Martin Wieland discusses seismic and hydrological design criteria for cofferdams and temporary structures at dam sites

MOST of the existing dams have been designed against earthquake actions using the pseudo-static approach with an acceleration of 0.1g. Although, this approach is considered obsolete today, it is still used for the design of cofferdams and temporary structures. This outdated concept is even considered to be adequate in regions of high seismicity. In regions of low to moderate seismicity, seismic action is ignored for cofferdams and temporary structures at the dam site. This is not unusual for seismic actions, as for example these are still ignored in the design of underground structures (tunnels and caverns).

For the hydrological design of cofferdams, a flood with a return period of 10 years is often used. The relatively short return periods of floods and earthquakes for the cofferdam design are in contradiction with the design criteria used for the dam. Both for the seismic and flood safety of large dams, the maximum credible earthquake (MCE) and the maximum probable flood (PMF) are used, which correspond to events with return periods of say 10,000 years.

Typical earthquake damage of earthfill dams caused by the 2001 Bhuj earthquake in Gujarat, India are shown in Fig. 1. Most of the 245 dams damaged during this earthquake were not designed against such an event. This kind of damage may also be expected in cofferdams if seismic actions are ignored in the design.

Flood damage of cofferdams during different stages of dam construction are shown in Figures 2 and 3. In the case of Rogun dam, which would be the world’s highest dam if completed, the cofferdam was washed away in a major flood before dam construction even began (Sirozhev et al., 1993; Fig. 2).

According to current practice large dams have to be able to withstand the effects of the MCE and the PMF. These are the most severe events that could affect the safety of a dam, and they are considered to have a return period of several thousand years. Typically 10,000 year floods are assumed, and in the case of seismic ground motions a 10,000 return period is taken in regions of low to moderate seismicity (icold Bulletin 72, 1989; Wieland 2003). Temporary structures do not have to satisfy such stringent criteria.

It should also be pointed out that in the case of seismic design, considerable improvement in the seismic resistance of cofferdams can be achieved if the general design requirements and recommendations outlined in ICOLD bulletins 120 (2001) and 123 (2002) are observed.

The two methods discussed in the subsequent sections may be used for the selection of the minimum seismic and hydrological design criteria for cofferdams and temporary structures. The first method based on the Eurocode 8 (2002) is only suitable for seismic design criteria, whereas the second method can be used for both the selection of seismic and flood design criteria (or any other type of action from the natural environment).

*Method 1*: Seismic ground motion for temporary structures according to Eurocode 8 ‘Design of structures for earthquake resistance’

The peak ground acceleration (PGA) for temporary structures and the construction phase should be at least 50% of the PGA of the design earthquake of the seismic building code (Eurocode 8, 2002). For important cofferdams a separate seismic hazard assessment may be needed. According to Eurocode 8, Part 2 bridges (2002), the design PGA for temporary structures and the construction phase, PGAc can be taken as

PGA_{c} = PGA (t_{rc}/t_{ro})k (1)

where the PGA is according to the building code, tro = 475 years (probability of exceedance of 10% in 50 years), for k a value between 0.3 and 0.4 can be used depending on the seismicity of the region and

t_{rc} = approx. t_{c}/p (2)

where tc is the duration of the construction phase and p is the acceptable probability of exceedance of the design seismic event during this phase, typically a value of p = 0.05 is selected.

Therefore, assuming k = 0.35 and a construction phase of three years, during which the cofferdam must be fully functional, results in PGA_{c} = 0.48 PGA, and for a cofferdam, which may stay for 10 years, we obtain PGA_{c} = 0.74 PGA (Note: For very important cofferdams, tro, may be larger than 475 years and thus the PGA shall be taken for that longer return period).

This numerical example shows that the seismic action for temporary structures and for construction phases can be quite substantial. In many cases the effects of seismic action during dam construction has been underestimated or ignored.

In general, building codes exclude dams, power plants, hydraulic structures, underground structures and other appurtenant structures and equipment. It is expected that separate codes or regulations cover these special infrastructure projects. However, only few countries have such regulations. Therefore, either the ICOLD Bulletins (ICOLD Bulletin 123, 2002) or the (local) seismic building codes (Eurocode 8, 2002) are used as a reference.

