RISK AND STANDARDS BASED APPROACH TO RIP RAP DESIGN ALTERNATIVES FOR GRAHAMSTOWN DAM STAGE 2 AUGMENTATION

Transcription

1 RISK AND STANDARDS BASED APPROACH TO RIP RAP DESIGN ALTERNATIVES FOR GRAHAMSTOWN DAM STAGE 2 AUGMENTATION M. B. Barker 1 and D. Holroyde 2 ABSTRACT. A detailed study was completed for the Stage 2 works of the Grahamstown Dam augmentation to investigate various alternatives for the slope protection of the Saddle Dam and Subsidiary Dam embankments, including a standards based and a risk management approach. The standards based approach required an evaluation of the slope protection level and least cost option based on the hazard rating of the dam. Due to the sand construction of the embankments, it was possible to apply a wave erosion model SBEACH to develop an economic risk model for optimising the slope protection alternatives. The erosion model included the effects of the wind direction, reservoir level and wind speed variation during flood events, embankment profile and material parameters. The risk management approach clearly showed that significant cost savings could be achieved by using the risk management approach. Furthermore, the cost curves indicated the sections of the embankments for which present capital works would not be economically justified and for which ongoing maintenance works would be economically advantageous. 1 Introduction Grahamstown Dam is a major water supply source for the Newcastle area and it is proposed to raise the present full supply by 2.4m from RL 10.4m to RL 12.8m. The dam, as shown on Figure 1 comprises the following embankments: The Pacific Highway to the north west of the reservoir The Main Dam to the West Figure 1 - Locality Plan 1 Principal Engineers Dams & Geotechnical, Gutteridge Haskins & Davey Pty Ltd, Brisbane, QLD 2 Water Resource Engineer, Planning, Hunter Water Corporation, Newcastle, NSW

2 The Subsidiary/Saddle Dam to the South The new embankment adjacent to the proposed spillway to the north west With the exception of the new embankment, all of the existing embankments have been constructed of sand. The main and saddle dam embankments have a central core while the subsidiary embankment has a bentonite sand cut-off. The raising is being completed in stages for which Stage 1 comprised raising the core level of the existing embankments to a level required for the Stage 2 full supply level and rip rap slope protection of the main embankment. The stage 2 works comprises construction of a new spillway and associated embankment, a culvert below the Pacific Highway to pass the new spillway flows, a protection bund for the Newline Road and pollution control works. To comply with the Supplementary Environmental Impact Statement for the Stage 2 works, approximately 3000m of the Saddle Dam and Subsidiary Dam upstream slopes required investigation and design of slope protection works. The objectives were to provide protection works in accordance with the ANCOLD 2000 Guidelines for Selection of Acceptable Flood Capacity for Dams to the satisfaction of the New South Wales Dam Safety Committee. 2 Hazard Classification The Main Dam has a hazard classification of High A due to the population at risk downstream of the main embankment and the high value of the stored water. This classification is applicable to the implementation of Surveillance and Operation and Maintenance procedures. Subject to New South Wales Dam Safety Committee approval, where there are distinct embankments comprising the dam, each structure may be considered separately for dam design. Based on the reduced consequences of Saddle Dam and Subsidiary Dam failure, the hazard rating to be used for design of the slope protection works for the Saddle Dam and Subsidiary Dam was assessed to be between Significant and High A. The acceptable flood capacity for a Significant Hazard Category Dam is in the range from 1:1000 to 1:10,000 AEP flood but not less than at least half the PMF while the acceptable flood capacity for the High A Hazard category dam is the PMF. As shown in Table 1, the calculated 1:10,000 AEP event is about half the PMF and was used for the standards based approach to the design of the Grahamstown Subsidiary and Saddle Dam slope protection works. Flood Event ARI (years) Outlfow (m 3 /s) Max RL (m) , PMF Table 1 - Grahamstown Dam Floodrouting Data 3 Embankment Descriptions The Saddle Dam and Subsidiary Dam from chainage 0m to 650m are sand embankments with an upstream slope of about 8H on 1V and a downstream slope of 4H on 1V. The Saddle Dam has a vertical impervious clay core of approximately 6.1m wide while the Subsidiary Dam has a 1.5m wide bentonite sand cut-off. Rip rap slope protection on these embankment sections was generally placed at a slope of about 2H on 1V up to RL 12.8m with a thickness of 910mm and a d 50 of 460mm. The Subsidiary Dam between chainage 650m to about 2000m comprises sand embankments on natural ground (sand). The upstream slope varies from about 14H on 1V for the natural ground surface to 6H on 1V for the placed embankment. The section profile and slope protection varies along this section of the embankment for which there are no design details. Rip rap slope protection has been placed in areas of the embankment which have suffered beach erosion in the past as well as a 300m length of the embankment (Embankment section 5 of Figure 3) where rip rap slope protection of about 2m width has been placed

