Experimental Study on Pressure Characteristics of Gravity Dam Surface under Impact of Landslide-Generated Impulse Waves

Abstract

Landslide-generated impulse waves of a mountain-river reservoir will endanger the dam body’s stability and the dam structure’s safety and even pose a significant threat to the property safety of downstream residents. Timely prediction of dam surface pressure is essential for dam safety assessment. The pressure distribution characteristics and variation law of the gravity dam surface under the impact of landslide-generated impulse waves are studied through a three-dimensional physical model test. The results show that the landslide volume and angle are the key control factors of the first wave amplitude in front of the dam. The maximum and minimum pressures are near the water surface and at two-thirds of the water depth, respectively. The maximum pressure has a power function relationship with the maximum amplitude of the wave in front of the dam. Furthermore, the maximum amplitude of the first wave in front of the dam significantly influences the total pressure of the single-width wave on the dam surface. Based on the research results, the single-width wave total pressure prediction method is constructed under different first wave amplitudes in front of the dam, which can provide theoretical guidance and technical support for dam safety assessment and landslide-generated surge risk assessment.

1. Introduction

With the continuous construction of river-type reservoirs in mountainous areas and the long-term high water level and operation and scheduling of reservoirs, serious slope stability and landslide-generated impulse wave problems have been created in reservoir areas. When a landslide source is close to the dam, the landslide-induced wave inflow cannot be fully attenuated. When the waves approach the dam, they maintain considerable standing wave heights. At this time, the waves have high energy and substantially impact the dam structure. In extreme cases, they can overtop the dam and rush downstream of the reservoir. This can cause significant losses to human safety and property downstream of the dam.

In the famous Italian Vaiont reservoir accident, huge landslide-generated impulse waves were created, which destroyed all the buildings in the dam area and caused severe economic and property losses downstream, with nearly 3000 deaths [1]. In 1967, the Tanggudong landslide occurred on the right bank of the Yalong River in Ya’an County, Sichuan Province. A landslide caused an overflow dam breach, resulting in a dam-break flood disaster [2]. In July 2019, a landslide suddenly occurred on the right bank of the water intake of a power station dam in Leshan City, Sichuan Province. About 50,000 m³ of the DEBRIS, SOIL, ROCK, etc., directly fell into the reservoir area, forming huge impulse waves and causing severe damage to the dam structure. The fluctuation of reservoir water levels makes landslides more prone to occur near dam areas. It is essential to timely predict the impact pressure of landslide-generated impulse waves on dams to respond to geological disasters and reduce the degree of secondary disasters.

The choice of landslide body is usually one of the most important factors for researchers. The correct choice is imperative for the success of the experiment. Therefore, in landslide wave-making, academic research focuses on rigid block, granular landslide wave-making [3,4,5,6,7]. Some studies on landslide-generated impulse waves combine blocks with granular and viscoplastic materials [8,9]. These studies analyze waveform characteristics and obtain the relationship among impulse waves, landslide parameters, and wave prediction equations to understand impulse wave characteristics under various conditions. However, most reservoir landslides are rock landslides. In a rock mass landslide, stress relaxation of rock masses occurs at joint fissures, which expand and cut the rock mass into blocks of different sizes [10]. Therefore, based on natural rock landslides, this paper uses different block-composed landslide sizes to simulate wave-making.

It is worth noting that still water can produce water pressure, and impulse waves produce hydrodynamic pressure [11]. Accurately predicting impulse wave effects on dams and other structures is critical [12]. Surge pressure research is mainly focused on physical model test research. Research in two-dimensional flumes mainly explores solitary and impulse wave pressures on the vertical wall or slope [13,14]. Researchers have explored the effect of impulse waves on slope pressure in a three-dimensional flume [15]. Other studies based on numerical simulations have focused on the dynamic pressure of solitary waves on dams [12,16]. Meanwhile, some have explored the impact pressure of impulse waves on curved and straight walls [17,18]. These studies have greatly enhanced our understanding of impulse wave pressure and basic behavior. However, the impulse wave’s waveform is complex, especially in river-type reservoirs. The characteristics of impulse waves are not consistent with the characteristics of a two-dimensional single-width flume, which has a relatively complex action process. Furthermore, the study of gravity dam surface pressure under impulse wave impact is less involved but very important. Therefore, this paper further reveals the mechanism of landslide-generated impulse waves acting on the surface pressure of a gravity dam through three-dimensional physical model tests. It provides a basis for later dam stability and safety assessment research.

