Gomal Zam Dam: RCC Design, Spillway Hydraulics & Geotechnical Challenges (2026)

1. Introduction and Structural Typography of Gomal Zam Dam

Situated across the Gomal River in the South Waziristan tribal district of Khyber Pakhtunkhwa, Pakistan, the gomal zam dam represents a benchmark achievement in modern hydraulic infrastructure and roller compacted concrete (RCC) engineering. Rising 133 meters (436 feet) above its deepest foundation rock with a crest length of 231 meters, this curved gravity structure impounds a gross reservoir storage capacity of 1,404,000,000 cubic meters (1.14 million acre-feet). The project provides multi-purpose benefits, including 17.4 megawatts of clean hydroelectric power generation, agricultural irrigation across 191,000 acres of fertile arid land, and vital flood attenuation in the downstream plain of Dera Ismail Khan.

                  GOMAL ZAM DAM CROSS-SECTION PROFILE
                             Crest Elevation 783 m
                           +------------------------+
                           |  Stepped Ogee Spillway |
                           |  Crest (El. 770 m)     |
     Upstream Face         |                        |\    Downstream Face
     Vertical (1.0 V:0.0 H)|                        | \   Stepped Slope
                           |                        |  \  (0.8 H : 1.0 V)
  Reservoir High Head      |   Roller Compacted     |   \
  ~~~~~~~~~~~~~~~~~|       |   Concrete (RCC)       |    \
                   |       |   Massive Interior     |     \
                   |       |                        |      \
                   |       |   Grout Curtain Zone   |       \==== Stepped Energy
                   |       |   +----------------+   |        \    Dissipator
                   |       +---| Bedding Mortar |---+         \___
                   |           +----------------+             +----+ Flip Bucket
  -----------------+------------------------------------------+    | (El. 680 m)
  /////////////////////////////////////////////////////////////////|
                     Canyon Bedrock (Sandstone & Shale)

The geometric layout of the structure employs a curved upstream radius of 270 meters. While analyzed conservatively as a pure gravity dam where self-weight resists destabilizing water pressures, the three-dimensional curvature transfers a portion of the hydrostatic thrust into the competent limestone and sandstone canyon abutments via secondary horizontal arching action.

Developing the hydraulic project presented complex technical challenges, ranging from extreme flash flooding in steep mountainous catchments to complex canyon seismicity and intricate mass thermal regulation.

2. Roller Compacted Concrete (RCC) Mix Design and Thermal Stress Management

2.1 Paste Content, Pozzolan Replacement, and Workability

The construction of the project required placing approximately 550,000 cubic meters of high-density roller compacted concrete. RCC technology combines the structural integrity and durability of conventional mass concrete with the rapid, mechanized placement economics of earth-fill embankment compaction.

                 RCC SPREADING AND COMPACTION CYCLE
         Heavy Vibratory Roller (10-12 Ton Twin Drum)
                   [ O========O ]
       <=====================================> Compaction Direction
      -----------------------------------------  Compacted Lift (0.30 m)
      .........................................  Fresh Uncompacted RCC
      =========================================  Bedding Mortar Film (10 mm)
      -----------------------------------------  Prior Cured Lift Surface

The concrete mix was formulated with a low water-to-cementitious materials ratio ($w/cm \approx 0.48$ to $0.52$) and a high percentage of natural pozzolan (up to 55% Portland cement replacement) to suppress peak hydration temperatures.

2.2 Adiabatic Temperature Rise and Thermal Crack Prevention

Mass concrete structures generate significant internal heat during hydration. If the core temperature rises unchecked, thermal tensile stresses during subsequent surface cooling exceed the tensile strength of the young concrete, causing through-going transverse cracks.

The peak adiabatic temperature rise $\Delta T_{ad}$ in the interior of the massive dam body was calculated as:

$$\Delta T_{ad} = \frac{C_h \cdot H_o}{\rho_c \cdot c_p}$$

where $C_h$ is the cementitious content ($200\text{ kg/m}^3$), $H_o$ is the total cumulative heat of hydration ($270\text{ kJ/kg}$ for pozzolanic blends), $\rho_c$ is concrete density ($2,400\text{ kg/m}^3$), and $c_p$ is concrete specific heat capacity ($1.05\text{ kJ/(kg}\cdot\text{K)}$).