3 along the embankment. The embankment sections are grassed on the upstream side above the level of any rip rap to the crest of the embankment. During the Stage 1 construction, the core sections of all embankemnts were raised using a 300mm wide bentonite/clay section placed along the centre line of the core and extending up to the crest level at about RL 14.8m. the existing embankment. Gabions placed on the existing rip rap with underlying geotextile on the embankment sand material to prevent washing out of the sand. 4. Slope Protection Options The following options were considered for the riprap protection as shown in Figure 2. RipRap layer placed along slope of the embankment with underlying filter or geotextile filter fabric to prevent washing out of sand from the existing embankment. Rip Rap Berm with underlying geotextile filter fabric to prevent washing out of sand from the existing embankment. Rip Rap Berm alternative design using a rip rap zone supported on earthfill with underlying geotextile filter fabric to prevent washing out of sand from the existing embankment. Reno Mattress placed on the embankment slope and keyed into the existing rip rap with a gabion at the top level for anchoring the mattress and underlying geotextile filter fabric to prevent washing out of sand form Figure 2 - Slope Protection Options The Saddle Dam and Subsidiary Dam vary in section along the embankment and typical cross sections and embankment lengths were selected for the study, as shown on Figure 3. Figure 3 - Location of Cross Sections used for Slope Protection Analysis

4 5 Standards Based Evaluation The standards based or deterministic approach to the design and selection of the preferred slope protection option was carried out as follows: Wind Data Analysis The 10minute, 3 hourly interval wind speed data for the Williamtown RAAF Base, which is located approximately 5km south east of the dam was analysed for the period from 1942 and The 1year, 10year and 100 year ARI peak wind speeds were estimated for various directions perpendicular to the embankments using Normal, Log-normal and Log Pearson III statistical methods. An alternative method of estimating wind speeds was carried out using the Australian Wind Code AS The maximum hourly wind speed obtained from the statistical analysis and the Australian Wind Code as well as the USBR design wind speed of 30m/s were used for the wave estimation and rip-rap design. Estimation of Wave Height and Run up The wave height and wave run up data for each embankment was calculated using the procedure given in the ACER Technical Memorandum No using the following steps: Calculation of the effective fetch for each embankment section; The effective fetch for the embankments was calcuated to be in the order of 4.8km Adjust the overland wind speed to obtain overwater speeds; The correction factors determined by USBR (1981) were used to select a wind velocity ratio of 1.26 for the effective fetch. Calculate the wind set up; The wind setup is the rise in the water level at the leeward end of the fetch resulting from the shear force of the wind over the water. Calculate the significant wave height, wave length and wave period; The significant wave height Hs, represents the average wave height of the highest one-third of the waves present in each interval. If the water depth is greater than one half the wave length, the waves can be considered to be deep water waves. In the case of Grahamstown Dam, which is a relatively shallow reservoir, the water depth was marginally less than half the wave length but the difference in the deep and shallow water wave heights for the Grahamstown Dam was not significant. Calculate the wave run-up on the embankment slope. Wave runup, R, which is the vertical difference between the maximum level attained by the rush of water up the slope and the stillwater elevation was estimated using the ACER formula: R = Where: H S 05. HS *cot( θ) L R = Wave runup (m) Hs = Significant Wave height (m) L = Wave length (m) θ = Angle of the dam face from the horizontal ( ) The wind set up and wave run up were calculated for upstream slopes of 2H:1V, 6H:1V, 8H:1V and 10H:1V using the 1, 10 and 100 year ARI wind speeds for the dominant wind directions as well as the USBR recommended over water wind speed of 30 m/s. The results of the analyses for the Saddle Dam with the USBR and 100yr North Westerly wind and an 8H on 1V slope are shown in Table 2. Similar results were obtained for the Subsidiary Dam which indicated that for the 8H on 1V slope, the minimum slope protection level for the rip rap or reno-mattress options should be RL 14.5m.

