(Site investigation report) 2500 ( civil and environmental engineering )
kash1
FoundationsinSoilandRock.pdf
Quiz
What is RMR System? What is the Q System? Is Rockmass usually weaker or stronger than a rock sample or core? What features reduce the performance or rock?
How do foundations fail in soil or rock What soil features can lead to foundation failure?
Lecture Structure
1. Introduction to different types of foundations
2. Foundation Failure Mechanisms in Rock and Soil: Karst, Swell shrink, bearing
capacity, sliding
3. Rock Foundations Design Parameters (derived from Rockmass Classification)
4. Bearing Capacity theory of shallow footings – Bells Approach
5. Example of pad foundation design in rock
6. Vertical, Horizontal & Moment loading in shallow footings
7. Example of offshore foundation design in soil
Types of Foundation
Foundations in Soil and Rock
Dam Supported by - Bearing capacity - Slide resistance
Tension anchors
Supported by: - Shear resistance
between anchors and rock mass
Socketed and Driven piles
Supported by - End bearing capacity - Side-wall shear
resistance
Spread footing Supported by: - Bearing capacity
Definition of Shallow Foundations
• A shallow foundation or footing is usually one with a breadth B z, the depth to the base of the footing.
B
z
• Shallows foundations are used when surface soils are sufficiently strong and stiff to support the imposed loads; they are generally unsuitable in weak or highly compressible soils, such as poorly-compacted fill, silts, clays and alluvial deposits.
Types of Foundation
Foundations in Soil and Rock
Spread or Pad Foundations
Pad foundations are used to support an individual point load such as that due to a structural column. They may be circular, square or rectangular.
They usually consist of a block or slab of uniform thickness, but they may be stepped or haunched if they are required to spread the load from a heavy column. Pad foundations are usually shallow, but deep pad foundations can also be used.
Types of Foundation
Foundations in Soil and Rock
Strip foundations are used to support a line of loads, either due to a load-bearing wall, or if a line of columns need supporting where column positions are so close that individual pad foundations would be inappropriate.
Types of Foundation
Foundations in Soil and Rock
Spread footing
Deep foundations
• Deep foundations are those founding too deeply below the finished ground surface for their base bearing capacity to be affected by surface conditions.
• They include piles, piers and caissons or compensated foundations using deep basements and also deep pad or strip foundations.
• Deep foundations can be used to transfer the loading to a deeper, more competent strata at depth if unsuitable soils are present near the surface.
Types of Foundation
Foundations in Soil and Rock
Driven Piles
Piles
Socketed Piles
Piles
• Used when it is necessary to transmit loads to strata beyond the practical reach of shallow foundations.
• In addition to supporting structures, piles are also used to anchor structures against uplift forces and to assist structures in resisting lateral and overturning forces
• A battered pile is an inclined pile that is used that can resist lateral forces as well as vertical forces.
Example: End bearing pile
Example:Bat tered pile
Types of Foundation
Foundations in Soil and Rock
Types of Foundation
Foundations in Soil and Rock
Piles
Piled Rock Foundations
Qb
QsQs QsQs
Qb
QsQs
Anchors
Wind turbines
Moorin
g chains
Pipelines
Floating LNG
Types of Foundation: Piles – these examples are driven piles
Foundations in Soil and Rock
Piles
Suction Caissons
• Suction Caissons are a form of deep foundation which are constructed above ground level, then sunk to the required level by suction. AKA suction buckets.
• Quicker to install than deep foundation piles and being
• Easier to remove during decommissioning.