$$\Delta T_{ad} = \frac{200 \times 270}{2,400 \times 1.05} = \frac{54,000}{2,520} \approx 21.43^\circ\text{ C}$$

By enforcing placing temperature limits below $18^\circ\text{ C}$ through aggregate shading, chilled mixing water, and flake ice addition, peak interior temperatures remained below $42^\circ\text{ C}$, preventing thermal stress fractures.

3. Canyon Geotechnical Features and Abutment Rock Mechanics

3.1 Geological Setting of the Narrow Khajuri Kach Gorge

The dam is founded in the narrow Khajuri Kach gorge, where the Gomal River cuts through highly folded Sedimentary Tertiary strata. The foundation geology consists predominantly of interbedded, massive sandstone beds alternating with thinner calcareous shale and siltstone layers.

               KHAJURI KACH GORGE GEOMECHANICAL PROFILE
      Left Abutment                           Right Abutment
     (Steep Canyon Wall)                    (Steep Canyon Wall)
      \\  Sandstone Ledges                   Sandstone Ledges  //
       \\  [===]                              [===]          //
        \\   Shale Interbed                     Shale Bed   //
         \\  [---]                              [---]      //
          \\   Fault Joint                     Joint Set  //
           \\   \                                  /     //
            \\___v________________________________v_____//
             |     GOMAL ZAM DAM RCC FOUNDATION PLINTH   |
             +-------------------------------------------+
             |   Consolidation Grouting Blanket (15 m)   |
             +===========================================+
             |   Deep High-Pressure Grout Curtain (60 m) |

Rock Mass Rating (RMR) values across the riverbed ranged from 62 to 74 (Class II – Good Rock), whereas the higher canyon walls exhibited localized jointing and stress relief fractures requiring systematic rock bolt reinforcement ($32\text{ mm}$ high-tensile anchors, $6\text{ m}$ to $9\text{ m}$ length) and steel-mesh reinforced shotcrete.

3.2 Deep Consolidation Grouting and High-Pressure Curtain Grouting

To mitigate foundation seepage and uplift pressures beneath the foundation footprint, geotechnical engineers executed a multi-line grout curtain:

1. Shallow Consolidation Blanket Grouting: Drilled on a $3.0\text{ m} \times 3.0\text{ m}$ grid to a depth of $10\text{ m}$ to $15\text{ m}$ across the entire footprint, consolidating loose joint systems under injection pressures of $0.3$ to $0.8\text{ MPa}$.
2. Deep High-Pressure Curtain Grouting: Drilled from the internal foundation drainage gallery down to depths of up to $60\text{ m}$ (equivalent to approximately 50% of the maximum hydrostatic head), using micro-fine cement grouts injected under pressures up to $2.5\text{ MPa}$.

4. Structural Analysis: Curved Gravity Arching Action and Stability

The structural integrity of the curved structure relies on gravity equilibrium, supplemented by 3D canyon boundary constraint effects. The governing differential equation for horizontal arch thrust transfer in curved gravity structures follows the Trial Load formulation:

$$\frac{d^2}{dx^2}\left( E I_z \frac{d^2 w}{dx^2} \right) + \frac{E A}{R^2} w = p_a(y)$$

where $w(x)$ represents the radial displacement, $R$ is the upstream curvature radius ($270\text{ m}$), $E$ is the concrete modulus of elasticity ($28\text{ GPa}$), $A$ is the horizontal section area, and $p_a(y)$ is the portion of total hydrostatic pressure carried by arch action at elevation $y$.

                    ARCH-CANTILEVER LOAD DIVISION
         Total Hydrostatic Pressure Profile p(y) = γ_w * y
                    +---------------------------+
                    |        \ Cantilever Load  |
                    |         \   p_c(y)        |
                    |          \                |
      Dam Height    |           \               |
          (H)       |   Arch     \              |
                    |   Load      \             |
                    |   p_a(y)     \            |
                    |               \           |
                    +----------------\----------+
                                Hydrostatic Head

Finite element simulations demonstrated that horizontal arch action transfers between 14% and 22% of peak hydrostatic thrust directly into the sandstone abutment rock walls, reducing base bending moments at the dam heel.

5. Stepped Spillway Hydraulics and Energy Dissipation Mechanics

5.1 Skimming Flow Regime and Turbulent Boundary Layer Growth

The central overflow spillway of the facility is an uncontrolled Ogee crest (crest elevation $770.0\text{ m}$) discharging onto a stepped downstream chute with steps $1.20\text{ m}$ high and $0.96\text{ m}$ wide ($0.8\text{ H} : 1.0\text{ V}$ slope). Stepped spillways accelerate turbulent energy dissipation along the face, significantly reducing the required dimensions of the downstream stilling basin or plunge pool.