2. Equipment and Methods

A landslide-generated impulse wave test was carried out in a large flume with a length of 48 m, a top width of 8 m, and a bottom width of 2.94 m at the National Inland Waterway Regulation Engineering Research Center of Chongqing Jiaotong University. The model device comprises three parts: flume, dam, and landslide device (Figure 1a–c), in which the flume and dam models are built by brick and mortar. The landslide device is a smooth steel device with an inverted chain-type hoist. By using the chain to pull the chute, the chute can be lifted or lowered to adjust the angle. The designed gravity dam size is shown in

Table 1. Gravity dam model size.

Height of Dam/m	Dam Bottom Length/m	Crest Length/m	Crest Width/m	Upstream Slope	Downstream Slope
1.00	2.94	7.23	0.1	1:0	1:0.75

. The dam model was 7 m from the center of the landslide device. According to the field survey, most landslides are rock landslides. According to the development of rock fractures, this paper uses five different-sized blocks to simulate landslides. The block size is shown in

Table 2. Parameters of landslide blocks.

Block Number	Length/m	Width/m	Thickness/m
A1	0.21	0.14	0.06
A2	0.18	0.12	0.05
A3	0.15	0.1	0.04
A4	0.12	0.08	0.03
A5	0.09	0.06	0.02

, and the landslide is stacked by the five blocks, as shown in Figure 1c.

In the experiment, the instantaneous water level in the flume was measured by an ultrasonic wave-measuring instrument, and the acquisition frequency was 150 Hz. A wave pressure acquisition system was used to measure the dynamic wave pressure on the dam surface, and the acquisition frequency was 300 Hz. A total of 22 groups of wave gauges were set up in the flume to record water level changes, numbered G1–G22 (Figure 1b). Six groups of embedded pressure sensors P1–P6 were used to record the dynamic wave pressure at different heights of the dam center. The pressure sensor’s position in the dam is shown in Figure 2, and the specific dimensions are shown in

Table 3. Specific location of pressure measuring point.

Wave Pressure Measuring Point Number	z/z0
P1	0.950
P2	0.910
P3	0.870
P4	0.673
P5	0.475
P6	0.050

Note: The depth of z/z₀ dimensionless dam surface pressure measuring point, where z is the vertical distance from the measuring point to the bottom of the dam, and z₀ is the height of the dam.

. This paper focuses on the vertical pressure at the dam’s center and the wave height propagation from the landslide point to the dam center. The wave gauge corresponds to G2–G5.

The hydrostatic depth h₀ = 0.95 m; the landslide angles α = 30°, 40°, 50°, 60°; and the landslide volume V (length × width × height) = 0.4, 0.6, 0.9 m³. These parameters are also largely covered in previous tests. By adjusting α and the landslide parameters, nonlinear oscillation waves and nonlinear transition waves are generated. At the same time, the pressure sensor is placed at the center of the dam surface according to the hydrostatic depth to study the pressure characteristics. As shown in

Table 4. Test conditions.

Working Condition	Length l/m	Width b/m	Thickness d/m	Volume V/m3	Angle α/(°)
M1	1	1.5	0.6	0.9	60
M2	1	1.5	0.6	0.9	50
M3	1	1.5	0.6	0.9	40
M4	1	1.5	0.6	0.9	30
M5	1	1.5	0.4	0.6	60
M6	1	1.5	0.4	0.6	50
M7	1	1.5	0.4	0.6	40
M8	1	1.5	0.4	0.6	30
M9	1	1.0	0.6	0.6	60
M10	1	1.0	0.6	0.6	50
M11	1	1.0	0.6	0.6	40
M12	1	1.0	0.6	0.6	30
M13	1	1.0	0.4	0.4	60
M14	1	1.0	0.4	0.4	50
M15	1	1.0	0.4	0.4	40
M16	1	1.0	0.4	0.4	30

, 16 groups of experiments were carried out by combining parameters.