• used extensively worldwide for anchoring large offshore installations, like oil platforms,
• In recent years, suction caissons have also seen usage for offshore wind turbines in shallower waters. https://www.youtube.com/watch?v=wr
O0yXG7g9k&ab_channel=NGI- NorgesGeotekniskeInstitutt
Piles
Types of Foundation: Piles – these examples are driven piles
Foundations in Soil and Rock
Types of Foundation: Tension Anchors
Foundations in Soil and Rock Tension anchors
Note: Rock Bolts in Rock Mass Classification Lecture are Tension Anchors
We covered how to design the bolt length and bolt spacings
Rock Anchor in bridge – Severn Bridges foundations could be a good topic
Types of Foundation
Foundations in Soil and Rock
Types of Foundation
Foundations in Soil and Rock
Dams often contain mixture of materials and not all are concrete
Zone U: Upstream fill Zone S: Core layer to control seepage. Zone C: Rock Fill. The duty of the rockfill zone (Zone C) is to support the core, Zones F & T: Filter The duty of the filter (Zone F) and transition (Zone T) is to collect any seepage coming through the core and to prevent fines from migrating out of it.
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
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Dam Tension anchors
Socketed piles
Spread footing
In this section we will discuss typical failure mechanism of the 4 Foundation Types
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
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Pile
• Side-wall slide
• Large settlements
• Creep at high stress levels
• Creep due to weathering
https://www.geplus.co.uk/news/piling-design-error-leads-to- demolition-of-sheffield-building-16-09-2020/
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
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Dam Foundation
• Sliding on base
• Rock mass failure due to water pressure
• Rock mass failure due to seepage
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Dam Foundation due to sliding
During a foundation failure event, movement occurs along a failure plane corresponding to the path of least resistance under different loading conditions.
This can occur at the base of the dam or at a weak soil layer such as this example from Mount Polley
The reasons for foundation failure can be complex and sometimes due to: • Discrete weak layers that
were missed in the Site Investigation phase
• Behaviour is difficult to interpret, particularly under different
25th April 1998 at the Los Frailes tailings dam in Spain
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
Foundations in Soil and Rock
Failures Mechanisms – Foundation Failure
. Dam Foundation due to sliding
Mount Polley
On 4th August 2014, shortly after completion of the 9th embankment raise, a section of the Perimeter Embankment suddenly and without warning failed, resulting in a partial breach that released an estimated 10.5 million m3 of supernatant water, 7.3 million m3 of solid tailings, together with over 7 million m3 of construction materials and interstitial water.
Foundations in Soil and Rock
Failures Mechanisms – Foundation Failure
. Dam Foundation due to sliding
https://www.youtube.com/watch?v=vg3yd8GPSnA&t=41s Skip to 1 minute
Foundations in Soil and Rock
Failures Mechanisms – Foundation Failure
. Dam Foundation due to sliding
Mount Polley
On 4th August 2014, shortly after completion of the 9th embankment raise, a section of the Perimeter Embankment suddenly and without warning failed, resulting in a partial breach that released an estimated 10.5 million m3 of supernatant water, 7.3 million m3 of solid tailings, together with over 7 million m3 of construction materials and interstitial water.
Foundations in Soil and Rock
Failures Mechanisms – Foundation Failure
.
Computer
Generated
Failure
Planes
Fine Grained: glacially-deposited layer of silt and clay
Coarse Grained Material
Dam Foundation due to sliding
The key findings of the subsurface investigations with regard to the failure mechanism can be summarized as follows:
• The Upper glaciolacustrine layer, (GLU) can be distinguished as a distinct foundation unit based on its water content and other properties.
• The failure occurred within fine
grained varved silts and clays of
the Upper GLU
• The strength behaviour of the GLU was misinterpreted.
https://www.youtube.com/watch?v= 2wZRluVKPPg&ab_channel=konvide oful
Failures Mechanisms – Foundation Failure
.
Foundations in Soil and Rock
Rock mass failure due to seepage: The Teton Dam Idaho, United States.
Dam was located in an area with highly permeable foundation materials. Geology of fissured rhyolite
Two major causes of failure: 1. fissured rhyolite terrain on which the dam was
built 2. brittle permeable loess used for the core.
Thus two geological factors combined to produce an engineering disaster.
Failures Mechanisms – Foundation Failure
.
Foundations in Soil and Rock
Rock mass failure due to seepage: The Teton Dam Idaho, United States.