5 Description Unit 100yr USBR Wind vel. over land m/s Wind vel. over water m/s Minimum duration hour Significant wave ht. m Wave run-up m Wind set up m Total Wet Freeboard m Minimum Rip Rap Level for 10,000 yr Flood RL13.73m m Table 2 - Wave Data for Saddle Dam using NW Wind and Upstream Slope 8H:1V The analysis with the 2H on 1V slope indicated that the wave set up and run up would be significantly higher than the flatter slopes and further analysis was performed to develop a reservoir level frequency curve for combined wind and flood events for the 2H on 1V and 8H on 1V embankment slopes using the following wind speeds derived from the statistical analysis of the wind data. Speed (m/s) Wind ARI (years) , The 1000 and 10,000 year wind speeds were derived from extrapolation of the available data and were only used for this frequency analysis. Figure 3 shows the frequency versus reservoir level curve for the 2H on 1 V slope. Exceedence Probability 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 Independent wind and wave Maximum Water Level (m) Dependent wind and wave Assumed design curve with transition from independent to dependent Flood Level Rip Rap Option Reno Mattress Option Berm Option Saddle Berm Option Alternative Gabion Option Figure 3 - Slope Protection Exceedence Curve for Embankment Slope 2H on 1V 4,000,000 3,500,000 3,000,000 2,500,000 2,000,000 1,500,000 1,000, ,000 Figure 3 - Frequency Reservoir Level Curve for a 2:1 Slope The reservoir level frequency data indicated that the minimum levels for the slope protection should be 14.3m for the reno-mattress and rip rap options and 15.2m for the berm and gabion option. However, as the analyses could not account for the combined berm and beach effect 0 Cost (AUD) up-slope of the berm, it was assessed that a minimum slope protection level of RL 14.9m would be required for the berm and gabion options. Slope Protection Design The approach recommended by US Corps of Engineers Shore Protection Manual (1984) was used for the design of the rip rap. Assuming a Rayleigh distribution for the waves, the design wave height was taken to be 1.27 times the significant wave height Hs. The significant wave height was calculated using a wind velocity over water of 30 m/s for the Subsidiary Dam and 33.0 m/s for the Saddle Dam as these were the highest wind speeds found from the wind analyses. The weight of the graded rock in the riprap was calculated using the formula: W 50 = Where: K γ γ * H r r D * 1 *cot( θ ) γ W 3 3 W 50 = weight of the 50% percent size in the riprap (kn) γ r = unit weight of the riprap rock (kn/m 3 ) γ w = unit weight of the water (kn/m 3 ) H = θ = design wave height (m) Angle of the dam face from the horizontal ( ) K D = stability coefficient (2.5 for angular quarried rock and non breaking waves) The maximum weight of graded riprap (W 100 ) was taken to be 4W 50 and the minimum 0.125W 50. These are equivalent to the maximum size of 1.5 times the D 50, and minimum size 0.5 times D 50. The equivalent sieve size of the riprap is approximately 1.15(W/γ r ) The rip rap requirements were determined for the existing upstream slope of the subsidiary dam and saddle dam which varies from 6H:1V to 10H:1V. As one of the alternatives for the slope protection is a berm placed as a continuation of the existing rip rap slope, the rip rap requirements were also determined for the

6 Saddle Dam using a slope of 2H on 1V. The rip rap sizes for the 2H:1V and 8H:1V slopes are presented in Table 3. The design of the bedding layer below the riprap was carried out with reference to US Corps of Engineers (1995) and Fell et al (1992). In the case of the reno-mattress design, a runup correction factor was applied to the values Option Cost ($M) RL 14.3m RL 14.9m Rip Rap Berm > Berm Reno Mattress 2.89 >3.04 Gabion Table 4 - Slope Protection Option Costs calculated for the rip rap using the following roughness reduction factors: R reno-mattress = 0.77 R riprap = 0.61 The ratio of these roughness factors of 1.26 was applied to the wave run up and set up to calculate the thickness of a Maccaferri Reno- Mattress. A geotextile fabric below the renomattress was selected to prevent erosion of the underlying material through the reno-mattress. The analyses