3. Results and Discussion

3.1. Evolution of Landslide-Generated Impulse Waves

To explore the evolution characteristics of impulse waves near the dam area, we analyzed the typical wave surface duration curve from the landslide point to the dam center line under a static water depth of 0.95 m (Figure 3). The results of the G2−G5 wave gauges show the wave surface duration curves under working condition M8. The ordinate is the dimensionless water depth H/h₀ and H is the instantaneous water level measured by the wave meter minus the still water depth. The abscissa is the dimensionless wave propagation time t(g/h₀)^0.5, and g is the gravity acceleration (maximum value of the first peak adjusted to the same abscissa position). According to the previous wave classification [19], we found that the waves generated by the swell gradually changed from nonlinear waves to linear waves near the dam. The initial wave height before the landslide point was the largest, and the peak was steep. The first peak of each wave train gradually decreased along the ray direction (G2−G4), and the peak flattened when the surge propagated to the front of the dam (G5). Due to the blocking effect of the dam surface, a large surge was often generated with a wave peak larger than the previous ones and smaller than the initial.

According to the previous research results [6], for the wave generation of a block or granular landslide, the fluctuation characteristics of initial waves are related to the release height h_0c of the landslide and the dynamic friction coefficient μ between landslides. The latter can be estimated by the following equation through the sliding test of a single block:

$$\mu =\tan \alpha -\frac{2S_{\mathrm{a}}}{\left(g{t}_{\mathrm{a}}{}^2\cos \alpha \right)}$$

(1)

where S_a is the sliding distance of the block along the chute, m; t_a is the sliding time of the block, s.

According to the experimental results, the average dynamic friction coefficient between the landslide and the sliding groove is μ = 0.50. Combined with previous research results [6], Equation (2) can be used to estimate the maximum initial surge amplitude of granular landslide, and the calculation results are shown in

Table 5. Maximum amplitude of initial wave A_m/h₀.

Working Condition	Experimental Value (G2 Measuring Point)	Calculated Value (Equation (2))	Fitting Result (Equation (3))
M1	0.0684	0.251	0.0658
M2	0.0601	0.231	0.0613
M3	0.0492	0.199	0.0541
M4	0.0410	0.127	0.0369
M5	0.0530	0.220	0.0459
M6	0.0435	0.202	0.0427
M7	0.0356	0.175	0.0377
M8	0.0280	0.111	0.0257
M9	0.0473	0.220	0.0459
M10	0.0380	0.202	0.0427
M11	0.0336	0.175	0.0377
M12	0.0257	0.111	0.0257
M13	0.0324	0.193	0.0320
M14	0.0308	0.178	0.0298
M15	0.0230	0.153	0.0263
M16	0.0189	0.098	0.0179

.

$$\frac{A_{\mathrm{m}}}{h_0}=0.605{\left(\frac{h_{0\mathrm{c}}\left(1-\mu \cot \left(\alpha \right)\right)}{h_0}\right)}^{0.408}{\left(\frac{V}{h_0{}^3}\right)}^{0.323}{\left(\frac{D_{\mathrm{s}}}{h_0}\right)}^{0.506}$$

(2)

where A_m is the maximum amplitude of surge, D_s is the average equivalent particle size.

The deviation between the test results and the calculated values was large, with an average error of 78% and a maximum error of 85%. There are three possible reasons for the analysis: (1) Huang et al. [6] overestimated the initial wave peak. (2) The direction of wave propagation in this paper is the ray direction. Huang et al. [6] studied the wave propagation in front of the landslide point, and the initial wave in the ray direction is smaller than that in front of the landslide point. (3) This paper uses different block combinations of landslides, so Huang et al.’s [6] results may not apply to such a landslide. Therefore, the calculation formula of Equation (3) (correlation R² = 0.933) was obtained by re-fitting in this paper, which can be used for wave generation calculation of such landslides.

$$\frac{A_{\mathrm{m}}}{h_0}=0.089{\left(\frac{h_{0\mathrm{c}}\left(1-\mu \cot \left(\alpha \right)\right)}{h_0}\right)}^{0.347}{\left(\frac{V}{h_0{}^3}\right)}^{0.891}$$

(3)

3.2. Pressure Characteristics of Dam Surface

The pressure P of the impulse wave action on the dam surface is defined as the difference between the total pressure and the initial hydrostatic pressure. In M8, the instantaneous variation of the wave pressure on the central section of the dam under the action of the front head wave (G5) is shown in Figure 4. The dimensionless wave pressure P/γh₀ and the dimensionless water depth H/h₀ are a function curve relative to the dimensionless time t(g/h₀)^0.5. We smoothed the wave height G5 curve with a Fourier filter for better visual results, and the wave pressure duration curve relative to the previous curve increased by 0.05. The wave pressure curve was consistent with the water surface process line, with a positive correlation.

