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4.11 Additional problems

4.11.1

The single-span bridge illustrated in the following figure is going to be founded on shallow square 6 m x 6 m footings, embedded at a depth equal to Df = 2 m. The structural analysis of the bridge resulted in a maximum axial force on the bridge’s piers under serviceability conditions equal to Qw = 10 MN. The site investigation revealed a rather heterogeneous soil profile under the bridge, consisting of loose sand underneath the left abutment, and of medium-to-dense sand underneath the right abutment, featuring the compressibility parameters noted on the figure.

Ignoring the shear resistance developing at the wall-soil interface, calculate: a) the maximum uniform settlement of the critical pier, and b) the angular distortion of the bridge’s foundation. Are these values tolerable, according to Poulos et al. (2001) criteria (Table 4.2)?

Schematic of a 30m-long single span bridge founded on shallow footings, embedded at 2m depth. The left footing is founded on loose sand with E' = 15 MPa and v' = 0.333. The right footing is founded on medium to dense sand with E' = 50 MPa and v' = 0.333.
Additional problem 4.11.1. Problem description and input parameters.

Answer:

Critical pier settlement = 0.083 m

Angular distortion Δ/L=0.00193

Allowable total settlement = 100 mm>83 mm OK

Allowable angular distortion = 0.005>0.00193 OK

4.11.2

A wind turbine is going to be founded on the surface (Df = 0) of a deep layer of homogeneous saturated clay, using a single circular footing. Triaxial laboratory tests on specimens of the foundation soil resulted to the following compressibility parameters: E′ = 10 MPa, v′ = 0.333. The maximum axial load on the foundation under serviceability conditions is, according to the Mechanical Engineer, equal to Qw = 5 MN. Determine the minimum radius of the footing, so that its immediate settlement will not exceed 50 mm.

Answer:

R = 3.33 m

4.11.3

The subsoil at the bottom of a lake consists of a normally consolidated clay layer of thickness 5m, overlaying an incompressible layer of dense sand. Estimate the consolidation settlement of the bottom of the lake:

  1. Due to an increase of the water level by 4m, and
  2. Due to a subsequent desiccation of the lake, with the ground water level dropping at the level of the clay-sand interface.

Use the results of the oedometer test shown below, and assume the unit weight of the clay to be γ = 18 kN/m3. For simplicity, do not divide the clay layer into sublayers.

The top left figure shows a normally consolidated clay layer of thickness 5m, underlaid by dense incompressible sand. The water table is at 1m above the ground surface. In the top right figure the water table has risen to 5m above the ground surface and in the bottom left figure the water table has dropped to the top of the dense sand layer. The bottom right figure presents results on an oedometer test performed in the clay layer, from which the coefficient of compression was found to be Cc=0.353.
Additional problem 4.11.3. Problem description and input parameters.

Answer:

  1. ρpc = 0
  2. ρpc = 0.33 m

4.11.4

A large cylindrical silo of diameter D = 30 m is going to be founded on a layer of soft saturated, normally consolidated clay of thickness 8 m, overlaying an incompressible layer of dense sand. The contact stress on the foundation of the silo is assumed uniform, and equal to qext = 160 kPa. Preliminary estimates indicated that ground improvement measures must be implemented to increase the bearing capacity of the clay layer, and reduce settlement. The cost-efficient method proposed for the improvement of the clay layer is its preloading via the construction of an extensive temporary embankment. Construction works will be implemented in 3 phases:

  • Phase 1: Construction of a temporary embankment at the area of the foundation. The height of the embankment will be 4 m, and the unit weight of the fill material will be γemb = 20 kN/m3.
  • Phase 2: Removal of the temporary embankment
  • Phase 3: Construction of the silo

Assuming 1-D consolidation conditions, estimate the elevation of the ground surface at the foundation area, at the end of each construction phase. For simplicity, do not divide the clay layer into sublayers.

The figure on the left presents Stage 1. A temporary embankment of thickness 4m and unit weight γ = 20 kN/m^3 is built on the surface of a soft saturated clay layer. The thickness of the clay layer is 8m and the groundwater level is found at its surface. The clay layer is underlaid by dense incompressible sand. The figure on the mid presents Stage 2, where the temporary embankment is removed. The figure on the right presents Stage 3, where a pressure of 160 kPa is applied on the surface of the clay layer. The properties of the clay layer are OCR =1, γ = 20 kN/m^3, e0 = 0.80, Cc = 0.40, Cr = 0.10.
Additional problem 4.11.4. Problem description and input parameters.
Graph showing results of an oedometer test performed in the clay layer from which it is inferred that Cr = 0.10 and Cc = 0.40.
Additional problem 4.11.4. Oedometer test results.

Answer:

Initial level of ground surface : 0.0 m

At the end of stage 1: -0.848 m

At the end of stage 2: -0.636 m

At the end of stage 3: -1.24 m

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Fundamentals of foundation engineering and their applications Copyright © 2025 by University of Newcastle & G. Kouretzis is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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