal cover with a metal halter on the concrete bottom of the lateral berm in .

(4) Effect
The suggested solution was approved by the local administration and expert committee, and as shown in Figure 8, reconstruction work on the lateral berm was finished in May 2010. One year later, on 16 June 2011, another debris flow event occurred. The inundated area was estimated as 38,720 m 2 , with the averaged deposition depth commonly around 0.7»0.9 m. As such, the actual mass volume of the 2011 event approximated 27,104»34,848 m 3 , obviously smaller than the 2008 Table 2. Abrasion ratios as revealed by different experiments.
Abrasion type E R (kg/(h¢m 2 )) Conditions Comprehensive abrasion by debris flow (Chen et al. 2004) 4.35 C30 (w/c = 0.32), sand content = 1314 kg/m 3 , boulder diameter = 6.31 mm Impact abrasion by water-borne sand (Liu et al. 2006) 0.59»0.90 C50 (w/c = 0.5), water content = 160 kg/m 3 ; boulder diameter ranges from 5 mm»25 mm 0.32»0.35 C28 (w/c = 0.28), water content = 140 kg/m 3 ; boulder diameter ranges from 5 mm»25 mm Friction abrasion by sand-water flow (Gao et al. 2014) 0 Note: E R denotes the abrasion ratio. w/c denotes water/cement ratio. C30, C28, and C50 represent different concrete types in reference to the water/cement ratio. event. Although the challenge by the event with a smaller magnitude was certainly reduced, the improvement of the mitigation effect of the reconstructed berm was observed. As shown in Figure 9, most of the boulders and debris mass were successfully directed through the highway bridge culvert towards the alluvial fan, and very little debris left in the berm. This observation also supports our overall finding in the study.

Discussion
(1) Sensitivity to the peak discharge As demonstrated in VanDine (1996), the maximum discharge is the main design consideration for lateral berms. To evaluate the influence of discharge, we tested different values (Q ranges from 10 to 110 m 3 s ¡1 ) and compared the results to reveal the sensitivity to Q. Figure 10 shows that both flow depth and velocity significantly increase with the discharge Q. As demonstrated in Section 4, a freeboard of 1.28 m remains for the back-analysed discharge of 60 m 3 s ¡1 . The satisfactory freeboard provides space for preventing overtopping due to superelevation and run-up. Such reliability of the lateral berm may be under threat because freeboard reduction with the increase of peak discharge is obvious. In the extreme situation of the sensitivity test in Figure 10, the freeboard of the berm exhausts when peak discharge extends upward to 110 m 3 s ¡1 . In this context, the sensitivity analysis suggests a maximum discharge of 110 m 3 s ¡1 for the reconstructed lateral berm.
(2) 'Deceleration solution' and 'acceleration solution' for the lateral berm design Currently, two conflicting solutions for the design of lateral berm exist: the 'deceleration solution', which dissipates debris flow energy but entails a risk of overtopping flow, and the 'acceleration solution', which maintains debris flow energy but results in freeboard reducing and structural abrasion.
'Deceleration solution' stresses the function of rerouting debris flows and the durability of the berm structure. Highly concentrated debris flows can transport large boulders at high velocities and are extremely erosive to the bottoms and sides of the berm. To prevent abrasions to the concrete structure, some early studies suggested decelerating debris flows in the berms by enlarging the width of the berms or using submerged sill on the bottom, such as with Dongchuan-type berms in China (Huang et al. 2009). However, Gao et al. (2010) indicated that such lateral berms do not perform well because heavy in-berm deposition often occurs.
In contrast to the 'deceleration solution', some recent studies (e.g. Prochaska et al. 2008;Pierson et al. 2014) recommended a second type, the 'acceleration solution'. These authors suggested that the lateral berm must be sufficiently smooth, steep, and narrow to maintain the flow depth needed to prevent in-channel deposition, implying that debris flows should maintain velocity or even accelerate in the berm. However, consequently, debris flows become more erosive, and the bottom and sides of the lateral berm must be revetted by concrete or stone masonry (Youssef et al. 2014). Meanwhile, the debris flow depth is likely to increase in a narrow berm, thereby increasing the risk of overtopping. If sidewalls of the berm are overtopped, the rapid erosion of back side of the berm can quickly cause their failure (Paguican et al. 2009).
Based on the previous studies above, we summarize the pros and cons of both the solutions in Figure 11. Nevertheless, owing to the lack of convincing evidence and theoretical support, a rational comparison of the two solutions is scientifically challenging. In the investigated case as described in this paper, we have found that the reconstructed lateral berm using 'acceleration solution' performs better. Through the rational estimation of flow depth and erosion in the berm, risk for overtopping and structure abrasion can be minimized. The case study in this paper also makes a supplement for the system of design consideration for lateral berms. It is suggested that for the either solution, berm width should be one of the main design considerations except of maximum discharge and flow depth in VanDine (1996).
(3) Limitations and ongoing work Some limitations still exist in the current study. First, the proposed method in this paper represents an alternative solution for evaluating the flow velocity and the mud depth of debris flows in lateral berms. However, strong phase separation in debris flow, which is an important feature of debris flows as substantiated by Pudasaini and Fischer (2016), could not be taken into account. Phase separation mechanically results in a solid-dominated front surge of debris flow, leading to a varying velocity profile through depth. Such effect owing to the phase separation has to be simplified by the velocity profile law in Equation (10), and a fitting parameter a is introduced, which turns the method into a semi-empirical law. Second, the mitigation effect of the 'acceleration solution'-based lateral berm still requests long-term monitoring and evaluation. Especially that the 2011 event was smaller than the 2008 event in magnitude. Although the reconstructed berm performed well because very little deposits left in the berm, the advantage of the 'acceleration solution' will be more convictive when undergoing a debris flow event with a comparable or much greater magnitude. As such, our ongoing work focuses on improving the method presented here by considering the two-phase model of debris flow, as well as collecting the data for supporting our conclusions.

Conclusion
In this paper, we introduce a monitoring case to discuss the rational design of lateral berms. We used the proposed numerical integral method in our previous study to analyse the mud depth and flow velocity distribution in the berm and found that the abrupt decrease in flow velocity from the natural channel to the concrete berm significantly reduced the transport capacity, thereby causing deposits in the berm. For the reconstruction, we suggested the acceleration solution and reduced the berm width from 26.0 m to 6.5 m. The reduction of the berm width increased the mean flow velocity from 2.97 to 4.84 m s ¡1 , and guaranteed a 1.24-m freeboard of the berm. The redesigned lateral berm was supposed to reduce the risks of debris deposition and overtopping flows. Reconstruction of the berm was completed in 2010, and the berm successfully transported a subsequent debris flow with a smaller magnitude in 2011. We suggest using the lateral berm based on the acceleration solution with an enhanced bottom to direct debris flows and protect highway bridge infrastructure.