This document serves as a comprehensive guide on bearing capacity equations according to Eurocode 7, highlighting the importance of understanding soil properties, foundational design, and the implications of inadequate bearing capacity. It details the core bearing capacity equation, factors influencing it, and the need for thorough geotechnical investigations to ensure safety and stability in structures. The document also discusses advanced considerations and future trends in bearing capacity analysis, emphasizing its critical role in safe and efficient foundation design.

1. Understanding Bearing
Capacity Equations in
Eurocode 7
Welcome to this comprehensive guide on bearing capacity equations
according to Eurocode 7. We'll explore the fundamental concepts, key
equations, and practical applications in foundation design.
by Prof Dr. Costas Sachpazis

2. What is Bearing Capacity?
Definition
Bearing capacity is the ability of soil beneath a foundation
to safely carry the load of a structure without failing. It's
crucial for ensuring the stability and safety of buildings and
infrastructure.
Key Components
• The Foundation: Base of the structure
• The Soil: Ground underneath
• The Load: Weight of the structure

3. Importance of Bearing
Capacity
Structural Integrity
Ensures the building
remains stable and doesn't
sink or tilt over time.
Safety
Prevents catastrophic
failures that could endanger
lives and property.
Cost-Effective Design
Allows for optimised
foundation design,
balancing safety and
construction costs.
Long-Term
Performance
Minimises settlement issues
and structural damage over
the building's lifespan.

4. Consequences of Inadequate Bearing Capacity
Shear Failure
The soil gets squashed sideways
and upwards, potentially causing
sudden collapse.
Excessive Settlement
The foundation sinks too much,
leading to cracks and structural
damage over time.
Tilting
Uneven settlement can cause the
entire structure to tilt,
compromising its stability.

5. Introduction to Eurocode 7
Standardised Guidelines
Eurocode 7 provides internationally
recognised rules for structural design
in Europe and beyond.
Safety Focus
Ensures the safety and reliability of
structures through standardised
approaches.
Wide Application
Used for geotechnical design,
including foundations and earthworks.

6. The General Bearing
Capacity Equation
The core of Eurocode 7's bearing capacity calculation is encapsulated in
this equation:
R/A' = c' * Nc * sc * ic + q' * Nq * sq * iq + 0.5 * γ' * B' * Nγ * sγ * iγ
This equation considers various factors to determine the ultimate
strength the soil can provide. Let's break it down in the following slides.

7. Components of the Bearing Capacity
Equation
1 R/A'
Design bearing capacity divided by the effective area of the foundation. This is
what we're solving for.
2 c'
Effective cohesion of the soil, representing the 'stickiness' of soil particles.
3 q'
Effective overburden pressure at the foundation level, influenced by foundation
depth.
4 γ'
Effective unit weight of the soil below the foundation, considering groundwater
effects.

8. More Components of the Equation
1 B'
Effective width of the foundation, the narrowest dimension in contact with the soil.
2 Nc, Nq, Nγ
Bearing capacity factors, dimensionless numbers dependent on the soil's friction angle.
3 sc, sq, sγ
Shape factors accounting for the foundation's shape (square, rectangular, circular).
4 ic, iq, iγ
Inclination factors considering the angle of load application.

9. Understanding Soil Friction Angle
Definition
The friction angle (φ') represents how well soil particles
interlock and resist sliding. It's a crucial parameter in
determining soil strength.
Importance
A higher friction angle indicates stronger soil. It directly
influences the bearing capacity factors (Nc, Nq, Nγ) in the
equation.

10. Effective Stress Concept
Definition
Effective stress is the stress
carried by the soil skeleton,
after accounting for pore
water pressure.
Importance
It's crucial for understanding
soil behaviour, as water
pressure reduces effective
stress and soil strength.
In the Equation
The primes (') on c, q, and γ indicate effective stress parameters.

11. Failure Mechanism in Soil
Concept
The bearing capacity equation is based on the idea of a specific failure pattern in the soil beneath the foundation.
Analysis
Engineers analyse these failure mechanisms to derive the bearing capacity factors (Nc, Nq, Nγ).
Importance
Understanding failure mechanisms helps in predicting how soil will behave under load.

12. Importance of Soil Properties
1
Cohesion (c')
Measures soil particle 'stickiness'
2
Friction Angle (φ')
Indicates soil particle interlocking
3
Unit Weight (γ')
Represents soil density
4
Accurate Soil Testing
Essential for reliable calculations
Accurate soil property determination is crucial for reliable bearing capacity calculations. This emphasises the importance of thorough
geotechnical investigations before foundation design.

13. Characteristic Values in
Eurocode 7
Definition
Characteristic values are
cautious estimates of soil
properties, considering
variability and uncertainties.
Application
Soil parameters (c', φ', γ')
used in the bearing capacity
equation are typically
characteristic values.
Purpose
They provide a conservative approach to ensure safety in design
calculations.

14. Design Approaches in
Eurocode 7
1 Concept
Eurocode 7 provides different Design Approaches for
incorporating safety into calculations.
2 Application
These approaches involve applying partial factors to loads,
soil parameters, or both.
3 Purpose
Ensures structure safety even if actual conditions are
slightly worse than anticipated.