The seismic building codes are very useful reference documents for checking the design criteria for a dam and the appurtenant structures. As the return period of the safety evaluation earthquake (SEE) of a large dam is usually much longer than the return period of the design earthquake for buildings, which in many parts of the world is taken as 475 years (Note: In the new building codes of the US and Canada the seismic forces are determined based on a reference return period of 2500 years and the resulting (effective) ground accelerations are multiplied by a factor of 2/3. This results in higher seismic forces in areas of low to moderate seismicity as compared to the traditional concept where a return period of 475 years is used irrespective of the seismicity of the region), the PGA values of the SEE should be larger than that of the design earthquake for building structures with a 475 year return period multiplied with the importance factor for high risk projects. If this basic check is not satisfied, then a building located at the dam site would have to be designed for stronger ground motions than the dam. This does not make sense. In such situations the seismic design criteria have to be reviewed thoroughly, additional seismic investigations may be needed or a sound justification must be given.

*Method 2*: Probabilistic approach for evaluation of return period of design earthquake and/or the return period of the design flood of a cofferdam or temporary structure

The probabilistic approach can be used to determine the return period, Td, of the design earthquake or design flood of a cofferdam or a temporary structure.

The derivation of the return period of the design earthquake or design flood (referred to as design event) is as follows:

Probability of non-occurrence of design event in one year

p_{1} = 1 – 1/ T_{d } (3)

Probability of non-occurrence of design event in T years (assuming that events are uncorrelated)

p_{T} = p_{1}^{T} = (1 – 1/ T_{d})^{T} (4)

Probability of exceedence of design event, p, in T years

p = 1 – p_{T} = 1 – (1 – 1/ T_{d})^{T} (5)

If T is large and T = T_{d,} then p = 0.634.

Solving for T_{d} from eq. 5, if p and T are given, yields

T_{d} = 1/[1 – (1 – p)1/T] (6)

In Table 1, the design return periods of floods or earthquakes for a cofferdam or a temporary structure, T_{d}, are given as a function of the duration of the service life of the temporary structure, T, (which can be taken as the duration of the construction work when the temporary structure is needed) and the probability of exceedance, p, of the design event during the service life. It can be noted that for low p-values, the return period of the design event for a temporary structure becomes rather long.

For the design of cofferdams the return period of the design flood is often taken as 10 years. If construction lasts two, five or 10 years then the probability of exceedence of the design event according to eq. (5) is 19%, 41% and 65% respectively. In such situations it is quite likely that a cofferdam will be damaged during a flood.

If the design flood of a cofferdam is taken as 50 years then for construction periods of two, five and 10 years the probability of exceedence of the design event is (eq. 5) 4%, 10% and 18% respectively.

It should be noted that in the case of an embankment dam the probability of exceedance of the design flood is practically equivalent to the probability of failure of the dam, as overtopping of the dam will result when the design flood is exceeded, causing erosion of the dam and the formation of a breach.

**Risk Considerations**

A risk analysis would be needed to determine the appropriate return period of the design flood (or earthquake). The main components of the risk analysis are: Evaluation of the probability of failure, pf, of the cofferdam as a function of the return period of the design event using eq. 5; Evaluation of the costs; C, of a cofferdam failure (this includes repair costs, damage caused by flood at the dam site and in the flood plain, time delays in completion of the project etc.); and Evaluation of additional costs, dC, of cofferdam construction if the return period of the design event is increased (strengthened structure).

The simplified risk analysis can be performed as follows (R: risk):

Risk of original structure with design event T_{d0}

R_{d0} = p_{f1}(T_{d0}) C (7)

Risk of strengthened structure with design event Td

R_{d} = p_{f1}(T_{d}) (C + d_{C}(T_{d})) (8)

Where the annual failure probabilities can be taken as

p_{f1}(T_{d}) = 1/ T_{d} and p_{f1}(T_{d0}) = 1/ T_{d0} (9)

If T_{d0} is the reference return period of the design event for the cofferdam or a temporary structure, then the risk reduction, dR = R_{d0} – Rd, may be balanced by the additional construction costs of the cofferdam, i.e.

dC(T_{d}) = p_{f1}(T_{d0}) C – p_{f1}(T_{d}) (C + dC(T_{d})) (10)

Rearranging eq. 10 yields in view of eq. 9

dC(T_{d}) = C [p_{f1}(T_{d0}) – p_{f1}(T_{d})]/(1 + p_{f1}(T_{d})) (11)

Assuming that the cost increase of a cofferdam (design event T_{d}) with respect to an initial design with an event characterised by T_{d0} (T_{d} > T_{d0}) can be expressed as follows

dC(T_{d}) = C_{0}/T log (Td/Td0) (12)

where C_{0} are the costs of the cofferdam designed for T_{d0}, then in view of eqs. 9 and 11 we obtain the following implicit equation for the optimum return period of the design event, T_{d}:

log (T_{d}/T_{d0}) = T C/C_{0} (1/T_{d0} – 1/T_{d})/(1 + 1/T_{d}) (13)

Equation 13 is an implicit equation for the unknown T_{d}, which can be solved by a standard equation solver as e.g. the one available in Excel.