               SKIMMING FLOW OVER STEPPED SPILLWAY
    Inflow Q
    =========>  Ogee Crest (El. 770 m)
             \
              \--+
                 |--+    Skimming Flow Free Surface
                    |--+   ~~~~~~~~~~~~~~~~~~~~~~~~
                       |--+    Recirculating Vortices
                          |--+   inside Step Cavities
                             |--+   (Turbulent Energy Loss)
                                |--+
                                   |--+
                                      |__\  Flip Bucket (El. 680 m)
                                         /

Under design flood discharge conditions ($Q = 2,830\text{ m}^3/\text{ s}$), flow operates entirely in the skimming flow regime, characterized by coherent water cascading over step edges while coherent recirculating vortices form inside each step corner. The onset of skimming flow occurs when:

$$\frac{d_c}{h_s} > 0.91 \cdot (\tan\theta)^{-0.14}$$

where $d_c = \sqrt[3]{q^2 / g}$ is critical depth, $h_s$ is vertical step height ($1.20\text{ m}$), $q$ is unit discharge ($q = Q / B = 2,830 / 64 = 44.22\text{ m}^2/\text{ s}$), and $\theta$ is chute angle ($51.34^\circ$).

$$d_c = \sqrt[3]{\frac{44.22^2}{9.81}} = \sqrt[3]{\frac{1955.4}{9.81}} = \sqrt[3]{199.33} \approx 5.84\text{ m}$$

$$\frac{d_c}{h_s} = \frac{5.84}{1.20} = 4.87 \quad \gg \quad 0.91 \cdot (\tan 51.34^\circ)^{-0.14} \approx 0.88$$

This confirms fully developed skimming flow with intensive macro-turbulent dissipation.

5.2 Flip Bucket Trajectory and Plunge Pool Scour Depth

At the downstream base (Elevation $680.0\text{ m}$), flow enters a cylindrical trajectory flip bucket (radius $R_b = 12.0\text{ m}$, exit angle $\phi = 35^\circ$) that launches the jet high into the air, dissipating residual kinetic energy before landing in a pre-excavated plunge pool. The throw distance $X_{throw}$ is calculated as:

$$X_{throw} = \frac{v_0^2}{g} \sin(2\phi) \cos\phi \left[ 1 + \sqrt{1 + \frac{2 g (z_0 – z_p)}{v_0^2 \sin^2\phi}} \right]$$

where $v_0$ is bucket exit velocity ($\approx 26.5\text{ m/s}$), $z_0$ is bucket lip elevation, and $z_p$ is riverbed plunge pool elevation.

6. Step-by-Step Worked Calculation: RCC Lift Joint Sliding and Overturning Stability

Evaluating an intermediate RCC lift joint at Elevation $720.0\text{ m}$ under Maximum Credible Flood (PMF) and pseudostatic seismic loading demonstrates the structural safety margins of the curved barrier.