•Zone 1 was the impervious center core, forming the water barrier of the dam (low-plastic to nonplastic silt compacted to ~ 98% Standard MDD at a moisture content 1.5% dry of optimum, with k ~ 1 x 10-8 m/s). The core was non plastic and brittle and when stressed by settlement would tend to lose its hydraulic integrity and allow passage of water. Zone 1 was easily
•Zone 2 overlaid Zone 1 and extended downstream to provide a layer to control seepage through the foundation.
•Zone 3 was downstream and its main function was to provide structural stability.
•Zone 4 consisted of the storage areas downstream from the control structure and the temporary enclosures built to permit the work to be done.
• Zone 5 was the rockfill in the outer parts of the embankment
Rock mass failure due to seepage :The Teton Dam Idaho, United States.
https://www.yout ube.com/watch?v =2wZRluVKPPg&a b_channel=konvi deoful
Failures Mechanisms – Foundation Failure
.
Foundations in Soil and Rock
Teton Dam Failure, 5 June 1976
Details
•Zone 1 was the impervious center core, forming the water barrier of the dam (low-plastic to nonplastic silt compacted to ~ 98% Standard MDD at a moisture content 1.5% dry of optimum, with k ~ 1 x 10-8 m/s). The core was non plastic and brittle and when stressed by settlement would tend to lose its hydraulic integrity and allow passage of water. Zone 1 was easily
•Zone 2 overlaid Zone 1 and extended downstream to provide a layer to control seepage through the foundation.
•Zone 3 was downstream and its main function was to provide structural stability.
•Zone 4 consisted of the storage areas downstream from the control structure and the temporary enclosures built to permit the work to be done.
• Zone 5 was the rockfill in the outer parts of the embankment
Foundations in Soil and Rock
Failures Mechanisms – Foundation Failure
.
• Failure of anchor
• Failure rock mass
• Failure of grout
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Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
General Shear Failure of soil &
weak rock
Punching Flexural Compression of open joints
Breaking of pinnacles
Collapse of cave or cavity Slope failure - rotational
Slope failure - planar
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Omitted is excessive settlements due to volume change of soil or freeze thaw action
Sink holes Caves,
subsidence
Concrete pouring into a 15 feet wide sinkhole The most extreme recent example of the awe-inspiring
power of a major sinkhole occurred in Guatemala in May 2010. Collapsing to a depth of 200-feet, it swallowed up an entire clothing factory.
Collapse of cave or cavity
Foundations in Soil and Rock
Collapse of cave or cavity
Sink holes Caves, subsidence
Foundations in Soil and Rock
Collapse of cave or cavity
Collapse of cave or cavity
Sinkholes formed on Chalk due to a
burst water pipe
Some result from the surface dissolution of the soluble rock (solution sinkholes) — for example limestone rocks dissolve when chemically weathered by rainfall or groundwater that is acidic.
Foundations in Soil and Rock
Sink holes Caves, subsidence
Collapse of cave or cavity
Collapse of cave or cavity
Sink holes Caves, subsidence
Foundations in Soil and Rock
Collapse of cave or cavity
Collapse of cave or cavity
https://www.youtube.com/watch?v=WLuVLfg3G1Q&ab_channel=BritishGeologicalSurvey
Foundations in Soil and Rock
Sink holes Caves, subsidence
Collapse of cave or cavity
Collapse of cave or cavity
Chemical Weathering - removal of rock in solution by acidic rainwater. In particular calcite (CaCO3), dolomite & gypsum is weathered by rainwater containing dissolved CO2, (this process is sometimes called carbonation).
CaCO3 (s) + H+ (aq) → Ca2+ (aq) + HCO3- (aq) More the acid (H+) more the weathering
Foundations in Soil and Rock
Sink holes Caves, subsidence
How does excess H+ (aq) ion can originate? from anthropogenic activities i.e emitting sulphur, nitric oxide and carbon dioxide into atmosphere. For example, carbon dioxide reacts with water to form carbonic acid.
Collapse of cave or cavity
Collapse of cave or cavity
• pH is a measure of how acidic/basic water is.
• pH is really a measure of relative amount of free hydrogen & hydroxide ions
• Water that has more free hydrogen ions is acidic,
• Water that has more free hydroxide ions is basic.
