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Section 21 HYDRO 2009 Paper 14 Progress - Potential - Plans Lyon, France

Structural Design of Dam; a feasibility level approach

N. A. Khan U. Latif Engineer (SED) Engineer National Engineering Services National Engineering Services Pakistan (Pvt.) Ltd. Pakistan (Pvt.) Ltd. NESPAK House Building # 17, F-6 Markaz Lahore, Pakistan Islamabad, Pakistan

Introduction At feasibility stage of a hydropower project, site specific data is usually unavailable and various parameters are to be conservatively assumed. This presents difficulties in initiating an optimum design of the dam. This paper provides guidelines to carry out structural design studies when the project is at its initial stages. The implementation of these guidelines to Dasu Hydropower Project is briefly described here for illustration. Different methodologies for structural analyses and inference to respective codes are also discussed. The feasibility studies at Dasu were carried out to a thorough standard, easily adequate to demonstrate the viability of the works proposed. Though detailed studies involving linear and non-linear analyses is imperative for the design of dams, these may not be economical in the early stages of the project.

1. Dam Features Dasu Dam is essentially run-of-river project to be constructed about 75 km downstream of Diamer Basha damsite with the sole purpose of hydropower generation. The project is a part of Pakistan Water and Power Development Authoritys - Vision 2025. Feasibility studies were carried out by joint venture consultants NESPAK (Pak), ACE (Pak), MWH (USA), CPE (Switzerland) in association with Binnie & Partners (Overseas). The objective of the feasibility structural design studies was to provide structural configurations of the roller-compacted concrete gravity dam and appurtenant structures that result in safe and economically viable solution. A maximum height of 233m, base width of 213.5m and dam crest length of 584m involving high volumes of RCC (approximately 4.2 MCM) makes Dasu dam one of the remarkable structures to be built in future.

2. Proposed Design Based on hydropower requirements, geotechnical and hydraulic studies, it was proposed that 233m high RCC gravity dam shall be constructed at Dasu. The design of an RCC dam balances the use of available materials, the selection of structural features and the proposed methods of construction. Sound rock foundations as encountered at Dasu damsite are considered the most suitable for RCC gravity dams. Favourable rock characteristics including high bearing capacity, good shear strength, low permeability and a high degree of resistance to erosion also governed the choice of an underground power system. The detailed layout of project is presented in Figure 1.

The structural design studies for Dasu dam were divided into following sections:

2.1 Stability Analysis of the Dam Stability analysis of the RCC gravity dam at Dasu was carried out to determine an optimum dam profile satisfying overall stability including safety against sliding, overturning and uplift. Pseudo-static, pseudo-dynamic and dynamic methods of analyses were undertaken to determine the dams stability under seismic loadings. In addition, parametric analyses for the sliding stability of dam were performed at the dam-foundation interface and at the concrete lift joints.

Software CADAM was used for stability analysis. CADAM is designed for use with gravity dams and is based on rigid body equilibrium and beam theory. Analysis assumptions and various loading conditions were based on USACE engineering manuals EM 1110-2-2200, 1995 Gravity Dam Design and EM 1110-2-2100, 2005 Stability Analysis of Concrete Structures. Pseudo-static analysis treats earthquake loads as an inertial force applied statically to the structure. The loadings are of two types: inertia force due to the horizontal acceleration of the dam and hydrodynamic forces resulting from the reaction of the reservoir water against the dam. Pseudo-


dynamic analysis is conceptually similar except that it considers dynamic amplification of the inertia forces along the height of the dam. The oscillatory nature of the amplified inertia forces is however, not considered. [4]

Figure 1: Proposed Layout of Dasu Hydropower Project

Table 1: Sliding Stability Factors of Different Codes

*Seismic acceptance based on post-earthquake analysis only (FERC). **Pseudo-static method not accepted. Dynamic methods required to determine level of damage for post-earthquake evaluation (FERC).

Minimum sliding safety requirements recommended by different codes are given in Table 1. Overturning stability criteria was based on the load resultant remaining in the middle 1/3rd of the base for the usual case and remaining in the middle for unusual cases. Extreme case results were deemed acceptable provided the resultant remained within the base. A special sensitivity analyses was also performed to check the sliding stability of the shortest monolith having peak spectral acceleration. In addition, sliding stability was determined for the case if passive resistance of rock disappears. The movement of sub-horizontal rock shear joints beneath the dam was also checked in stability analysis.