       WORKED EXAMPLE GEOMETRIC SCHEMATIC AT ELEVATION 720 m
   Reservoir Level El. 780 m
   =========================|
                            |  Lift Joint Level El. 720 m (h = 60 m Head)
                            |  Section Width B = 48.0 m
   Hydrostatic Pressure     |  Unit Slice Width = 1.0 m
   Triangular Wedge (U)     +-----------------------------------+
   ------------------------->                                   | Downstream Face
   ------------------------->         RCC Lift Joint            |
   ------------------------->  [=== Bedding Mortar Layer ===]   |
   =========================+-----------------------------------+

6.1 Hydrostatic and Hydrodynamic Load Assembly

Given Structural & Hydraulic Input Data:
* Structural height above considered joint: $H_j = 60.0\text{ m}$

• Reservoir head above joint: $h_w = 60.0\text{ m}$

• Width of horizontal joint: $B = 48.0\text{ m}$

• Concrete unit weight: $\gamma_c = 24.0\text{ kN/m}^3$

• Water unit weight: $\gamma_w = 9.81\text{ kN/m}^3$

• Joint cohesion: $c = 1.20\text{ MPa} = 1,200\text{ kPa}$

• Joint friction angle: $\phi = 42^\circ \implies \tan\phi = 0.9004$

• Seismic horizontal coefficient: $k_h = 0.15$

• Uplift reduction factor with operational drainage: $k_u = 0.33$

Step 1: Calculate Gravity Self-Weight ($W$)
Assuming a trapezoidal section with top width $8.0\text{ m}$ and base width $48.0\text{ m}$:
$$A = \frac{8.0 + 48.0}{2} \times 60.0 = 1,680.0\text{ m}^2$$
$$W = A \times \gamma_c \times 1.0 = 1,680.0 \times 24.0 = 40,320.0\text{ kN/m}$$

Step 2: Calculate Horizontal Hydrostatic Thrust ($P_w$)
$$P_w = \frac{1}{2} \gamma_w h_w^2 = \frac{1}{2} \times 9.81 \times (60.0)^2 = 17,658.0\text{ kN/m}$$

Step 3: Calculate Total Uplift Force ($U$)
Under operational drainage line efficiency:
$$U = \frac{1}{2} \times k_u \times \gamma_w h_w \times B = \frac{1}{2} \times 0.33 \times 9.81 \times 60.0 \times 48.0 = 2,330.9\text{ kN/m}$$

Step 4: Calculate Inertial Earthquake Horizontal Force ($F_{eq}$)
$$F_{eq} = k_h \times W = 0.15 \times 40,320.0 = 6,048.0\text{ kN/m}$$

Total driving horizontal shear force:
$$\sum V = P_w + F_{eq} = 17,658.0 + 6,048.0 = 23,706.0\text{ kN/m}$$

Total effective vertical normal force:
$$\sum N’ = W – U = 40,320.0 – 2,330.9 = 37,989.1\text{ kN/m}$$

6.2 Shear Friction Factor of Safety ($FS_{sliding}$) Evaluation

According to USACE and USBR standards, the Shear-Friction Factor of Safety across a bonded RCC bedding lift joint is formulated as:

$$FS_{sliding} = \frac{c \cdot A_j + \sum N’ \cdot \tan\phi}{\sum V}$$

where $A_j = B \times 1.0 = 48.0\text{ m}^2$.

Evaluate terms:
* Cohesive resistance: $c \cdot A_j = 1,200\text{ kPa} \times 48.0\text{ m}^2 = 57,600.0\text{ kN}$

• Frictional resistance: $\sum N’ \cdot \tan\phi = 37,989.1 \times 0.9004 = 34,205.4\text{ kN}$

• Total available shear resistance: $R_s = 57,600.0 + 34,205.4 = 91,805.4\text{ kN}$

$$FS_{sliding} = \frac{91,805.4}{23,706.0} = 3.87$$

Assessment: The factor of safety $FS_{sliding} = 3.87$ exceeds the required USBR seismic limit ($FS \ge 2.0$), verifying full bedding plane shear stability.

6.3 Eccentricity and Overturning Factor of Safety ($FS_{overturning}$)

Step 1: Compute Resisting and Overturning Moments about Dam Toe
* Lever arm of gravity self-weight: $x_w \approx 28.5\text{ m}$ from upstream face $\implies d_w = 48.0 – 28.5 = 19.5\text{ m}$ to toe.

• Moment of Self-Weight: $M_R = W \times d_w = 40,320.0 \times 19.5 = 786,240.0\text{ kN}\cdot\text{ m}$

• Overturning Moment of Hydrostatic Thrust: $M_{Ow} = P_w \times \frac{h_w}{3} = 17,658.0 \times 20.0 = 353,160.0\text{ kN}\cdot\text{ m}$

• Overturning Moment of Uplift: $M_{Ou} = U \times \frac{2 B}{3} = 2,330.9 \times 32.0 = 74,588.8\text{ kN}\cdot\text{ m}$

• Overturning Moment of Earthquake Inertia: $M_{Oeq} = F_{eq} \times \frac{H_j}{2} = 6,048.0 \times 30.0 = 181,440.0\text{ kN}\cdot\text{ m}$

$$\sum M_O = 353,160.0 + 74,588.8 + 181,440.0 = 609,188.8\text{ kN}\cdot\text{ m}$$

$$FS_{overturning} = \frac{M_R}{\sum M_O} = \frac{786,240.0}{609,188.8} = 1.29 \quad \text{(Under Combined Extreme PMF + Seismic Load)}$$

Assessment: Under extreme multi-hazard load combinations, the resultant falls inside the middle third kern ($e \le B/6$), precluding heel tensile liftoff.