• pH ranges from 0 to 14, with 7 being neutral. pHs less than 7 are acidic while pHs greater than 7 are alkaline (basic).
Abandoned Mine
pH is reported in "logarithmic units". Each number represents a 10-fold change in the acidity/basicness of the water, i.e. Water with a pH of five is ten times more acidic than water having a pH of six.
Foundations in Soil and Rock
Sink holes Caves, subsidence
Collapse of cave or cavity
Collapse of cave or cavity
• pH of water determines the solubility (amount that can be dissolved) • pH is an important indicator of water that is changing chemically. • Low-pH water will corrode or dissolve metals and other substances such as rock
What influences the pH of water? Natural and human processes: • Natural processes such as formation of
carbonic acid from detritus • Human processes, e.g. Pollution in runoff
from abandoned mines and increased level of CO2 in air.
How to measure pH of water? • Electronic pH meter • Estimate using litmus paper.
Foundations in Soil and Rock
Collapse of cave or cavity
Foundations in Soil and Rock
Slope failure - rotational
Slope failure - planar
Slope Failure
Slope Failures
• Commonplace • Triggered by water
pressure in soil/ rock (see next slide)
Slope Failure
Foundations in Soil and Rock
Multiple landslides block A83 at Rest and Be Thankful - Scotland, U.K.
Slope failure - rotational
Slope failure - planar
Natural Landslides, soft soil e.g Peat
• Instability / failure is triggered when the embankment is exposed to shear stresses which exceed the shear resistance of the construction material,
• leads to a rotational style failure or a simple sliding style failure.
• The phreatic surface is the other critical factor controlling slope instability; rising pore pressures due to elevated phreatic levels decrease the effective stress and shear strength.
• High pore pressure (alone) can lead to soil failure, this is very important in natural slopes
• How is water pressure measured?
Foundations in Soil and Rock
Slope Failure
https://www.youtube.com/watch?v=aBys49OtAyk
https://www.youtube.com/watch?v=UJsoCWqCsJ8
https://www.youtube.com/watch?v=a5bU65XFzmA&ab_channel=ViralHog
Foundations in Soil and Rock
Slope Failure: Quick Clays Video Slope failure - rotational
Slope failure - planar
A natural soil will have an undisturbed shear strength greater than the remoulded strength (due to the soil developing structure over geological time).
The ratio of the undisturbed strength to the remoulded strength is known as the sensitivity of the soil
• For ordinary clays St = 1 to 4,
• sensitive clays 4 to 8,
• ‘quick’ clays 16 - 100.
• Some Post glacial and offshore soils have high sensitivity.
Sensitivity, 𝑆𝑡 = 𝑢𝑛𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑒𝑑 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑟𝑒𝑚𝑜𝑢𝑙𝑑𝑒𝑑 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
Foundations in Soil and Rock
Slope Failure Slope failure - rotational
Slope failure - planar
• Quick clay is mostly found in Norway and Canada. • Norwegian ‘quick clays’ have an liquidity index Il of >>1.0, i.e. a liquid • From field measurement, undisturbed shear strength of Norwegian ‘quick clay’
~ 20 kPa • However if it is disturbed (remoulded) it turns liquid causing landslides • Remoulded shear strength <<2 kPa.
Sensitivity, 𝑆𝑡 = 𝑢𝑛𝑑𝑖𝑠𝑡𝑢𝑟𝑏𝑒𝑑 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ
𝑟𝑒𝑚𝑜𝑢𝑙𝑑𝑒𝑑 𝑠ℎ𝑒𝑎𝑟 𝑠𝑡𝑟𝑒𝑛𝑔𝑡ℎ =
20 𝑘𝑃𝑎
2 𝑘𝑃𝑎 = > 10
Foundations in Soil and Rock
Slope Failure: Quick Clays Slope failure - rotational
Slope failure - planar
Building overturn in
Shanghai, China.
General Shear Failure of soil &
weak rock
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
General Shear Failure of soil &
weak rock
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
Building overturn in Shanghai,
China.
Punching
General Shear Failure of soil &
weak rock
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
Characteristics:
• Well defined continuous slip surface up to ground level.