Figure 2: Dam Section in River Channel

Design Code

Sliding Safety Factor Vertical Earthquake in

Stability Comments Usual Unusual Extreme

USACE 2.0 1.7 1.3 No No site specific ground motion USACE 2.0 1.5 1.1 No With site specific ground

motion USBR 3.0 2.0 >1.0 Yes Rock to foundation contact USBR 4.0 2.7 1.3 Yes Any plane of weakness in foundation FERC 3.0 2.0 1.3* ** With Cohesion FERC 1.5 (worst

static case) 1.3 (PMF) 1.3* ** Without Cohesion

Section 21 HYDRO 2009 Paper 14 Progress - Potential - Plans Lyon, France Table 2: Typical Sliding Stability Results and Safety Factors

Load Case Uplift Relief

Min. Flotation

Safety Factor

Flotation Safety Factor

FRL MRL OBE MCE only Shear Friction Usual FRL - - - 67% 1.50 3.00 1.30 2.22 3.14 1.84 2.90 3.76 0

Unusual (1) - MRL - - 67% 1.30 2.00 1.20 2.09 2.97 1.58 2.94 3.53 0

Unusual (2) FRL - OBE - 67% 1.30 2.00 1.20 1.65 2.33 0.91 3.84 3.76 0

Unusual (3) - - OBE - - 1.30 2.00 1.20 7.51 10.15 5.60 0.24 - 0

Unusual (4) FRL - - - 50% 1.30 2.00 1.20 2.11 3.02 1.51 2.90 3.25 0

Unusual (5) FRL - - - 25% 1.30 2.00 1.20 1.93 2.85 1.16 2.90 2.70 0

Unusual (6) FRL - - - 0% 1.30 2.00 1.20 1.75 2.67 0.76 2.90 2.30 0

Extreme FRL - - MCE 67% 1.00 1.10 1.10 1.16 1.58 0.00 5.35 3.76 24.02

Post-Seismic

with pre-seismic uplift (OBE) FRL - - - 67% 1.50 2.00 1.20 2.22 3.14 1.84 2.90 3.76 0

with Modified uplift (MCE) FRL - - - 0% 1.00 1.30 1.10 1.67 2.48 0.59 2.88 2.16 58.51

Base Pressure (MPa) Crack Length

(m)

Reservoir Level Earthquake Minimum Sliding Safety Factors Sliding Safety

Factors

Criteria Result -Psuedo Dynamic Analysis

2.2 Stress Analysis of the DamLinear elastic finite element analyses were carried out for the dam to determine the magnitude and distribution of associated stresses and deformational states under static and dynamic loadings. Software SAP2000 version-11 was used for 2D modeling of the dam body and the rock foundation considering dam-water-foundation interaction and seismic loadings, using design response spectra for MCE and OBE. 4500 plane strain elements were modeled for the stress analyses. SAP2000 determines total dynamic response using a modal combination method. Response spectrum analyses determined absolute maximum values of dynamic response. These absolute maximum values were converted into actual response using manually configured worksheets which were later used to determine modified stresses and sliding safety factors.

Under dynamic loadings, 30% compressive strength increase and 50% tensile strength increase was assumed for mass concrete as per ACI 207.5R-99. Based on this, selected allowable stresses for mass concrete in compression were 6.3 MPa for usual and 8.19 MPa for unusual and extreme cases. For mass concrete in tension, allowable stresses of 1.05 MPa were used for usual and 1.58 MPa for unusual and extreme load cases.

The primary purpose of the finite element analysis is stress evaluation. The finite element analysis provides more stress details for evaluation compared to rigid body stability. It also provides more realistic frequency based response to earthquake motions. Although finite element method is used more for stress analysis and evaluation, the stability of the structure can also be evaluated. The resultant force and shear at any plane can be computed using stress integration. For static FEM analysis, resultant forces should be the same as for rigid body stability as static equilibrium should be satisfied for both methods. For dynamic FEM analysis using response spectrum methods, stability evaluation can be considered to be a good estimate. In reality, the peak stresses along the plane of integration may not occur at the same time step. The steps to obtain resultant forces for stability evaluation at various elevations are presented below:

i. Import of nodal stress values from software to spreadsheet for all the load cases. ii. Calculation of normal stresses and shear stresses for static load cases.

iii. Modification of response spectrum results for seismic load cases to positive and negative stresses by judgment based on the dam behaviour.

iv. Calculation of uplift pressures at respective selected layers of the model. v. Calculation of total vertical stresses by summing up adjusted seismic stresses, usual stresses due to static

load cases and uplift pressures. vi. Calculation of individual forces developed in each elements of the layer under consideration and summing

up these forces to determine total vertical force developed in that layer. vii. Calculation of the total moment for a particular layer by multiplying the vertical forces of each element of

that layer with its respective moment arm.


viii. Determination of location of resultant by dividing the total moment of the selected layer with the total vertical force calculated in step- vi.

ix. Determination of un-cracked length along the selected layer using formulae given below. x. Determination of total horizontal force along the selected layer using the procedure discussed in step-i.

xi. Calculation of sliding safety factor.