7. Hydropower Generation, Flood Control, and Irrigation Impact

The completion and commissioning of the hydraulic scheme transformed the socio-economic and hydrologic dynamics of the Gomal River basin:

               GOMAL ZAM DAM INTEGRATED BENEFIT MATRIX
            +-------------------------------------------+
            |      Gomal Zam Multi-Purpose Benefits     |
            +---------------------+---------------------+
            |                     |                     |
            v                     v                     v
   [ 17.4 MW Hydropower ]   [ 1.14 MAF Storage ]   [ 191,000 Acres Cultivated ]
   (Annual: 91 GWh Clean    (Flood Attenuation     (Warana Canal Irrigation
    Renewable Energy)        Peak Scour Reduction)  D.I. Khan Agricultural Belt)

1. Clean Energy Generation: The powerhouse houses two Francis turbine units rated at $8.7\text{ MW}$ each, supplying $91\text{ GWh}$ annually to the National Grid.
2. Irrigation Network: A $60.5\text{ km}$ long main canal and extensive distributary network convert parched barani lands into perennial agricultural fields producing wheat, cotton, and sugarcane.
3. Downstream Flood Protection: Severe flash floods carrying sediment loads up to $40,000\text{ ppm}$ are regulated within the reservoir basin, safeguarding urban centers and transportation corridors.

8. Hydrotechnical Engineering Synthesis

The successful execution of gomal zam dam demonstrates how advanced roller compacted concrete technology, combined with three-dimensional canyon arching mechanics, can conquer demanding geotechnical and hydrological environments. By harmonizing pozzolanic cement chemistry, stepped spillway energy dissipation, and high-pressure curtain grouting, engineering precision ensures this curved RCC monument provides durable water storage, power, and regional protection for generations to come.

References & Standards Cited

1. U.S. Bureau of Reclamation (USBR), Design of Small Dams & Concrete Gravity Dam Standards, Department of the Interior, Denver, CO.
2. U.S. Army Corps of Engineers (USACE), Roller-Compacted Concrete, Engineering Manual EM 1110-2-2006, Washington, D.C.
3. Chanson, H., Hydraulics of Stepped Chutes and Spillways, Balkema Publishers, Rotterdam, Netherlands.
4. Pakistan Water and Power Development Authority (WAPDA), Gomal Zam Dam Project Completion and Technical Report, Lahore, Pakistan.
5. International Commission on Large Dams (ICOLD), Roller Compacted Concrete Dams – State of the Art, Bulletin 126, Paris.

Frequently Asked Questions (FAQ)

What type of dam is Gomal Zam Dam and what are its main dimensions?

Gomal Zam Dam is a curved roller compacted concrete (RCC) gravity dam. It has a structural height of 133 meters (436 feet), a crest length of 231 meters, an upstream radius of curvature of 270 meters, and a gross storage volume of 1.14 million acre-feet (1.404 billion cubic meters).

Why was Roller Compacted Concrete (RCC) selected instead of a conventional concrete arch or rockfill dam?

RCC combines the strength and durability of mass concrete with the high-speed placement economics of earthmoving equipment. In the remote Khajuri Kach gorge, RCC significantly compressed the construction schedule and provided superior overtopping resistance during seasonal mountain flash floods.

How does the stepped spillway at Gomal Zam Dam dissipate kinetic energy?

The spillway chute incorporates 1.20-meter vertical steps configured at a 0.8 H : 1.0 V slope. Operating in the skimming flow regime, water flows across step tips while intense recirculating vortices form in step recesses, dissipating up to 60% of kinetic energy before the flow reaches the flip bucket.

What measures were taken to prevent thermal cracking during RCC placement?

The mix incorporated high pozzolan replacement (up to 55% Portland cement substitution) to reduce adiabatic heat of hydration. In addition, aggregates were shaded and concrete was mixed with chilled water and flake ice to maintain placement temperatures below $18^circtext{C}$.

How does the curved geometry of Gomal Zam Dam improve structural stability?

Although designed conservatively as a gravity structure, the 270-meter upstream radius engages horizontal arching thrust into the steep sandstone abutments during high reservoir head, transferring 14% to 22% of lateral water pressure into canyon rock walls and reducing base moments.