Engineering Geology and Geotechnics - Lecture 5 Notes

Field Trip to Cragside

Meeting point: Turn circle next to Business School
Meeting time: 9:00 AM, 6th March 2025 (Thursday)
Further details will be added to Blackboard.
PPE Required:
- Safety shoes
- High vis-vest
- Hard hat
No PPE = no visit
No personal vehicles

Module Overview & Engineering Geology & Shallow Foundations

Lectures & Seminars Schedule:
- Site Investigation Eurocode 7:
  - Lectures (3), Seminars (3): Weeks 1-3, Weeks 2-4.
  - Topics: Planning investigations (desk study), soil and rock sampling, groundwater measurements, field tests in soil and rock.
- Engineering Geology:
  - Lectures (4), Seminars (3): Weeks 4-5, 7-8, Weeks 5, 7-8.
  - Topics: Introduction to Earth, weathering, geological mapping, geological structures.
- Shallow Foundations:
  - Lectures (3), Seminars (3): Weeks 9-11, Weeks 9-11.
  - Topics: Bearing capacity, settlement, soil improvement.
- Exam Revisions: Week 12
- Activity Week: Week 6

Recap - Site Investigation Methods

Standard Penetration Test (SPT):
- The N-value is the number of blows required to penetrate the last 30 cm.
- Mainly used for coarse soil (e.g., sand).
- Returns soil samples, useful for general soil classification.
Cone Penetration Test (CPT):
- Collects continuous data (profiles of soil behavior at various depths).
- Measurements include: tip resistance ( $qc$ ), friction resistance ( $fs$ ), and pore water pressure ( $u_2$ ) (if CPTu).
- SCPTu includes measurement of shear wave velocity.
- Mainly for sand, silt, clay, and peat; penetration can be restricted in gravel, soft and hard rocks.
- Does not return soil samples.
Field Vane Test (FVT):
- Measures the undrained shear strength of cohesive soils (e.g., clay).
- The maximum torque ( $C_{fv}$ ) required to rotate the vane is recorded.
- $Cu = μ C{fv}$ , where μ is a correction factor.
Plate Loading Test (PLT):
- Determines the vertical deformation and strength properties of the ground in situ.
- Records the load and corresponding settlement when a rigid plate loads the ground.
- Predicts the behavior of spread foundations.
Slug Test:
- Determines the permeability of unconfined aquifers or shallow soil layers.
- Involves rapidly introducing a "slug" of water (or air) into a well and measuring how the water level changes over time.
Ground Penetrating Radar (GPR):
- Maps subsurface features by sending high-frequency electromagnetic waves into the ground and recording the reflected signals.
- Non-destructive and provides real-time results.
- Works best in dry, sandy soils or materials with lower conductivity (e.g., rock or concrete).
- Clay-rich soils and wet environments can absorb or attenuate the radar waves, limiting its use for deeper investigations.
Downhole/Cross-hole Testing:
- Uses a source and receivers at different depths to measure wave velocities.
Ambient Vibrations Analysis:
- Uses the horizontal-to-vertical spectral ratio (HVSR) technique to obtain the fundamental frequency of soil deposit (clause 10.7.2, BS EN 1997-2:2024).
Monitoring:
- Tiltmeter
- Extensometers
- Geodetic GNSS
- Piezometer

Lecture Outline

Introduction to foundation
Foundation classification
Design according to the Eurocode 7
Bearing capacity
- Basis concept
- Terzaghi equation
- General equation

Reading

Soil Mechanics: principles and practice - Graham Barnes 2016
Bond, A. J., and Harris, A. J. (2008). Decoding Eurocode 7, London: Taylor & Francis, 598 pp.
BS EN 1997: Eurocode 7: Geotechnical design (EC7) Part 1: General rules (EC7 Part 1)

Definition of Foundations

Foundations constitute the part of the structure at the interface between the foundation soil and the structure itself.

Role of Foundations

The foundation transfers vertical (e.g., the weight of the building) and horizontal (e.g., wind forces) forces to the underlying soil or rock.
The foundation controls the amount of movement in the building due to changes in stress in the ground or changes in water level.
Prevents damage to adjacent structures.
Transmits the load beneath zones affected by seasonal change.
Prevents damage to structures due to subsequent changes in the use of the building.

