I performed an independent QC review of the finite element model (FEM) for the Westview Reservoir, a City of Calgary water infrastructure project in the southwest quadrant near Alpine Park. The reservoir consists of two 15 ML cylindrical reinforced concrete cells, each 50 m in outside diameter and 9 m tall, partially buried 4 m below grade. A pump station with a 50 ML/d design flow is adjacent. I was selected for the review based on my experience with advanced and complex FEM work.

My role

As a Structural Engineer, I performed the independent QC review of the FEM prepared by another engineer. The review was commissioned by the firm’s National Technical Specialist for Water Retaining Structures.

What I did

Independent FEM model

  • Built a separate ETABS model of the cylindrical reservoir to independently verify the design forces extracted from the original model.
  • Modeled the reservoir as a 40-sided polygon using flat shell elements with fixed base and free top boundary conditions, matching the original model’s geometry (49 m internal diameter, 500 mm wall thickness, 8.9 m height).

Flat shell limitation analysis

  • Identified that flat shell elements approximating a curved cylinder do not properly resolve hoop stresses at shell edges. Resultant stresses get resolved into out-of-plane shear (V13) rather than axial hoop tension.
  • Verified this by comparing against a curved-wall model, which showed V23 shear dropping to near zero with a corresponding increase in V13 and hoop stresses. The flat shell model underestimates hoop stress.
  • Maximum V13 from the flat shell approximation reached 40 kN/m – elevated but acceptable for the 40-segment discretization.

Thermal loading evaluation

  • Reviewed ACI research papers by Vitharana and Priestley (ACI 95-S22 and 96-S81) on temperature-induced loading in cylindrical reservoir walls.
  • Determined that the original model applied temperature loads with uncracked section properties, which overestimates thermal stresses. Running with fully cracked sections showed a 70% reduction in thermal hoop stresses.
  • Developed stiffness modifier recommendations for cracked concrete under combined thermal and hydrostatic loading:
    • Hoop membrane (f11): 0.3 to 0.5
    • Vertical membrane (f22): 0.6 to 0.8
    • Circumferential bending (m11): 0.25 to 0.35
    • Vertical bending (m22): 0.4 to 0.5
  • Documented the temperature parameters: stress-free temperature of 15 degrees C, winter water temperature of 4 degrees C, and exterior ambient down to -30 degrees C, with 100 mm spray foam insulation on the exterior (cold side) reducing the gradient through the concrete wall.

Mesh refinement check

  • Calculated the decay length for boundary effects: lambda = sqrt(R x t) = sqrt(24.5 m x 0.5 m) = 3.5 m, giving a zone of influence of 4 lambda = 14 m from the fixed base.
  • Confirmed the provided mesh density of 8 vertical elements (approximately 1 m each) was adequate, since the maximum element size in the boundary zone is 1.75 m.
  • Recommended refining the mesh near the base slab to the wall thickness (500 mm) to better capture the steep stress gradient at the fixed support.

Hand calculation verification

  • Verified FEM hoop tension results against hand calculations using hydrostatic pressure (78.5 kPa at tank bottom) and the standard formula N_h = gamma_w x H x R.
  • Checked the cracking moment under simultaneous hoop tension using the reduced tensile strength f_t = 0.4 sqrt(f’c) MPa from the research papers, rather than the code value of 0.6 sqrt(f’c).

Additional observations

  • Noted that sloshing loads were not included in the original model.
  • Identified that the top boundary condition (pin) in the original model caused the wall to bulge outward at mid-height, engaging one-way bending rather than pure hoop tension, further underestimating hoop stress.

Deliverables

  • Independent ETABS FEM model of the cylindrical reservoir for comparison against the original design model.
  • QC observations and notes document with findings on flat shell limitations, hoop stress underestimation, thermal loading issues, and mesh refinement.
  • Temperature loading guide with stiffness modifier recommendations, SAP2000/ETABS implementation notes, and a QC checklist for thermal analysis of cylindrical reservoirs.
  • All findings were delivered to the design engineer for implementation into the original model. The project is in preliminary design.