15. Verification Process
1
Calculate Design Bearing Capacity
Use the bearing capacity equation
2
Determine Design Load
Calculate the load applied by the structure
3
Compare Values
Ensure design bearing capacity > design load
4
Safety Margin
Confirm sufficient margin for safety

16. Simplified Analogy: Block Stacking
Bearing Capacity
Equation
Like a rulebook telling you
how many blocks you can
safely stack based on the
ground type and base size.
Soil Properties
Equivalent to knowing if
the ground is firm sand or
soft clay.
Load
Represents the number of
blocks you want to stack.
Eurocode 7
Acts as inspectors
ensuring you're following
the rules and stacking
blocks safely.

17. Limitations of the Bearing
Capacity Equation
Simplification
The equation makes certain
assumptions about soil and
loading conditions. Real-
world scenarios can be more
complex.
Groundwater
Consideration
While accounted for through
effective stress, groundwater
effects can be complex.
Settlement Analysis
The equation helps prevent
shear failure but doesn't
directly calculate settlement.
Data Dependency
Accuracy heavily relies on
the quality of soil data from
geotechnical investigations.

18. Importance of Geotechnical
Investigations
Soil Testing
Laboratory tests to determine soil
properties like cohesion and
friction angle.
Site Investigation
Field tests (SPT, CPT, CBR Test, etc.)
and borehole sampling to
understand soil layers and
groundwater conditions.
Data Analysis
Interpreting test results to obtain
reliable soil parameters for design
calculations.

19. Determining Soil Parameters
1 Cohesion (c')
Determined through triaxial or direct shear tests on soil samples.
2 Friction Angle (φ')
Obtained from triaxial tests or estimated from standard penetration
tests (SPT).
3 Unit Weight (γ')
Measured by weighing a known volume of soil, considering moisture
content.
4 In-Situ Tests
Cone penetration tests (CPT) or pressure meter tests for additional data.

20. Calculating Bearing Capacity Factors
Nc, Nq, Nγ Factors
These factors are crucial components of the bearing
capacity equation. They are dimensionless numbers that
depend on the soil's friction angle (φ').
Calculation Methods
Factors can be obtained from charts or calculated using
specific formulas. The choice of method can affect the final
bearing capacity result.

21. Shape, Depth, and
Inclination Factors
Shape Factors (sc, sq,
sγ)
Account for foundation shape
(square, rectangular, circular).
Calculated based on
foundation dimensions.
Depth Factors
Consider the embedment
depth of the foundation.
Deeper foundations generally
have higher bearing capacity.
Inclination Factors (ic, iq, iγ)
Account for inclined loads. Calculated based on load angle and soil
properties.

22. Types of Foundations
Shallow Foundations
Used when competent soil is near the
surface. Includes strip, pad, and raft
foundations.
Deep Foundations
Used when competent soil is at greater
depths. Includes piles and caissons.
Combined Foundations
Hybrid solutions like pile-raft
foundations, combining elements of
shallow and deep foundations.

23. Effects of Groundwater on
Bearing Capacity
Buoyancy Effect
Reduces effective soil weight, lowering bearing capacity.
Soil Strength Reduction
Can decrease cohesion and friction angle in some soils.
Seasonal Variations
Fluctuating water table can cause changes in bearing
capacity over time.

24. Settlement Calculations
Importance
While bearing capacity ensures against shear failure,
settlement calculations predict vertical movement of the
foundation under load.
Types of Settlement
• Immediate Settlement
• Consolidation Settlement
• Secondary Settlement

25. Advanced Considerations in
Foundation Design
Soil-Structure
Interaction
Considers how the structure
and soil influence each
other's behaviour.
Dynamic Loading
Accounts for earthquake or
machine vibrations in
bearing capacity
calculations.
Numerical Modelling
Uses finite element analysis
for complex soil-foundation
systems.
Sustainability
Considers environmental
impact and long-term
performance of foundations.

26. Case Studies: Bearing Capacity in Action
Leaning Tower of Pisa
A famous example of inadequate
bearing capacity leading to excessive
differential settlement.
Burj Khalifa
Demonstrates successful application of
advanced bearing capacity analysis for
a supertall structure.
Millennium Tower, San
Francisco
Illustrates the importance of
considering long-term settlement in
foundation design.

27. Future Trends in Bearing
Capacity Analysis
AI and Machine Learning
Potential for more accurate
prediction of soil behaviour and
bearing capacity.
Virtual Reality
Enhanced visualization of
subsurface conditions and
foundation behaviour.
Smart Foundations
Embedded sensors for real-time
monitoring of foundation
performance.

28. Challenges in Bearing Capacity Analysis
1
Soil Variability
Natural variations in soil properties
2
Complex Soil Behaviour
Non-linear and time-dependent responses
3
Climate Change Impact
Changing groundwater levels and soil conditions
4
Urban Development
Interactions with existing structures

29. Key Takeaways
1 Fundamental
Importance
Bearing capacity is crucial
for safe and efficient
foundation design.
2 Eurocode 7
Framework
Provides a standardised
approach to bearing
capacity calculations.
3 Comprehensive
Analysis
Considers soil properties,
foundation characteristics,
and loading conditions.
4 Ongoing Research
Continuous improvements
in understanding and
predicting soil behaviour.

30. Conclusion and Next Steps
Understanding bearing capacity equations in Eurocode 7 is crucial for
geotechnical engineers and structural designers. It forms the foundation of safe
and efficient building practices.
Further Study
Delve deeper into specific aspects of geotechnical engineering.
Practical Application
Apply these concepts in real-world projects under supervision.
Stay Updated
Keep abreast of new research and updates to Eurocode 7.

31. Understanding Bearing
Capacity Equations in
Eurocode 7
Thank you
by Prof Dr. Costas Sachpazis