Foundations: Design Issues

Requirements:
- Bearing capacity:
  - Capacity of the ground to resist loads.
  - Loads: dead, live, wind, inclined thrusts, and uplift.
- Settlements:
  - Kept within allowable limits.
  - Uniform versus differential settlement.
- Others:
  - Site considerations: water table levels, seismic activity, flooding potential, or freeze-thaw.
  - Feasibility: technical and economical.

Problems with Poorly Designed Foundations

A poorly designed foundation can render the building unfit for purpose:
- Building cracks/tilts due to differential settlement of the foundations → fails serviceability limit criteria.
- Building collapses due to failure of the soils beneath the building → fails ultimate limit state criteria.

Problems to be Investigated

(I) Failure:
- Soil shear strength.
  - Shear strength of a soil is the maximum internal resistance to applied shearing forces.
  - To determine the resistance to failure such as in foundation loading or slope instability.
- Parameters required:
  - i. Long-term (drained) calculations:
    - c’ (effective cohesion) and
    - 𝜙’ (effective angle of shearing resistance)
  - ii. Short term (undrained) calculations:
    - Su (undrained shear strength), also called cu (undrained cohesion)
(II) Settlement:
- Soil compressibility.
- Parameters required:
 - e (void ratio)
 - Cc (compression index)
 - Cs (swelling index)
 - OCR (overconsolidation ratio)
- Soil’s stress history
 - OCR = 1: normally consolidated
 - OCR > 1: over-consolidated
 - OCR < 1: under-consolidated

Types of Foundations

Shallow foundations:
- Depth to formation level is less than the breadth.
  - Pad footings for columns
  - Strip footings for walls
  - Rafts for whole structures
Deep foundations Depth to base is much greater than the breadth
- Piles in group beneath a building or a column
- Pier or caisson beneath a major structural element (e.g. bridge piers)

Shallow Foundations

Isolated/Pad foundation: an individual foundation designed to carry a single column load although there are occasions when a pad supports two or more columns.
Strip foundation: or continuous footing, has a length significantly greater than its width. It is generally used to support a series of columns or a wall.
Slab/mat/raft foundation: a large, continuous slab of concrete that covers a wide area beneath a structure.

Deep Foundations

Pile foundation: Long slender columns (piles) driven or drilled deep into the ground to transfer the load to deeper, more stable soil or bedrock.
- End-bearing piles: transfer the load directly to a hard stratum (like rock or very dense soil) at the pile's tip.
- Friction piles: transfer load by friction along their length, typically in deep, soft soil that doesn’t have a solid base layer.
Caisson foundation: large, hollow, cylindrical structures (called caissons) which are sunk into the ground to support heavy loads.
- Open Caissons: These have an open bottom and are typically used for shallow foundations. They are particularly useful for sinking through loose or waterlogged soil.
- Box Caissons: These are closed at the top and bottom and are often used for underwater construction, such as for pier foundations in rivers or harbors.

Shallow vs Deep Foundations

If a soil layer near the surface is capable of adequately supporting the structural loads, it is possible to use shallow foundations.
If the soil near the surface is incapable of adequately supporting the structural loads, piles or caissons and piers are used to transmit the load to suitable layers (of soil or rock) located at greater depth.

Shallow Foundations: Design EC-7

The design of a foundation normally needs to consider:
- Spatial variability of soil type/soil properties
- Sensitivity of structure to movement (e.g., machinery hazardous work)
A foundation needs to be safe and economic.

Shallow Foundations: Design EC-7 - Loading Conditions

self weight of the structure
environmental loads, e.g. snow, wind, earthquake
service loads, e.g. fixtures, fittings, people
loads due to adjacent structures
The distribution of loads can change during the life of the structure.

