**2. Methods and materials**

Risk management is a key issue in dam construction [1]. Technically speaking, risk is described as the likelihood and severity of adverse impacts acting on life, environment, and property. According to an international specification [29], the risk is generally predicted by combining the probability of its occurrence and the impact of the scenario on the associated outcome and defined by a simple formula (Eq. (1)). In this equation, P means conditional probability depending on variables X and Y and also C represents outcomes [9].

$$\text{Risk} = \lfloor \text{P} \lceil \text{LoadEvents} \rceil \times \text{P} \lceil \text{Responses} \rceil \text{Loads} \rceil \times \text{C} \lceil \text{Loads}, \text{Responses} \rceil \tag{1}$$

In the construction industry, the term "risk" can primarily refer to economic concerns, but can also refer to life loss. Technical specifications mostly use a "risk curve" to measure safety. Seismic hazard, on the other hand, represents the uncertain relationship between seismic intensity level and the probability that at least excitation level will occur at the given location. The hazard curve represents a graph that correlates the seismic intensity of a particular location on the horizontal axis and the annual exceedance frequency in vertical axis [7].

There are various techniques to quantify a dam's overall risk factors. The ICOLD method takes into account seismic hazards belonging to dam site and structure's risk separately [30]. In this method, the seismic hazard can be classified into four groups, regardless of the dam type [31, 32]. This is an easy manner to evaluate earthquake hazard via way of means of figuring out the hazard class. ICOLD introduces that the whole risk of dams includes structural and socio-monetary factors [33]. The first is especially based upon at dam height and ability of the reservoir. The second one is the capability for downstream damage and evacuation requirements. The summation of these four risks represents the Risk Factor (RF). Four danger classes, which can be used for deciding on seismic parameters of floor motion, are described on the idea of the RF values. ICOLD states that big dams (peak is extra than 90 meters and a storage potential of extra than 1200 hm3 ) require unique protection considerations [30].

In general, a dam hazard evaluation must be decided primarily based totally on reservoir capacity, dam height, evacuation requirements, and capability downstream damage. Generally, seismic evaluation and risk evaluation are evaluated separately. However, Bureau [33] combines those elements to outline the overall hazard factor for dam structures (TRF), as given in Eq. (2). In the equation, TRF refers to total risk factor. The first three phrases cowl dam-based elements, and HRF covers dam-based

*Risk Management of Large Dams under Operation Stage and Case Studies for Cascade System DOI: http://dx.doi.org/10.5772/intechopen.113342*

elements. Downstream risk as a feature of population and properties at risk is described as a feature of specific elements (Eq. (3)) [34, 35]. In this equation, ERF is the evacuation demand component and DRI is the downstream damage risk index. The Downstream Evacuation Requirement (ERF) component relies upon the population at risk. The Downstream Damage Risk Index is primarily based on the value of private, commercial, and industrial properties in the capability flood path. Finally, the PDF shows the anticipated damage component (Predicted Damage Factor), which is a feature of the dam's determined overall performance in addition to the locationbased seismic hazard.

$$\text{TRF} = \left[ \left( \text{CRF} + \text{HRF} + \text{ARF} \right) + \text{DHF} \right] \times \text{PDF} \tag{2}$$

$$\text{DHF} = \text{ERF} + \text{DRI} \tag{3}$$

Vulnerability evaluation represents the location-based seismic risk described by the Predicted Damage Factor (PDF), which is assigned to every dam consistent with Eq. (4). In this equation, PDI is the Predicted Damage Index, calculated the usage of the dam fragility curve advanced with the aid of using Bureau and Ballentine [36]. The PDI relies upon the dam type and the seismic risk of the dam site and is calculated as a feature of the Earthquake Severity Index (ESI), which represents the predicted ground motion on the dam site as given with the aid of using Eq. (5). In this equation PGA is peak ground acceleration in g; and M is the Richter or moment magnitude.

$$\text{PDF} = \text{2.5} \times \text{PDI} \tag{4}$$

$$\text{ESI} = \text{PGA} \times \left(\text{M} - \text{4.5}\right) \tag{5}$$

The author proposed a qualitative evaluation framework that shows the relative impact of dams within a cascade system. Five different risk rates (very low, low, moderate, high, and very high) are defined for every structure in the system. The principles are listed in **Table 2** according to dam type, reservoir storage capacity, and dam location. All dams fall into two basic groups: "rigid" and "flexible." "Flexible" refers to earth-fill dams, rock-fill dams, and combinations thereof; "rigid" refers


*\*Flexible means earthfill dams, rockfill dams, and their combination while rigid describes concrete dams (gravity, ach, buttress), roller compacted dams and hardfill dams.*

#### **Table 2.**

*Risk ratio for dams of a cascade system.*

to concrete dams (gravity, arch, and buttress), roller-compacted concrete dams, and hardfill dams. Another factor considered is the number of downstream dams that may fail. This is based on the relative storage capacity of the dam. The dam risk assessment considered how much damage downstream dams would suffer if the dam completely collapsed. This model is based on the number of dams in the downstream area and assumes that the rigid dam acts as an overall spillway structure and is not damaged. For composite types, it may make sense to consider weaker ones. The author first mentioned this problem in ICOLD symposiums held in Prague and Chania in 2017 and 2019, respectively [37, 38] and in a recent study published in an international book project [39]. This problem was also considered by some scientists from east-south Asia [40, 41].