indicated that a reno-mattress thickness of 170mm was required. Description Unit 2:1 8:1 Unit Weight of Riprap kn/m Wind vel. over water m/s Significant wave ht m Design wave ht m Max wt of riprap kn % Wt of riprap kn Min. weight of riprap kn Max. size of riprap m % size of riprap m Min. size of riprap m Table 3 - Saddle dam Riprap Design Cost Estimation and Option Selection The quantities and costs for each slope protection option were estimated using the calculated rip rap layer thicknesses and berm dimensions for each slope protection option as shown on Figure 3 and Table 4 for the levels of protection at RL 14.3 and 14.9m. The rip rap option and the reno-mattress option were significantly more costly than the berm and gabion options. While the gabion option was the lowest cost alternative for all levels of slope protection, the wave run-up characteristics and erosion potential differ from the flatter slopes applicable to the other options. There was also some concern over the long term durability of the gabions. The reno-mattress, berm and gabion options were used for the risk analysis to determine the required protection level and preferred option for each section of the embankments. 6 Risk Analysis Due to the sand construction of the embankments, it was possible to apply a wave erosion model SBEACH to determine the likelihood of embankment failure or damage resulting from beaching of the sand in unprotected or partly protected areas and to produce a risk model to evaluate the least cost option for the slope protection. Risk Analysis Methodology 1. The wind and rain data were evaluated to determine the likely wind pattern for the 1, 10 and 100 year events and the coincidence of the peak winds and rainfall events; 2. The SBEACH model was checked for sensitivity to the input parameters and calibrated using historical erosion of the embankments; 3. The erosion potential of the waves on each embankment section was determined for a selected number of combined wind and flood events to evaluate the likelihood of embankment breach and damage and estimate the cost of erosion repair works; 4. A risk model was developed to derive the failure and damage likelihoods for each flood and wind event likely to occur using the reno-mattress, berm and gabion options constructed to various levels; 5. Annual risk costs for failure and erosion damage of the saddle dam and subsidiary

7 dam sections were determined and the present value of the annual risk cost calculated and compared with the capital cost of slope protection works required to prevent erosion or damage of the embankments; 6. The present value for the maintenance, if carried out on a five yearly basis, was calculated and the equivalent annual maintenance cost determined for each option to assess the effect of the reduced costs on the decision regarding the least cost option; 7. The results were used to determine rip rap level required to minimise the risk cost of failure and repair/maintenance for each embankment section considering annual and five yearly maintenance programmes. Wind Data Analysis The half hourly wind data available from the Bureau of Meteorology, was plotted together with the three hourly data to review the wind patterns which indicated the following: the wind direction for the more extreme events is generally within a 30 arc; Wind direction for the more frequent events (1 year ARI) can be in any direction. The maximum wind speeds generally occurred with the wind direction from the west (270 ) to the north west (315 ); The peak wind is not sustained for more that 3 hours for the higher wind speed events (30m/s) for the wind speeds in the order of 20m/s, the wind can oscillate about this peak for an extended period, as observed in 1956 where the speed varied between 18m/s to 23m/s for about 48 hours. It was clear from the data that two distinct wind patterns could be generated, as shown on Reservoir Level (m) Time (hrs) Figure 6 - Flood Hydrographs for 1:200,000 AEP Flood with various Storm Durations Figures 4 and 5 which were assessed to be likely 10 and 100 year ARI events respectively. From discussions with the Bureau of Meteorology, it was established that during major rainfall events, the wind direction is generally from the south east while the maximum wind speeds can occur during or after the peak rainfall event. Wind Speed (m/s) Wind Speed (m/s) Time (hrs) 12h 24h 36h 48h 72h Composite Figure 4 - Composite Maximum Wind Event 1 in 10 yr ARI Composite Time (hrs) Figure 5 - Composite Maximum Wind Event 1 in 100 yr ARI It was conservatively assumed that the wind direction would be normal to the embankments. The wind peak was assumed to occur six hours

