Probable reliability prediction of the dam constructed with ground materials of the Nam Chien hydraulic power system in Vietnam using the Monte Carlo method

. The current method of probabilistic safety assesses dams with ground material by the criterion of water overflow through the dam crest. Due to the stochastic nature of the material properties, loads and impacts method involves the use of the Monte Carlo method (statistical tests). The algorithm was tested on the example of the ground material dams of Nam Chien hydropower in the Vietnam. Calculation and design of modern hydraulic engineering works require assessment of their reliability and safety on the basis of probabilistic methods. Quite a common type of water power systems backwater front structures are dams constructed of ground materials. In this paper, a modern method of probabilistic assessment of the reliability of dams constructed of ground materials is applied. The criterion of ensuring the edge state is water overflow over the dam crest. During the study of the dam reliability, the probabilistic nature of the loads and influences perceived by the dam is taken into account. Reliability assessment of the dam is fulfilled in the software complex Math Cad with the use of modern numerical Monte-Carlo method (statistical simulations method). The algorithm was tested on the example of the earth-and-rockfill dam Nam Chien in Vietnam. The earth-and-rockfill dam is designed homogeneous with a clay soil core with upstream slope pavement using reinforced concrete 0.5 m thick slabs on a 0.4 m thick gravel layer. The slope base of the upstream slope is 1:1.1. From the downstream slope, topsoil ramping is carried. The slope base of the downstream slope is 1:1.2.

Calculation and design of modern hydraulic engineering works require assessment of their reliability and safety on the basis of probabilistic methods. Quite a common type of water power systems backwater front structures are dams constructed of ground materials. In this paper, a modern method of probabilistic assessment of the reliability of dams constructed of ground materials is applied. The criterion of ensuring the edge state is water overflow over the dam crest. During the study of the dam reliability, the probabilistic nature of the loads and influences perceived by the dam is taken into account. Reliability assessment of the dam is fulfilled in the software complex Math Cad with the use of modern numerical Monte-Carlo method (statistical simulations method). The algorithm was tested on the example of the earthand-rockfill dam Nam Chien in Vietnam. The earth-and-rockfill dam is designed homogeneous with a clay soil core with upstream slope pavement using reinforced concrete 0.5 m thick slabs on a 0.4 m thick gravel layer. The slope base of the upstream slope is 1:1.1. From the downstream slope, topsoil ramping is carried. The slope base of the downstream slope is 1:1.2. (Fig. 1).
According to the Monte Carlo method, N simulations are performed. The sequence of calculations for each simulation is accepted as follows.
1. Water level marks in front of the dam PQ are given by evenly distributed random probability in the range from 0 to 1, caused by the maximum flood flow.
2. The quantile is determined by the value of PQ, -the mark of the static water level in front of the dam ZQ caused by the maximum flood flow, according to the relation ZQ 4. Wind speed РV is given by evenly distributed random probability in the range from 0 to 1. 5. The quantile is determined by the value of PV -wind speed V. 6. Using the normative technique based on the known values of fetch L, the average water depth in the reservoir H and wind speed V, the wave parameters are calculated.
6.1. The average wave height is found. 6.2. Average wave periods are calculated. 6.3. The average wave length is determined. 6.4. The wave length 1% of exceedance probability in the wave system is calculated. 6.5. The height of wave run-up on the slope is determined. 6.6. The wind setup height is found. 7. The water level mark in front of the dam Z is determined. 8. The fulfillment of the condition Z <Zdc is checked. According to the numerical experiment program, the planned number of statistical simulations was carried out. The number of statistical simulations, in which the condition that the water level elevation in front of the dam would be less than the earth dam crest mark was not fulfilled, was attributed to the total number of simulations and determined the probability of the risk of water overflow over the dam crest.
After performing all N simulations, the probability of water overflow over the dam crest РOVT is calculated as the ratio of the number of simulations N1, with Zul< Zdc, to the number of all simulations N.
It should be noted that due to the smallness of the values ROVT, the number of statistical simulations should be relatively larger in order to provide sufficient probability of the derived values.
To determine the risk of water overflow over the earth dam crest, random probability of wind speed pV is set distributed from 0 to 1 (see Fig. 2). According to the outcoming data, the probabilities of annual maximum wind speed can be represented by a normal distribution. The quantile is determined by the value of PV -wind speed V. Random probability pZ of water level mark Z in front of the dam constructed of ground materials is set, distributed from 0 to 1, m (see Fig. 3).
where 0.3 and 0.09 -empirical coefficients, g -gravitational acceleration, m/s 2 , αw -the angle between the longitudinal axis of the reservoir and the airflow direction.
Depending on average wave period Tav, average wave length λav, m is determined using formula 4: where 0.001, 1, 390 -empirical coefficients; 0.01 -wave height exceedance probability; Gvalue of the gamma-function. Depending on the wave height 1% of exceedance probability in the wave system h1%, m the wave run-up on the slope hrun1%, m is determined according to the formula 6: where kr -coefficient of slope paving roughness; kp -coefficient of slope paving penetration; ksp -coefficient, which depends on wind speed and slope ratio; kruncoefficient, which is determined using formula 7: where α is the angle between the wave line and the normal line to the bank line; φ -canting angle of the slope. Depending on the water level mark Z, m, the height of wave run-up on the slope hrun1%, m and the wind setup height dh, m the water level mark in front of the dam Zf, m is determined using formula 8 (see Fig. 7): The fulfillment of the condition 9 is checked where ZDC is the mark of the earth dam crest. Calculation of the earth-and-rockfill dam of the hydraulic power system Nam Chien under the condition of preventing the water overflow over the crest was carried out according to the normative method for the first and for the second settlement cases.
The results of the calculations of the earth-and-rockfill dam of the hydraulic power system Nam Chien under the condition of preventing the water overflow over the crest carried out according to the normative method for the first settlement case are given in Table 1, for the second settlement case -in Table 2, the results of the probabilistic calculations of the earth-and-rockfill dam -in Table 3.  The earth-and-rockfill dam of the hydraulic power system Nam Chien CC3 110 6 210 -5 1.6610 -5 -1.8310 -5 510 -5

Conclusions
According to the probabilistic assessment of the dam of the hydraulic power system Nam Chien, it may be concluded that the probability of water overflow over the crest of the dam pest. = 210 -5 and it does not exceed the accepted value of pacc. = 510 -5 , and the reliability of the earth-and-rockfill dam is provided.