Shallow foundation design

Question 1

Foundation Type

Answer 1

Pad - Square, rectangular or circular only supports one or two column
Strip - Has a length mush larger than it s width and supports walls or a row of closely grouped piles
Raft - Supports part or all of the structure. If theres a void inn the middle its a compensated raft

Question 2

Drained vs Undrained Analysis

Answer 2

Undrained means low permeability in relation to the loading rate
- Tresca therefore Total Stress analysis

Drained mean high permeability in relation to the loading rate
- Mohr coulomb therefore effective stress analysis

Terzaghi - “ All measurable effects of change in effective stress ( compression, distortion, change in shearing resistance) are all exclusively due to changes in effective stress”

Question 3

Drained vs Undrained
- FoS

Answer 3

Drained
- change in total stress carried by the structure, therefore change in effective stress
- this results in a change of volume and inresed strength
- strength properties are proportional to the total stress (Mohr coulomb)

Undrained
- No change in volume therefore the change in total stress is carried by change in PWP
- No change in effective stress so short term is critical
- PWP dissipates leading to an increase in effective stress until the PWP is in equilibrium with the hydraulic boundary conditions

Fos = sum(shearing resistacne)/sum(disturbing forces)

Question 4

Bearing Capacity

Answer 4

The amount of pressure a foundation can take before the geoology bellow undergoes shear failure

Depends on
- Soil properties
- Foundation shape, size , depth
- Inclination of loading and eccentricity
- Soil failure modes
- Application of moments

Question 5

Bearing capacity symbols

Answer 5

qf = bearing capacity at failure
qw = working bearing capacity
qs = safe bearing capacity (apply FoS to qf)
qi’ = effective qi
qi,net = qi - p0 since its the change in pressure that causes changes. This is opposed to qi,gross

Question 6

Analytical approches to bearing capactiy

Answer 6

Limit Equilibrium
Limit Analysis (Upper Bound an Lower Bound)
Stress Field Analysis

Top two are approximates
- Good for geometries which are complex for stress feild
- Gives insights into failure mechanisms

Question 7

Assumption made throughout?
Information each analytical approach provides

Answer 7

• Assumed plain strain for strip footing

Stability = all
Movements = only upper bound limit analysis does this crudely
Adjacent structures = none

Alternatives
- Numerical does it all
- Closed Form solutions doesnt give stability but does give movements and effect on adjacent structures

Question 8

Limit equilibrium

Answer 8

• Selects an arbitrary slip surface an assumes failure all along it
• Assumes failure throughout a rigid-plastic block
• Find internal forces for equlibrium

Solution:
- qf = 5.52Su + po

Question 9

Limit Analysis (Upper bound)

Answer 9

Applies kinematically admissible mechanism of deformation
- Splits the domain into rigid sliding blocks
- Assume a displacement of delta of the foundation and equate internal and external work using a hodograph to get relative displacements
- Gives an unsafe value with q>=qf

Question 10

Limit Analysis (Lower Bound)

Answer 10

Applies a balance of internal and external loads, assuming that everywhere is in equilibrium
- Split the domain into stress blocks, regions of constant stress
- Determine the forces required for equilibrium using a mohrs circle for each region
- safe q<= qf

Assumes
- Equilibrium across stress discontinuitys
- Stress shouldnt violate the failre crtiterion

Question 11

Limit Analysis
- Comparison of upper and lower bound

Answer 11

Upper boud and lower bound conversge to the same solution, one from the top and the other from below with increase in deformation blocks/strress regions

Called the Prandtl Solution

Question 12

Stress Field Solution

Answer 12

• Most accurate for idealised foundations
  Considers stress equilibrium at a point and applied the appropriate failure criterion

Prandtl Solution can be obtained from upper and lower bound Limit analysis therefore “exact”
qf = Nc,strip Su + po
qf’ = c’Nc,strip+p0’Nq,strip +B/2(gamma’)Ngamma,strip

Nc,strip = 2 + pi for an infinite strip
Ni,strip varries with phi’, with a rapid increase after 30 degrees

Question 13

Limitation of analytical approaches (prandtl)

Answer 13

• assumed infinite strip
• Foundation on soil (no depth)
• Smooth foundation
• Vertical load (no horizontal or moment)
• Idealised soil response ( homogeneous and no water table)

Question 14

Multiplication factors

Answer 14

Assumes the variation of one property at a time then multiplies them all therefore approximate
- Shape
- depth –> for drained this is only applied to c’ ad still found using drained methods. Not applied to the others since its taken into account in po’ and has no affect on the foundations self weight
- load inclination

Can be applied for base and ground inclinations as well

Question 15

Shape Factor

Answer 15

Squares have increased bearing capacity since there is a greater volume of soil for the failure surface to pass through per unit of pressure to form a complete failure mechanism

Question 16

Depth factor

Answer 16

-A deeper foundation requires a the failure surface to travel through more ground for a complete failure mech
-Increases the overburden preassure

Question 17

Horizontal Loading

Answer 17

-Must check base sliding

Hf = A’Su (undrained) with A’ =B’L’
Hf = VTan(delta) (Drained)
delta = phi’crit for insitu cast conc or 2/3phi’crit for precast foudations

Question 18

Eccentricity and Moment

Answer 18

-Non-uniform loading can lead to non-unifrom stress distribution below the foundation so to avoid lifting e <= B/6, uin the middle third
- Reduce the area to A’
B’ = B - 2eb
L’ = L - 2el

• Moment decomposed to eccentricity and load

Question 19

Varying undrained strength

Answer 19

Su increaces with depth
- Sum is at the GL
-Su0 is at the foundations base level

K determined using circular foundations
- Nc,strip changes
- sc found from sc circle

Question 20

Varying ground water level

Answer 20

Water reduced the nit weight therefore use the worst case scenario for a fluctuating water table

Cases
1. GWT bellow foundation depth
- No affect, failure in the dry soil

2. GWT at or above the foundations depth
   
   • Failure through submerged soil
     gamma’ = gamma_sat - du/dz
   • For hydrostatic du/dz = gamma_water, other
     variation occur in pumped cofferdams or the
     construction river piers

Sketches of the cases also contained
-po
-p_surcharge
-q_gross/q’

Question 21

FoS general definitions

Answer 21

Fb = applied the net bearing capacity (loads)
Fs = applied to strength
- Su
- phi’
- c’

Question 22

FoS (Undrained)

Answer 22

Fbu = qf,net/qw,net
Fsu = Su,design/Su,mobilised

• qf varies linearly with Su therefore Fbu=Fsu and should be 2.5 to 3 but often taken as 1.4
• qw gives Su,mobilised

Question 23

FoS (Drained)

Answer 23

Fbd = qf,net’/qw,net’ , 2.5 to 3.5
Fs(phi’) = Tan(phi’_design)/Tan(phi’_mobilised), 1.25
Fsc’ = c’_design/c’_mobilised, 1.25

• Fs(phi’) affect all Ni while Fsc’ only affects c’
• c’ harder to measure than phi’ so usually a higher Fos is used for Fsc’
• Generally Fbd > Fs(phi’)
• Nonlinear relationship that varris with phi’,
  increased angle means a steeper curve