8 after the flood peak. A sensitivity analysis on the coincidence of wind and flood peaks indicated that the selected offset of the peaks was likely to be the worst case scenario, however, longer duration peaks could result in about an additional 10% erosion. The longer duration storm events have extended periods of relatively high reservoir levels as shown on Figure 6 for the 200,000 year flood event hydrographs. Flood Event Storm Duration (hrs) Peak RL Max. Erosion PMF 12 or or 24 1:200, :2, : Table 5 - Critical Storm Durations for Flood Level and Erosion Model The storm durations shown in Table 5 were relevant to the reservoir level and erosion potential of the embankment slope for which the maximum erosion storm duration hydrographs were used for the risk analysis. Erosion Model The wave erosion was evaluated using the US Army Corps of Engineers Waterways Experiment Station program Storm Induced Beach Change (SBEACH 32 Version 2.0). SBEACH is an empirically based numerical model for simulating two dimensional cross shore beach change. The model was initially formulated using data from prototype scale laboratory experiments and further developed and verified on field measurements and sensitivity testing. In calculating the beach profile change, the model assumes that the cross-shore sediment transport is produced by breaking waves and changes in water level. Wave transformation and sediment transport rates are calculated using random wave properties. The random wave generation assumes that the wave height follows a Raleigh distribution with adjustments made for use of the significant wave height and wave decay over either a monotonic or nonmonotonic profile. In the case of the nonmonotonic profile, a predictive equation is included in the model to determine the number of waves that reform along the negatively sloping sections of the slope i.e. upslope of the berm options used for Grahamstown Dam. The random wave model uses the conservation of wave energy to solve wave energy flux equations and compute the wave height decay across the surf zone where the waves are breaking on the embankment slope. Wave and wind induced water level setup are included in the calculation by solving a cross-shore momentum equation. Computations of random wave parameters are performed across the profile at each time step based on input wave and water level information and the wave parameters are used to calculate the sediment transport rates. Figure 7 - Description of Shore Profile The input for the model included the flood hydrograph, wind speed and direction,, significant wave height and period, embankment section and embankment material properties including: Effective grain size diameter; Avalanching angle which defines the steepest profile that can develop before avalanching of the beaching material occurs and was assumed to be 45 for the well compacted material which had evidence of near vertical erosion faces. A transport rate coefficient (K) which influences the rate at which transport occurs when the energy dissipation per unit volume is greater than the equilibrium energy dissipation per unit volume. Slope Dependent Transport term (ε) which influences the slope of the eroded profile. Higher values of this parameter result in profiles with gentler slopes and flatter bars