The formulae used in these calculations are given below:

i

n

i

ii UAF 1 22 ni ii AH 1 12 ni iii eAM 1 22

F

Me

H

cLFFOS s

tan where, 22i = Vertical stress in any element i 21i = Shear stress in any element i Ui = Uplift pressure in any element i F = Sum of all vertical forces acting on a plane H = Sum of all horizontal forces acting on a plane = Angle of internal friction c = Cohesion e = Location of resultant L = Length of base in compression for a unit strip of dam equals to 3X X = Location of resultant form the downstream face of the dam

2.3 Thermal Analysis of the dam Thermal cracking is a concern for mass concrete structures and is undesirable in mass concrete dams. When cement combines with water, an exothermic chemical reaction takes place resulting in a temperature rise of the concrete mass. Subsequent differential cooling between different areas of the mass concrete or overall cooling combined with significant foundation restraint can produce considerable thermally induced stresses. The peak temperature is reached a few days after placement, whereas the cooling process usually takes several weeks, months or even years until a stable state is reached. It is important that the cooling process is controlled to minimize the potential for thermally induced cracking.

Dasu dam is situated at high altitude and the mean monthly temperature varies from 2.2C in winter to 45.6C in summer. This difference is large and will present challenges in controlling temperature during construction. For these feasibility studies, a preliminary thermal analysis was carried out to estimate maximum temperatures that would be anticipated within the dam body. This gives an insight into possible crack patterns and determination of block sizes and location of joints for construction.

The thermal analysis adopted for Dasu was a three step process involving data collection, finite element analysis and mass and surface cracking analysis. The thermal properties were assumed based on data obtained on similar projects as no material testing was carried out at this stage. A summary of these values is given in Table 3.

At Dasu dam, MSC.MARC - version 2005 programme was used to solve the thermo-mechanical and heat transfer problems encountered. The main body of the dam was modeled using 540 plane strain elements. Non-linear incremental structural analysis was performed on a time step of 1 month for duration of 10 years after completion of dam construction. Dynamic transient analysis procedure was also utilized in which MSC.MARC

Figure 3: Typical Stress-Stability Analysis (Extreme Load case)


divides the analysis duration into various increments according to the convergence requirements. The results obtained from this feasibility level analysis are described as follows.

Table 3: RCC and Rock Foundation properties used in Thermal analysis [2] Properties RCC Foundation

Modulus of Elasticity, (MPa) 20,000 20,000 Poissons Ratio 0.20 0.25 Unit Weight, (kg/m3) 2600 2900 Co-efficient of Thermal Expansion, (per C) 9 10-6 4 10-6 Thermal Conductivity, (W/mC) 2.7 2.7Specific Heat, (kJ/kgC) 115 80 Creep Strain Rate, (per MPa) 10 10-6 -

a. Thermal Gradient Analysis The output of the thermal gradient analysis are nodal values i.e. the temperature is given at every node at every increment. These temperature values were subsequently used for thermal stress analysis. The maximum temperature observed in the dam body was 46C with a constant temperature of 24C attained 4 years after construction. The plot of temperature contours 10 years after construction is shown in Figure 4.

Figure 4: Temperature in the dam body after 10 years of construction

b. Thermal Stress Analysis The Software presented strain values at nodal points which were converted into stresses and then compared with allowable stress limits. High tensile stresses were caused near the base of dam due to foundation restraint coupled with the noticeable temperature change. Compressive stresses also developed due to differential temperatures but these are not of concern in these crack analysis studies.

c. Thermal Crack Analysis The number of cracks and their spacing were determined in longitudinal and transverse directions. Thermal strain values were compared with limiting values as provided by USACE ETL 1110-2-542 (1997). These studies revealed that transverse joints can be accepted at fairly wide spacings, however, based on RCC placement rates, block widths were kept variable between 20 to 25 m. The final selection depends on contractors expertise and construction methodologies. A longitudinal gallery was proposed parallel to the dam axis which will be used for future monitoring, drainage and grouting. A second, lower longitudinal gallery will also be constructed just above the foundation. A longitudinal joint will be constructed between these two galleries by impressing a slot vertically through RCC lifts using pneumatically driven steel plates and a geo-grid inserted at the bottom of the respective lift.

Concrete dams crack at points of least resistance and greatest restraint. Vertical transverse cracks do not affect the stability of RCC gravity dam. The problem associated with such cracks is the potential for seepage. For


Dasu, it was noted that the potential for cracking increased near the base of the dam due to restraint effect and so special measures would be taken during construction to minimize this. Post cooling is possible but expensive for such large structures and therefore the focus will be more on temperature control during concrete placement using such measures as incorporating flaked ice in the mix and the pre-cooling of aggregates before mixing. Effective curing during construction will also be required.

2.4 Other Structures The power generation system at Dasu will be constructed underground. Its components include power tunnels, powerhouse complex, draft tube and tailrace tunnels. The feasibility level structural designs of these structures involved determination of adequate thickness for concrete and steel linings to resist all internal and external loading.