Shallow Foundations: Design EC-7 UK - Depth to Formation Level (D)

The foundation base should be located at a depth such that frost action ( 0.5m in the UK), seasonal swelling and shrinkage are minimised;
The foundation base should be located below made ground ( 0.5 ÷ 1.5m) and safe from groundwater level oscillations;
Different parts of the structures should ideally be built onto the same foundation level;
The construction/excavation on existing structures should be possible.

Shallow Foundations: Design EC-7 UK - Width of Foundation (B)

Exceeds width of element it supports
Ideally load distributed through foundation at about 45˚ to enable effective transfer of load.
If L is the width of the structural element and H the depth of the base of the structural element, the optimum foundation width is: $B = L + (D - H) \times 2$

Shallow Foundations: Design EC-7 - Limit States

"2.1 (1) P For each geotechnical design situation, it shall be verified that no relevant limit state, as defined in EN 1990:2002, is exceeded."
Serviceability limit states:
- Excessive settlement (or heaving) leading to excessive angular distortion
- Vibration resulting in unacceptable effects such as settlement and soil liquefaction.
Ultimate limit states:
- Bearing resistance failure caused by shear failure of the surrounding soil
- Failure by sliding under inclined loading
- Loss of overall stability due to the development of a deep slip surface within the surrounding soil

Shallow Foundations: Design EC-7 - Soil Type and Conditions

The bearing capacity calculation method depends on the soil type:
- Both undrained and drained conditions have to be checked in the case of saturated clays, although the undrained condition is usually more critical.
- Only long-term analyses (i.e., drained conditions) are performed in the case of granular soil deposits.

Shallow Foundations: Design EC-7 - Partial Factors

Apply partial factor:
- The design bearing resistance $R_d$ is calculated using the factored shear strength parameters.
- The vertical design action $F_d$ is calculated from factored loads without subtracting the weight of the overburden soil.

Shallow Foundations: Design EC-7 - Parameters

Actions, $F_{rep}$ : Loading transferred from the superstructures, self-weight of foundation
Material properties, $X_k$ :
- $c_u$ - undrained shear strength of clay (used for undrained, short-term conditions in clays).
- $c'$ - effective cohesion (used for drained, long-term conditions in clays).
- $𝜙'$ - effective angle of shearing resistance (used for drained conditions, long term in sands and in clays).
- $𝛾$ - unit weight, $𝛾 = 𝜌 \times 𝑔$ where 𝜌 is density, 𝑔 is gravity (9.81 m/s2).
Geometrical data: Foundation depth, height, breadth, length, GWL (Main purposes of lab and field tests!)

Shallow Foundations: Design EC-7 - Factored values

Actions, $F{rep}$ , Material properties, $Xk$ , Geometrical data
Factored material properties, $Xd = XK/γ_M$
Factored actions, $Fd = F{rep} . γ_F$
Design resistance, $Rd= qu A$

Bearing Capacity of Soils

Zone of influence
Distribution of force within the soil
*Bearing capacity failure due to soil liquefaction
Mechanism of how surface loads exceed the strength of the soil beneath the foundation
*Bearing capacity failure examples

Definition of Bearing Capacity

Ultimate bearing capacity $q_u$ is the maximum vertical pressure a soil can support without failure.
Net ultimate bearing capacity $q{nu}$ is the ultimate bearing capacity subtracting the weight of the soil ( $𝝲$ ) multiplied by the foundation depth (D), i.e., $q{nu} = q_u - 𝝲D$ .
Net safe bearing capacity $q{ns}$ : the net ultimate bearing capacity ( $q{nu}$ ) divided by a factor a safety (typically this will be 3), i.e, $q{ns} = q{nu}/F$ .
Safe bearing capacity $qs$ : dividing the ultimate bearing capacity by a factor of safety, i.e, $q{ns} = q_u/F$ .
Net safe settlement pressure $q_{np}$ : the maximum load the soil can take before it exceeds the allowable amount of soil settlement.
Net allowable bearing capacity ( $q{na}$ ): often simply referred to as the ‘allowable bearing capacity’. $q{na}$ is equal to either the net safe bearing capacity ( $q{ns}$ ) or the net safe settlement pressure ( $q{np}$ ), whichever is the lower figure.