9 while lower values result in steeper near shore profiles and steeper bars. Depth of Foreshore Parameter DFS which defines the landward end of the surf zone in the model and affects the magnitude of transport in the swash zone. A higher value, corresponding to a greater depth at the boundary between the surf and swash zones, typically increases the transport rates in the swash zone producing more erosion at the foreshore. Erosion Model Sensitivity and Calibration Sensitivity analyses and model calibration were carried out on a section of the Subsidiary Dam using the annual wind with the reservoir at the FSL and a sand size of 0.35mm. The following parameters were used: Grid spacing 5m, 3m, 2m, 1m. The model was found to be particularly sensitive to the grid spacing for which a 1m spacing was required to correctly model the gabion and berm options. Larger grid spacing underestimated the erosion potential. Particle Size Sensitivity analysis was performed with particle sizes from 0.25mm to 0.35mm. The particle size of 0.25mm is consistent with wind blown material in the area while the 0.35mm was the average of the main embankment particle size. Transport Rate Coefficient The transport rate coefficient (K) was varied and finally selected to provide a reasonable depth of erosion. Slope Dependent Transport term (ε) The slope dependent transport term had a significant impact on the erosion potential and was reduced from the default value of 0.002m 2 /s to 0.001m 2 /s to improve the erosion prediction. Depth of Foreshore Parameter DFS Level (m) The erosion was found to be relatively insensitive to this parameter which was kept Figure 10 - Subsidiary Dam Section 1 Erosion Plot for FSL & Existing Slope Protection at the default value of 0.3m Erosion Analysis The wave erosion model was run for each of the representative embankment sections using the PMF; 200,000 year; 2,000 year; and 10 year ARI flood events and the FSL using the 100, 10 and 1 year ARI wind events. In the case of the FSL condition, the erosion was analysed using a 10,000year ARI wind event for each embankment to determine the likelihood of failure under this extreme event. A typical input hydrograph and wind speed data for the 200yr flood and the 10yr wind is shown on Figure 8. RL (m) Level (m) Original Profile 100 yr Wind (Sand 0.25mm) 100 yr Wind (Sand 0.3mm) 100 yr Wind (Sand 0.35mm) 10 yr Wind (Sand 0.25mm) 10 yr Wind (Sand 0.3mm) 10 yr Wind (Sand 0.35mm) 1 yr Wind (Sand 0.25mm) 1 yr Wind (Sand 0.3mm) 1 yr Wind (Sand 0.35mm) Original Profile 10,000 yr Wind (Sand 0.3mm) 100 yr Wind (Sand 0.25mm) 100 yr Wind (Sand 0.3mm) 100 yr Wind (Sand 0.35mm) 10 yr Wind (Sand 0.25mm) 10 yr Wind (Sand 0.3mm) 10 yr Wind (Sand 0.35mm) 1 yr Wind (Sand 0.25mm) 1 yr Wind (Sand 0.3mm) 1 yr Wind (Sand 0.35mm) Chainage (m) Time (hrs) Flood Level Wind Velocity over Water Figure yr Flood and 10 yr Wind Chainage (m) Figure 9 - Saddle Dam Erosion Plots for FSL & Existing Slope Protection Wind Velocity (m/s)

10 The models were run using the existing embankment configuration and at least two levels of slope protection for each option in order to provide data for the risk analysis and cost optimisation. Repair Costs ($) 16,000 14,000 12,000 10,000 8,000 6,000 Subsidiary Dam Section 1 - Repair Costs versus Flood Frequency Berm Slope Protection at RL 13.0m 100yr Wind 10yr Wind 1yr Wind and the cost for the repairs calculated using a rate for replacement of eroded sand. Repair cost versus frequency curves were developed for each embankment section and level of slope protection for all of the options. A typical plot is shown on Figure 12 for Section 1 of the Subsidiary Dam with the Berm protection option to RL 13.0m. Risk Model The following assumptions and limitations applied to the risk analysis. 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E Flood Frequency 13 Figure 12 - Typical Plot of Repair Cost versus 12 Level (m) 4, , Frequency Original Profile 100yr Wind 10yr Wind 1yr Wind Chainage (m) Figure 11 - Subsidiary Dam Section 1 Erosion Plot for FSL & Berm Slope Protection Erosion Analysis Results Typical erosion plots are shown on Figures 9, 10 and 11 for the Full Supply Level conditions and the annual wind for the existing Saddle Dam and Section 1 of the Subsidiary Dam with and without the proposed slope protection in this embankment section. The models showed that the beach erosion forms relatively rapidly and then maintains a stable profile. The erosion of the embankment does not extend through the core zone below the FSL of RL12.8m, however, considerable damage occurs for a number of flood events. The erosion for the full supply level condition indicated that the erosion will progress about 5m to 10m into the face of the embankments to a depth of up to 