**Numerical examples**

Example a: Assuming a return period of the design event of Td0 = 10 years, a service life of T = 5 years, and damage costs of C = 3 C0, we obtain the following equation for T_{d}

log T_{d} = 15 ( 0.1 – 1/ T_{d})/(1 + 1/T_{d}) + 1

The solution is: Td = 275.7 years.

Example b: If the service life of example (a) is reduced from five to two years we obtain

log T_{d} = 6 ( 0.1 – 1/ T_{d})/(1 + 1/T_{d}) + 1

The solution is: Td = 17.5 years.

Example c: If the damage costs of a cofferdam failure are only local and amount, e.g. to 50% (or less) of the initial construction costs, i.e. C = 0.5 C0, then we obtain for a service life of T = 5 years:

log T_{d} = 2.5 ( 0.1 – 1/ T_{d})/(1 + 1/T_{d}) + 1

The solution is: T_{d} = 10 years, i.e. a strengthening of the dam is not necessary from the point of view of risk as the annual costs of strengthening of the dam would be higher than the reduction in risk. In this case it would be more economical to buy, e.g. an insurance coverage rather than strengthening the dam.

Example d: If for C = 0.5 C0, the service life of the cofferdam of example c is increased from T = five to 20 years, we obtain

log T_{d} = 10 ( 0.1 – 1/ T_{d})/(1 + 1/T_{d}) + 1

The solution is: T_{d} = 70 years. Thus, dam strengthening would be cheaper than buying an insurance coverage.

From the above examples it can be noted that the design period must be increased substantially if the consequences of a cofferdam failure become larger than the initial construction costs and if the duration of the construction period becomes rather long, which is not that unusual for many large dam projects.

Although these examples are rather theoretical, because the relation between cofferdam costs and design period Td may not be expressed by the simple expression of eq. 13. In practice, we would have to perform cost estimates for different cofferdam designs with design return periods of say 10, 50 and 200 years and to use interpolation between these values to get the costs for other Td-values.

Because of the large amplification of the acceleration response in the crest region of most concrete dams – amplification factors from 7 to 10 are possible for concrete dams subjected to moderate earthquake action – it is necessary to design any equipment located in this region for the corresponding crest response spectra.

Mass movements are common features during strong earthquakes in mountainous regions and also during heavy rainfall and large floods. Therefore, the possibility of earthquake or rainfall-triggered landslides, debris flows, rockfalls and avalanches etc. must be considered when assessing the general hazards of mass movements at dam sites also during construction. The freeboard of cofferdams should account for waves caused by landslides into the reservoir.

**Conclusions**

Based on the analyses carried out in this study the following conclusions may be drawn for the seismic and/or hydrological design of cofferdams and other temporary structures of a large dam project:

• The return period of the design event (flood, earthquake) depends on the service life of the temporary structure and the accepted probability of failure during the service life

• In the seismic design of structures (Eurocode 8) a probability of failure of less than 5% during the construction period is accepted. For a construction period of 4 years that would result in a return period of the design event of 78.5 years.

• For the construction of large dams, cofferdams are needed, which have to be functional for periods of up to 10 years, in such cases a design event with a return period of 195.5 years would be needed for a failure probability of 5%, if a failure probability of 10% is accepted, then the return period would reduce to 95.4 years.

• For a service life of 5 years, a cofferdam should be designed for an event with a return period of 22.9 years (failure probability of 20%) or 98 years (failure probability of 5%) respectively. These return periods are considerably longer than the 10 year design flood, which is often used for cofferdam design. Thus flood damage of cofferdams is not unusual.

• The need for strengthening of a temporary structure of cofferdam can be determined quantitatively based on a risk analysis in which besides the probability of failure also the consequences of failure and the cost for strengthening are taken into account. If the service life of a cofferdam is relatively long and/or the consequences of a cofferdam failure are large then relatively long return periods of the design event are needed.

• It is problematic to accept a standard flood with a return period of 10 years as a guideline for the design of cofferdams. There is a need for a more rational assessment, which can be carried out on the basis of a probability of failure analysis or a simplified risk analysis, which accounts for the consequences of a cofferdam failure.

• In the case of seismic design considerable improvement in the seismic resistance of cofferdams can be achieved if the general design requirements and recommendations outlined in ICOLD bulletins 120 (2001) and 123 (2002) are observed.

Author Info:

Dr. Martin Wieland, Chairman, ICOLD Committee on Seismic Aspects of Dam Design, Electrowatt-Ekono Ltd. (Jaakko Pöyry Group), Tel. +41 76 356 29 57; Fax + 41 1 355 55 61; E-mail: martin.wieland@ewe.ch

Tables

Table 1