Structural models were developed in SAP2000 for control sections of power house, intake structure, penstock, tailrace tunnel and diversion tunnel. Interaction among rock mass, surrounding concrete and steel lining in penstock was modeled and underground openings were subjected to relevant internal and external pressures based on criteria set forth in USACE EM 1110-2-2901, 1997 Tunnels and Shafts in Rocks. The load sharing by the materials depends on the moduli of elasticity, Poissons ratios and shear and flexural thickness of all elements.

Rock modulus of deformation was taken as 8.3 GPa whereas reduced moduli equal to 3.5 GPa was assumed due to the disturbance effects in the periphery of excavated opening. Eight power tunnels were proposed in the Dasu project each having a dedicated penstock. The power tunnels consisted of two portions a) square tunnel of size 8.5 m 8.5 m provided before the vertical gate shaft b) circular tunnel of diameter 8.5 m provided after the gate structure.

The penstocks layout was such that they run in close vicinity of underground structures and any possible leakage from penstock will be detrimental for electrical installations. Structural dimensions of the linings for the penstocks were established to resist the internal design pressures. Structural analysis was carried out for different loads and it was observed that the internal pressure carried by concrete lining is 1229.5 kN/m2 while that carried by steel lining is 910.1 kN/m2. Steel lining was analysed for resistance to external water pressure assuming that whole load is to be carried by steel lining alone. Curves based on Jacobsens equations developed by E.T. Moore were used to determine critical buckling pressure for 40mm thick steel lining. Stiffeners were not considered in this analysis. Critical buckling pressure was determined to be 967 kN/m2 and the applied external water pressure was 655 kN/m2.

Analysis of underground powerhouse requires input from electrical and mechanical, geological and structural engineers to evolve an optimized design. Lining and rock support elements are less affected by seismic waves but any structural member present inside the cavern experience seismic shears since the natural time period differs from the period of earthquake. This was considered in the design of crane supports and machine foundations in the powerhouse complex.

Four D-shaped, long tailrace tunnels of size 10m by 12.5m were proposed for Dasu project to convey discharges emerging from powerhouse through draft tubes and surge tanks, back to the river. As the 2.6 km long tunnels cross Khoshe fault, so fissured and jointed rocks are expected in the surrounding of the tunnel. Therefore, concrete lining was proposed for preventing the rock pieces from falling in the tunnel in addition to resisting the hydrostatic pressure.

3. Conclusions At feasibility stage, the main emphasis is laid on determining the optimum dam profile which is safe against all anticipated loads and at minimum cost. Each dam is a prototype and special methodologies have to be established for analyzing the structural integrity at the expense of huge resources. A number of conservative assumptions are generally inherent at this stage. As the project progresses, refinements are incorporated based on site specific data and material properties. RCC gravity dams behave similar to conventional concrete dams and plenty of design techniques are available in literature.

At Dasu, all efforts were made to establish sufficiently accurate methodology for analyzing various structures with minimum allocated resources. The results achieved from this feasibility study satisfy the basic principles of stability and economy and hold a good precedence for future works.


References [1] American Concrete Institute 207.5R-99 Roller Compacted Mass Concrete Reported by ACI Committee

207. [2] Berga, Jofre and Chonggang Roller Compacted Concrete Dams, Proceedings of the 4th international

symposium on RCC Dams, 2003. [3] Gravity Dam Design, EM 1110-2-2200, US Army Corps of Engineers, 1995. [4] Leclerc M. et-al, CADAM Users Manual version 1.4.3. cole Polytechnique de Montral, 2001. [5] Non linear Incremental Structural Analysis of Massive Concrete Structures, EM 1110-2-536, US Army

Corps of Engineers, 1994. [6] Stability Analysis of Concrete Structures, EM 1110-2-2100, US Army Corps of Engineers (USACE),

2005. [7] Thermal Studies of Mass Concrete, EM 1110-2-542, US Army Corps of Engineers, 1997. [8] Tunnels and Shafts in Rock, EM 1110- 2-2901, US Army Corps of Engineers, 1997

The Authors

Nabeel A. Khan graduated in Civil Engineering from University of Engineering & Technology Lahore, Pakistan. He is currently employed as Structural Engineer in National Engineering Services Pakistan (Pvt.) Ltd. and has worked on the feasibility studies of Dasu Hydropower Project. He has also been involved in the detailed design of different small hydropower projects and industrial units in Pakistan.

U.Latif also graduated in Civil Engineering from University of Engineering & Technology Lahore, Pakistan and is working as Structural Engineer in NESPAK (Pvt.) Ltd. and has co-worked at the feasibility studies of Dasu Hydropower Project. He was involved in carrying out the stability and stress analyses of the dam. Currently he is involved in the design of high rise building structures.

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