1m. The volume of material eroded was calculated for each embankment using the level difference at each 1m grid point between the original profile and the eroded profile. A damage factor was used to account for the non uniformity of the erosion along the full length of each section The likelihood of coincident winds occurring with floods increases with flood magnitude to the point where at the PMF, the 100 year wind may be coincident with the peak flow ( Met. Bureau). The peak flood levels for the PMF event occur during the 12hr or 24hr storm event. The PMF event was also evaluated using a 72 hour storm duration. Peak winds occur at about 6hrs after the peak flood level. Sensitivity analysis to the occurrence of the wind was carried out. The annual wind speed occurrs continuously for 30% of the year. Only the critical storm durations for each flood have been used. The risk assessment applies only to the flood and wind events. Slope Protection PMF to 100, ,000 to 10,000 10,000 to 1,000 1,000 to to to 1 100yr Wind 10 yr Wind 1 yr Wind Damage No Damage Figure 13 - Part Event Tree Failure No Failure

11 The risk model combined the likelihood of the flood and wind events with the potential damage and failure probabilities assessed using the wave erosion results. A typical model, as shown in Figure 13 for the Saddle Dam existing slope protection, included the following event sequences occurring during a flood event. Flood and Wind The flood and wind combinations are shown on Table 6. Erosion Damage Embankment Failure Embankment OK The model was run for each embankment section with the slope protection levels appropriate to each option. Flood Event Interval (years) Wind ARI (years) 1 to 10 1, 10, to 100 1, 10, to , 10, 100 1,000 to 10,000 10, ,000 to 100, ,000 to PMF 100 Table 6 - Flood and Wind Event Combinations for Risk Analysis The total annual risk cost of damage or failure and the present value of each was calculated using a discount rate of 8% and lifetime of 100years. The present value maintenance risk cost was also determined using a 5 yearly interval for the annual risk cost and the equivalent annual series costs determined for this maintenance cost. Risk Analysis Results and Evaluation The risk analysis provided failure and damage risk costs and total risk cost for each flood and wind event range for present conditions. The results for each flood range are shown in Tables 7 for Section 1 of the Subsidiary Dam. The capital cost, annual and present value failure and maintenance costs for each slope protection option were obtained for the embankment sections. The results for the Section 1 of the Subsidiary Dam are shown on Table 8 and the data for the berm option of this embankment section is shown on Figure 14. Risk Cost ($) 180, , , , ,000 80,000 60,000 40,000 20,000 Failure and Maintenance Total PV Risk Cost Maintenance Annual Risk Cost Maintenance PV Risk Cost Capital + PV Maintenance Initial Capital Cost Slope Protection Level (m) 180, , , , ,000 80,000 60,000 40,000 20,000 Figure 14 - Risk Analysis Berm Option The results for this embankment are typical of the other embankments and showed the following: The majority of the damage risk cost with the existing conditions occurs with the more frequent annual flood events. The majority of the damage risk costs for the wind events occurs as a result of the annual wind event. This is due to the extended duration of the wind events and the high percentage damage expected from the annual wind; Increasing the slope protection level results in increased present value costs for Capital + PV Maintenace Risk Cost ($) Flood Event Range Failure Risk Cost Damage Risk Cost Total Risk Cost (years) Risk Cost ($) Percent of Total Risk Cost ($) Percent of Total Risk Cost ($) Percent of Total 10 to % 12, % 12, % 100 to % % % 1,000 to % % % 10,000 to 1, % % % 100,000 to 10, % 2 0.0% % PMF to 100, % 0 0.0% 8 0.1% Totals $ 1, % $ 12, % 13, % $ 13,979 Table 7 - Summary of Risk Costs for Subsidiary Dam Section 1 with Existing Conditions

