Foundation design capstone: the fleet storage building

The last lesson brings the course together in the foundation design package for the Kestrel Bay site: the fleet storage building on driven piles, the garage on preloaded ground with spread footings, and the pump station, whose concrete box must neither float nor be lifted by the artesian till. Dr. Kowalczyk's team must produce the foundation design report, with the design basis, the calculations summarized for each limit state, the drawings and specifications that the contractor will price, and the inspection and monitoring plan that will confirm the design in the field. Owen prepares the calculations; Sofia's final script checks them in one place.

The design basis

A design report begins by stating its basis, so that anyone who reads it later knows what was assumed. For Kestrel Bay, that means:

• Codes and standards: the Ontario Building Code (based on the NBC) for loads and limit states, the CFEM 5th edition for geotechnical methods and resistance factors, CSA A23.3 and CSA S16 for the concrete and steel elements.
• The ground model: the stratigraphy, groundwater and design parameters of the CIV-340 soils report, supplemented by the four new boreholes and two CPTs at the fleet building, which confirmed the same sequence with the till 4.0 to 4.5 m (13 to 15 ft) thick over rock.
• The loads: column loads from the structural engineer, separated into dead, live, snow, wind and crane components, with the sustained part identified for settlement and drag.
• Performance criteria: total settlement of the fleet building not more than 25 mm (1 in.), angular distortion not more than 1/1,000 along the crane rails; for the garage, 1/500 between adjacent columns; for the pump station, a factor of safety against flotation of at least 1.25 at the design high water level.

The fleet storage building

The fleet building is supported on closed-end steel pipe piles, 406 mm diameter with a 12.7 mm wall and a reinforced conical toe, driven to a toe level of about 15.0 m in the dense till and filled with concrete. Each interior column bears on a cap with four piles at 1.2 m centres. The design summary is:

Because the piles end in till that does not settle significantly, the building is effectively isolated from the consolidation caused by the yard fill. The ground floor slab is a different matter: placed on the fill over the clay, it would settle with the yard. Dr. Kowalczyk and the structural engineer choose a structural slab spanning between the pile caps on grade beams, with a void former beneath it, rather than a slab-on-grade, because the fleet building floor carries loaded trucks and must remain level at the doors and the crane rail supports. The aprons outside the doors are designed as hinged approach slabs that can rotate as the yard settles.

The garage

The garage foundations are the spread footings designed in CIV-330, founded at 2.0 m on the sand, on ground preloaded with 2.5 m of sand for at least three months with prefabricated vertical drains at 1.5 m spacing. The bearing check governed by the clay gives a utilization of 0.74, the immediate settlement in the sand is 10 to 20 mm, and the consolidation settlement after preloading is about 34 mm at the interior footings, with an angular distortion of about 1/690. The preload may be removed when settlement plates show that the settlement has levelled off at about 90 % of the predicted final value and the piezometers in the clay show that the excess pore pressure has fallen correspondingly.

The pump station

The pump station is a reinforced concrete box 6.0 m square in plan, with its base at 4.5 m below grade in the sand. Near BH-4 the sand extends to 7.0 m and the clay to 12.0 m, over the artesian till. Two checks control the design. The first is flotation: when the station is empty for maintenance and the water table is high, the uplift of the groundwater on the base must not exceed the weight of the structure with a margin. The second is the uplift of the clay plug beneath the station by the artesian pressure in the till, which CIV-340 found critical during excavation, with a factor of safety of 1.35, and which the completed structure relieves by adding its weight.

Sofia's script assembles the column check for the fleet building and completes the pump station checks: flotation for normal and high water, uplift of the clay plug during and after construction, and the rebound of the clay caused by the net unloading.

# Capstone: foundation design summary for the fleet storage building and checks of the pump station
from math import pi, sqrt, atan2, log10
# --- fleet storage building, typical interior column on four 406 mm pipe piles
D, L, W_cap = 1900.0, 1100.0, 166.0                 # kN
Pf = 1.25*(D + W_cap) + 1.5*L
Ru, phi = 1781.0, 0.6                                # static analysis, confirmed by the static test (Davisson 1,968 kN)
n = 4
print(f"Column: Pf = {Pf:.0f} kN; {n} piles x phi Ru = {n}*{phi*Ru:.0f} = {n*phi*Ru:.0f} kN "
      f"-> utilization {Pf/(n*phi*Ru):.2f}")
print(f"Drag (lesson 10): maximum unfactored load in a pile 1,237 kN vs structural resistance about 6,800 kN; "
      f"settlement at the neutral plane under 1 mm")
print(f"Lateral: 30 kN service per pile, fixed-head deflection 1.6 mm; factored 45 kN vs 0.5 Hu = 257 kN")
print(f"Settlement of the group: 9.4 mm below the equivalent footing + 1.0 mm shortening = {9.4 + 1.0:.1f} mm\n")