Modes of Failure

The mode of failure depends on the compressibility of the soil and the depth of the foundation relative to its breadth.
General shear failure
Local shear failure
Punching shear failure
Modes of shear failure:
- General shear: Soils of low compressibility. Very dense sands or saturated clays subjected to undrained shear (i.e. fast loading).
- Local shear: Soils of moderate compressibility. Medium dense sands.
- Punching shear: Soils of high compressibility. Very loose sands, partially saturated clays, Normally consolidated clay under drained conditions (slow loading) or peat.
General shear:
- Continuous failure surfaces develop between the edges of the footing and the ground surface.
- As the pressure is increased towards the ultimate bearing capacity ( $q_u$ ) the state of plastic equilibrium is reached initially in the soil around the edges of the footing and then gradually spreads downwards and outwards.
- Ultimately the state of plastic equilibrium is fully developed throughout the soil above the failure surfaces.
- Heaving of the ground surface occurs on both sides, although the final slip only on one side, accompanied by tilting.
Local shear:
- In this case there is a significant compression of the soil under the footing and only partial development of the state of plastic equilibrium.
- The failure surfaces do not reach the ground surface and only slight heaving occurs.
- Tilting of the foundation would not be expected.
  *Relatively large settlement (which would be unacceptable in practice).
It occurs when there is relatively high compression of the soil under the footing.
- Accompanied by shearing in the vertical direction around the edges of the footing.
- No heaving of the ground surface away from the edges.
- No tilting of the foundation.
Large settlement (which would be unacceptable in practice).

Terzaghi Analysis

The evaluation of the ultimate bearing capacity of a foundation is usually obtained from an analysis of general shear failure and considering the plasticity theory.
Terzaghi (1943) derived a formula for qu considering separately:
- effects of cohesion
- overburden pressure acting on the foundation level
- self-weight of the soil below the foundation level
The superposition of components of bearing capacity is theoretically incorrect for a plastic material but the resulting error is considered to be on the safe side.
Hypotheses:
- Failure mode of general shear;
- Rigid-perfectly plastic homogeneous soil;
- Strip footing;
- Vertical and centred load;
- Horizontal foundation level and ground surface.
 $qu = cNc + 𝛾1DNq + frac{1}{2}𝛾2BN𝛾$
$q_u$ - ultimate bearing capacity (unit: Pa or N/m², or kPa)
$𝛾$ - unit weight of the soil
c – cohesion(unit: Pa or N/m², or kPa)
$φ$ - angle of shearing resistance
Nc, Nq, N_ - bearing capacity factors depending on φ only
General shear failure
The Terzaghi’s equation does not consider factors that may affect bearing capacity such as inclined loading, base and ground surface, and other foundation shapes.
The general form proposed by Hansen (1970) includes shape, load inclination, depth, base and ground surface inclination factors.
The Hansen (1970) method gives conservative values and has been adopted for calculating bearing capacities in Eurocode 7.
dry soil case: $qu = c'Nc + 𝛾1DNq + frac{1}{2}𝛾2BN𝛾$
Saturated soil case: $qu = c'Nc + γ'1DNq + frac{1}{2} γ'2BN𝛾$ where $𝛄′ = 𝛄 − 𝛄w$ , 𝛄w = 9.81 kN/m^3$