12 maintenance and initial capital cost. As the beach erosion model indicated that the beaching is likely to be stable and not progress to failure, it was considered appropriate to extend the maintenance period to a 5 yearly interval which significantly reduced the total maintenance risk cost taken over a 50 year lifetime. As shown on Table 8, the capital and present value of the risk cost for the Subsidiary Dam Section 1 was reduced from $154,241 to $26,291. Of all of the embankment areas analysed, only Section 1 of the Subsidiary Dam could be shown to have similar capital costs for the slope protection option compared with ongoing maintenance of the do-nothing option. The results for the remainder of the embankments indicated that the present value of the reduced maintenance cost and capital cost was significantly higher than the maintenance costs for the do-nothing option. Based on the results of the risk analysis, the following recommendations were made for the Slope Protection works for the Grahamstown Saddle Dam and Subsidiary Dam: provide additional slope protection for the Section 1 of the Subsidiary Dam from the present level of RL 11.5m to RL 13.0m during the present Stage 2 augmentation works. The slope protection will be required over a length of about 100m of the embankment at a cost of about $35,000; apart from Section 1 of the Subsidiary Dam, provide no additional slope protection for the Saddle Dam or the Subsidiary Dam during the present Stage 2 augmentation works; perform maintenance and remedial works at five yearly intervals; monitor the embankments for signs of excessive erosion beyond that predicted by the erosion model. If this occurs, slope protection should be constructed using either the berm or gabion options to a level considered appropriate to the observed damage and as necessary to minimise the total risk cost; Plant water resistant grass between RL 10.4m and RL 12.8m along Section 2 of the Subsidiary Dam and between RL 11.5m Protection Level (m) Initial Capital Cost ($) Failure and Maintenance Cost Annual PV Risk Risk Cost Cost ($) ($) Annual Risk Cost Reno Mattress Maintenance Cost ($) PV PV Risk Annual Risk Cost - 5yr Maint. for Cost Interval 5yr Risk Cost Capital + PV Maint. ($) , ,011 12, ,241 26,291 2, , ,018 2,274 27, ,043 1, , , , , ,280 Berm , ,011 12, ,241 26,291 2, , ,523 1,666 20, , , , , ,510 Gabion (Risk Model Assumed to be the same as the Berm Option) , ,011 12, ,241 26,291 2, , ,000 1,666 20, , , , , ,687 Table 8 - Risk Analysis Results Subsidiary Dam Section 1

13 to 12.8m along Section 1 of the Subsidiary Dam; Where required, grass of the runner type should be planted above the existing rip rap or the water resistant grass up to the embankment crest level to bind the sand together and provide some resistance to wind and wave erosion. 7 Summary and Conclusions An economic risk model was developed for the Grahamstown Dam Saddle and Subsidiary embankment sections with various types and levels of slope protection. The costs for slope protection options were developed using slope protection levels based on a standards approach for slope protection. A risk management approach was then used to develop damage risk costs for each slope protection level and a present value analysis performed to provide cost curves of total cost versus slope protection level. The cost curves were finally used to determine the required slope protection measure and the level to which the protection was required for each of the representative embankment sections. The risk management approach clearly showed that a significant cost savings in the order of $1M could be achieved by using the risk management approach rather than the standards approach. Furthermore, the cost curves clearly showed the sections of the embankments for which present capital works would not be economically justified and for which ongoing maintenance works would be economically advantageous. References Risk View Palisade Corporation, Windows Version 1996 ANCOLD (2000) Guidelines on Selection of Acceptable Flood Capacity for Dams, March 2000 CEC (1993), Augmentation of Lake Grahamstown Report on Final Spillway Layout, Civil Engineering Consulting, February 1993 SBEACH (1996), SBEACH Numerical Model for Simulating Storm Induced Beach Change Report 4, US Army Corps of Engineers, Waterways Experiment Station, Technical Report CERC-89-9, April 1996 Decision Tools (1996), Decision Tools Suite Precision Tree, Top Rank, Best Fit and