In the landslide-generated impulse wave test, the maximum amplitude of the dimensionless first wave (A_m/h₀) changed between 0.017 and 0.043. The test results show that the first wave amplitude increased with landslide angle when the landslide volume was constant. When the landslide angle was constant, the first wave amplitude increased with landslide volume. When the landslide volume and angle were constant, the first wave amplitude increased with landslide width. The first wave amplitude was greatly affected by the slope angle and volume. Under these dimensionless first wave amplitudes, the maximum wave pressure P/γh₀ at different heights z/z₀ on the dam surface is shown in Figure 5. It is noteworthy that the minimum wave pressure was near two-thirds of the water depth (z/z₀ = 0.673). The maximum wave pressure generally appeared on the still water surface and occasionally at the bottom, especially when the landslide volume was small. Since the bottom is affected by other signals, a high-frequency interference signal is prone to occur. The interference signal has not been eliminated after filtering, but its average value is slightly smaller than the hydrostatic wave pressure. Overall, the wave pressure in the water depth direction increased first, then decreased, and then increased. The decrease rate was faster than the increase rate.

Through nonlinear curve regression analysis, when A_m/h₀ changes between 0.017 and 0.043, dimensionless pressure value near water surface P/γh₀ can be expressed by the following formula (R² = 0.979):

$$\frac{P}{\gamma h_0}=0.34{\left(\frac{A_{\mathrm{m}}}{h_0}\right)}^{0.615}$$

(4)

The fitting curve can be seen in Figure 6. The wave pressure was greatly affected by the first wave, following a power function relationship.

3.3. Total Pressure Per Unit Width of Waves on Dam Surface

F is the total pressure of the single width of the impulse waves on the dam surface, based on the pressure integration. The change of dam surface pressure under the first wave’s action in front of the dam (Figure 7). The pressure on the dam surface gradually increased with the first wave height in front of the dam. To better obtain the dam surface’s pressure, the maximum dam surface pressure and first wave height in front of the dam were fitted by a function. The fitting curve is shown in Figure 8, and the results are as follows (R² = 0.986):

$$\frac{F_{\mathrm{m}}}{\gamma h_0{}^2}=-3.72{\left(\frac{A_{\mathrm{m}}}{h_0}\right)}^2+0.95\frac{A_{\mathrm{m}}}{h_0}$$

(5)

4. Conclusions

In this paper, a three-dimensional physical model test was carried out to study the pressure characteristics of the gravity dam surface under the impact of landslide-generated impulse waves. The following conclusions can be drawn:

(1)

When the wave propagates, the ray waves are nonlinear oscillation waves and nonlinear transition waves. The amplitude decreases along the way. However, when the surge propagates to the dam front, the wave amplitude blocked by the dam increases instantaneously.

(2)

The maximum amplitude of the initial surge in the test was far less than that calculated by Huang et al. [6]. The average error reached 78%, indicating that the initial wave peak formula obtained by Huang et al. [6] based on a granular test may not be suitable for estimating the maximum amplitude of the initial landslide surge with different-sized block combinations. The comparison shows that the attenuation degree of the surge in the three-dimensional physical model test is larger than that in the two-dimensional single-width flume physical model test.

(3)

The landslide volume and angle are the key control factors of the first wave amplitude in front of the dam, and the dam surface pressure is positively correlated with the maximum first wave amplitude.

(4)

The wave pressure distribution in the water depth direction is small in the middle and large on both sides; the maximum value is obtained near the water surface, and the minimum value is obtained at two-thirds of the water depth. The maximum pressure has a power function relationship with the maximum amplitude of the wave in front of the dam.

(5)

The total pressure of the single-width dam surface increases with the increase in the maximum amplitude of the wave in front of the dam, and it has a quadratic function relationship with the maximum amplitude of the wave in front of the dam.