Long-term analysis – Drained conditions

(Terzaghi equation)
General form of bearing capacity equation:
\frac{R}{A'} = qu = cNcscicbc + 𝛾1DNqsqiqbq + \frac{1}{2}𝛾2BN𝛾s𝛾i𝛾b𝛾 $*General form of bearing capacity equation: *Eccentric loading: The width B should be substituted by an effective width B’: B’ = B – 2eB , where$ e𝐵 ≤ \frac{𝐵}{6} $ Effective length L’ : L’ = L – 2eL, where$ e𝐿 ≤ \frac{𝐿}{6} $Effective area$ 𝐴′: 𝐴′ = 𝐵′ × 𝐿′ $*Bearing capacity factors: Only a function of$ \phi $!!$ {𝑁q = tan^2 (45^o + \frac{\phi}{2}) e^{\pi tan \phi}} $ $ {𝑁c = \frac{𝑁q − 1} {cot \phi}} $ $ {𝑁𝛾 = 2 (𝑁q − 1) tan\phi} $<h3 id="7e72edfd-69d2-4a1e-8c18-07344ec6b9fd" data-toc-id="7e72edfd-69d2-4a1e-8c18-07344ec6b9fd" collapsed="false" seolevelmigrated="true">Shape Factors</h3>$ \begin{array}{|l|l|l|l|} \hline & {sc} & {sq} & {s𝛾} \hline {Strip} & {1.0} & {1.0} & {1.0} \hline Rectangular& {\frac{sq Nq - 1}{Nq - 1}} & {1 + \frac{B'}{L'} sin\phi } & {1 - 0.3 \frac{B'}{L'}} \hline {Square or circular} & {\frac{sq Nq - 1}{N_q - 1}} & {1 + sin\phi} & {0.7} \hline \end{array} $<h3 id="c08ed206-e3bd-4906-bfa7-4afe5d06688e" data-toc-id="c08ed206-e3bd-4906-bfa7-4afe5d06688e" collapsed="false" seolevelmigrated="true">Load Inclination factors</h3>$ { ic = iq - \frac{1 - iq}{Nc tan\phi}} $ $ { i𝛾 = (iq)^{\frac{m+1}{m}} } $ where: $ {m = mB = \frac{2 + \frac{B'}{L'} }{ 1+ \frac{B'}{L'} }} $H acts in the direction of B’ ;$ {m = mL = \frac{2 + \frac{L'}{B'} }{ 1+ \frac{L'}{B'} }} $H acts in the direction of L’ ; $ {m = m\theta = mL cos^2{\theta} + m_B sin^2{\theta}} $H acts in a direction forming an angle θ with L’<h6 id="de701d44-7e1a-4326-acf4-287ef63dfced" data-toc-id="de701d44-7e1a-4326-acf4-287ef63dfced" collapsed="false" seolevelmigrated="true">Base Inclination factors:</h6>$ {bc = bq - \frac{1 - bq}{Nc tan\phi}} $ $ {bq = b𝛾 = (1 - \alpha tan{\phi})^2} $ where 𝛼 is base inclination angle [in radians] from the horizontal.<h3 id="58d90634-ef71-42a9-8363-344a1222f9c8" data-toc-id="58d90634-ef71-42a9-8363-344a1222f9c8" collapsed="false" seolevelmigrated="true">Short-term analysis – Undrained conditions</h3>General form of bearing capacity equation: $ \frac{R}{A'} = qu = (𝜋 + 2)cuscicbc + 𝛾1D $ *Base Inclination factor: $ { bc = 1 - \frac{2 \alpha}{𝜋 + 2} } $*Load inclination factor:$ { ic = 0.5 + 0.5 \sqrt{1 - \frac{H}{A' cu}} } $*Shape factor:$ { sc = 1 + 0.2 \frac{B'}{L'} (rectangular) } $ $ { s_c = 1.2 } (square or circular)$

Shallow Foundations: Design EC-7 - Design Procedure

*Steps of design procedure:
1) Calculate the loads to be applied through the foundation throughout the life of the structure
2) Determine the zone of influence – characterisation of soil properties
3) Estimate initial foundation size and depth based on prescriptive method and the minimum depth
4) Calculate the bearing pressure - Check the bearing resistance
5) Adjust foundation size and depth until bearing resistance meets criteria

Summary

Introduction to foundation
- Role of the foundation: transfer loads to the ground, limit movements, etc.
- Foundation types: shallow foundation VS deep foundation
Shallow foundation: classification
- Pad footing
- Strip footing
- Raft foundation
Shallow foundation: Design according to the Eurocode 7
- Serviceability limit state: settlements
- Ultimate limit state: bearing capacity
Bearing capacity of soils
- Significant depth
- Modes of failure: general, local, punching shear failures
Bearing capacity: Terzaghi (1943) analysis
General form of bearing capacity eq.: Hansen (1970) formula
Bearing capacity: long and short term
*Bearing capacity of layered soils