4 - Stresses and settlements below shallow foundations Flashcards
(37 cards)
What does elastic theory allow us to link in soil mechanics?
Elastic theory links changes in stress to changes in strain in soil.
In the point load stress formula, what do r and z represent?
r is the horizontal distance from the load, and z is the depth below the load.
What is a key assumption of elastic loading in soils?
That the soil will return to its original state after the load is removed.
What type of stress is largest directly beneath a loaded area like a strip footing?
Vertical stress (σz).
What is the significance of the 0.2q contour in stress diagrams under footings?
It defines the “bulb of pressure,” the zone that significantly contributes to settlement.
To what depth does the bulb of pressure extend for a strip footing?
Approximately 3 times the width (3B) of the footing.
Why are graphical solutions used for circular and rectangular loaded areas?
Because analytical solutions are complex and difficult to compute manually.
What is the general formula for vertical stress beneath a uniformly loaded circular area?
σz = q × Iσ, where Iσ is found from a chart based on x/r and z/r values.
In the circular loading case, what do the variables x, r, and z represent?
x = distance from center, r = radius of loaded area, z = depth below the surface.
How is Iσ determined for a uniformly loaded circular area?
From a graph based on the ratios x/r and z/r.
What is the formula for vertical stress beneath the corner of a uniformly loaded rectangular area?
σz = q × Iσ, where Iσ is found using Fadum’s chart.
What parameters are used in Fadum’s chart to determine Iσ?
The ratios B/z and L/z, where B = width, L = length, and z = depth.
What is Newmark’s Chart used for in geotechnical engineering?
To estimate vertical stress under any shape of loaded area using a graphical method.
How much vertical stress does each segment in Newmark’s Chart contribute?
Each of the 200 segments contributes 0.005q.
How do you scale the foundation shape when using Newmark’s Chart?
Scale the shape based on depth, e.g., 1 m = 5.5 mm if estimating stress at 4 m depth using a 22 mm scale.
What is the expected error range when using Newmark’s Chart?
Approximately ±5%.
Why is estimating stress at a single point not sufficient for foundation design?
Because foundations affect a zone of soil; stress distribution must be used to calculate total settlement.
What are the two main approaches to calculating settlement of shallow foundations?
(1) Elastic theory approach and (2) One-dimensional settlement approach.
What is the basic formula for vertical strain (ε₁) used in settlement calculations?
ε₁ = (1/E) × (Δσ₁ – νΔσ₂ – νΔσ₃)
What is the formula for vertical settlement (ρ) using elastic theory?
ρ = (Δσ / 2G) × [B(1 – ν)Ip]
What does the influence factor (Ip) in settlement equations depend on?
The geometry and rigidity of the loaded area or foundation.
How does settlement under a rigid footing compare to that under a flexible footing?
ρ_rigid ≈ 0.8 × ρ_flexible,centre
Why is the shear modulus (G) the same for both drained and undrained conditions?
Because water cannot carry shear stress, so shear strain response is the same in both cases.
What is the difference between Eu and E′ in soil mechanics?
Eu is Young’s modulus for undrained conditions; E′ is for drained conditions.