# --- pump station: a 6.0 m square concrete box with its base at 4.5 m (BH-4: sand to 7.0 m, clay to 12.0 m)
B, z_base, t_base, t_wall, t_roof, gc = 6.0, 4.5, 0.8, 0.4, 0.3, 24.0
V = B*B*t_base + 4*(B - t_wall)*t_wall*(z_base - t_base + 0.3) + B*B*t_roof
W = V*gc; A = B*B
for zw, case in ((2.5, 'normal water table 2.5 m'), (1.0, 'design high water 1.0 m')):
    U = 9.81*(z_base - zw)*A
    print(f"Flotation, {case}: W = {W:.0f} kN, U = {U:.0f} kN, FS = W/U = {W/U:.2f}")
# uplift of the clay plug by the artesian till (piezometric level 1.5 m below grade), at the base of the clay
u_till = 9.81*(12.0 - 1.5)
during = 19.8*(7.0 - z_base) + 18.0*(12.0 - 7.0)    # cofferdam dewatered to the base, before the structure
after = during + W/A
print(f"Basal uplift at 12.0 m: u = {u_till:.0f} kPa; FS during excavation {during/u_till:.2f}, "
      f"after construction {after/u_till:.2f}")
# rebound (heave) of the clay from the net unloading under the station
def corner(a, b, z):
    m, nn = a/z, b/z; s = m*m + nn*nn + 1
    return (2*m*nn*sqrt(s)/(s + m*m*nn*nn)*(s + 1)/s + atan2(2*m*nn*sqrt(s), s - m*m*nn*nn))/(4*pi)
removed = 18.0*2.5 + 19.8*(z_base - 2.5)
q_un = removed - W/A
heave = 0.0
for k in range(10):                                  # clay from 7.0 to 12.0 m in 0.5 m sublayers
    z = 7.25 + 0.5*k
    s0 = 18.0*2.5 + 19.8*4.5 + 18.0*(z - 7.0) - (9.81*4.5 + (u_till - 9.81*4.5)*(z - 7.0)/5.0)
    ds = 4*q_un*corner(B/2, B/2, z - z_base)
    heave += 0.5*0.047/2.06*log10(s0/(s0 - ds))
print(f"Net unloading {q_un:.0f} kPa (soil removed {removed:.0f}, structure {W/A:.0f}); clay rebound {1000*heave:.1f} mm")

Column: Pf = 4232 kN; 4 piles x phi Ru = 4*1069 = 4274 kN -> utilization 0.99
Drag (lesson 10): maximum unfactored load in a pile 1,237 kN vs structural resistance about 6,800 kN; settlement at the neutral plane under 1 mm
Lateral: 30 kN service per pile, fixed-head deflection 1.6 mm; factored 45 kN vs 0.5 Hu = 257 kN
Settlement of the group: 9.4 mm below the equivalent footing + 1.0 mm shortening = 10.4 mm

Flotation, normal water table 2.5 m: W = 1811 kN, U = 706 kN, FS = W/U = 2.56
Flotation, design high water 1.0 m: W = 1811 kN, U = 1236 kN, FS = W/U = 1.46
Basal uplift at 12.0 m: u = 103 kPa; FS during excavation 1.35, after construction 1.84
Net unloading 34 kPa (soil removed 85, structure 50); clay rebound 8.4 mm

Reading the results

The fleet building column has a utilization of 0.99 with four piles and the test-confirmed resistance factor, so the four-pile cap stands, but with little margin: a significant increase in the loads from the structural engineer would require a five-pile cap, and Owen flags it in the report. The pump station has a factor of safety against flotation of 2.56 at the normal water table and 1.46 at the design high water. The uplift of the clay plug, 1.35 during excavation, rises to 1.84 once the structure is in place, so the critical period is the few weeks between reaching the base and casting the slab, when the relief wells and the piezometer trigger levels from CIV-340 must be in operation. The net unloading of 34 kPa, the soil removed less the weight of the structure, causes a rebound of about 8 mm in the clay, most of it during the excavation.

Owen notices that the rebound and the later settlement of the pump station differ from those of the pipes connecting it to the garage and the yard drains. The connections are therefore made with flexible couplings designed for 25 mm (1 in.) of differential movement.

Specifications, inspection and monitoring

A foundation design is only as good as its execution. The report includes a construction section, and the specifications turn it into contractual requirements:

• Pile installation: the hammer approved on the basis of a wave equation analysis; the driving criterion, a minimum toe level in the till and a minimum final set, established on the test pile; records of every pile; redriving of any pile heaved by more than a few millimetres by adjacent driving; internal inspection of each pipe before concrete is placed.
• Testing: a static load test on the test pile before production; dynamic testing at the end of driving and on restrike of the test pile and of at least 5 % of production piles.
• Preloading: placement of the preload in lifts, settlement plates and vibrating wire piezometers, and a hold until the agreed criteria are met.
• Pump station: sheet piling to the specified tip, a piezometer in the till inside the cofferdam with alert and action levels, relief wells ready before excavation reaches the clay, and no over-excavation.
• Inspection of footing bases by the geotechnical engineer before concrete is placed, and protection of exposed soil from water and frost.
• Monitoring after construction: settlement points on selected garage and fleet building columns, read monthly for the first year and quarterly for two more, compared with the predictions.

Looking back

Owen reflects on what the course has taught him. The bearing calculations were the easy part: almost every bearing check passed with a comfortable margin. The decisions that mattered were about deformation and water. The thin sand over the clay made the garage settle unevenly; preloading, not stronger footings, solved it. The heavy fleet building needed piles because of settlement, not bearing, and the piles had to end in the till so that the yard fill would not drag them down. The artesian till, discovered by a single piezometer, controlled the pump station. And at each step, a cheap investigation or test bought a large saving or avoided a serious risk: a CPT that calibrated the clay strength, a load test that saved two piles under every column, a piezometer that revealed the uplift.

Dr. Kowalczyk's last comment is the one that Terzaghi and Peck would have made. Every number in the report is an estimate, and the ground will not read it. The design is complete only when construction confirms that the ground behaves as predicted, and the monitoring plan is the part of the report that makes sure it does.

Practical points

• State the design basis: codes, ground model, loads and performance criteria.
• Summarize every limit state for each structure, with its result and the lesson or calculation behind it.
• Identify the critical construction stages, such as excavation to the base of the pump station, and protect them.
• Turn recommendations into specifications with measurable acceptance criteria.
• Plan monitoring that will reveal whether the predictions were right while there is still time to act.