• Heaving occurs on both sides with final collapse and tilting on one side.
• Failure is sudden and catastrophic ultimate value is peak value.
Typically occurs in:
• low compressibility soils/ weak rock • Very dense sands • Saturated clays (Normally consolidated
and Over consolidated) undrained shear (fast loading).
General Shear Failure of soil &
weak rock
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
Characteristics:
• Well-defined slip surfaces only below foundation, none on either side.
• Large vertical displacement produces by soil compressibility.
• No heave, no tilting or catastrophic failure. • No ultimate value, increased compression
densifies sand.
Typically occurs in:
• High compressibility soils. • Very loose sands. • Partially saturated clays. • NC clay in drained shear (very slow loading) • Peats.
Foundation failure mechanisms in soil and rock
Foundations in Soil and Rock
Punching
General Shear Failure Xerte Presentation
Shallow foundations Xerte Presentation:
https://xerte.uwe.ac.uk/play.php?template_id=4090#page1
Settlement or Expansion
Foundation failure mechanisms in soil and rock (Settlement)
Foundations in Soil and Rock
Ground shrinkage / expansion is caused by clay (only certain types)
Clay minerals are made up of stacks of basic 2-layer or 3- layer sheets
Linkage (bonds) between the sheets (to form the clay particles) may be:
Very strong or Strong. Water has difficulty separating sheets
Weak. Water can penetrate between individual sheets, resulting in a tremendous capacity to absorb water (and hence to swell when wet, and shrink when dry).
As the clay gets wetter, it swells and pushes the ground above it upwards damaging foundations and structures
Foundations in Soil and Rock
Settlement or Expansion
https://www.youtube.com/watch?v=WLuVLfg3G1Q&ab_channel=BritishGeologicalSurvey
Foundations in Soil and Rock
Settlement or Expansion
Foundations in Soil and Rock
Hydrogeologic setting of the Pissouri area. Geological units (after Stow et al., 1995) are projected on the distorted relief of the Pisourri hill (exaggerated vetical scale H/V 2:1). Location of the landslide
• Carried out a site visit in 2019 • South Coast of Cyprus • Geology contains Swelling Clay –
referred to as Marl • Area is near a fault • Pissouri located near natural Springs
Settlement
Examples of settlement/ expansion causing a slow moving landslide: Case Study
Pissouri, Cyprus 2019
Foundations in Soil and Rock
• Residential development began in 1980 • Population approx. 1000 • 70 houses affected (see damage next..) • worst-affected buildings have been
abandoned
Examples of settlement/ expansion causing a slow moving landslide: Case Study
Pissouri, Cyprus 2019
Foundations in Soil and Rock
Examples of settlement/ expansion causing a slow moving landslide: Case Study
Pissouri, Cyprus 2019
What is causing the Pissouri Landslide: Hydrology, Geology, Hydrogeology, Geotechnics
Foundations in Soil and Rock
Hydrology contains:
• Average Yearly Rainfall approx. 500 mm
• Wet seasons have becoming wetter, see 250 mm per month in figure.
• Situation has worsened significantly as a result of the very wet winter season of 2018 to 2019,
• 2018, 2019 second wettest on record, and probably resulted in the highest recent water condition on the slope.
• In 2018 to 2019, Ground movement increased by a factor of three both during and following the very wet winter of with average rates of displacement of 7 to 9 mm per day between October 2018 and May 2019,
Foundations in Soil and Rock
Typical appearance of the
bedded calcareous marl and the
overlying weathered crust.
Geology contains: • A base of sound Marl dipping towards the coast • Overlying Weathered Marl • Potential Fault shown in red
What is causing the Pissouri Landslide: Hydrology, Geology, Hydrogeology, Geotechnics
Foundations in Soil and Rock
Hydrogeology contains: • High water table • Natural Springs (see seepage face above) • Water table varies due to rain fall
What is causing the Pissouri Landslide: Hydrology, Geology, Hydrogeology, Geotechnics
Foundations in Soil and Rock
Weathered Marl Geotechnical Properties:
Atterberg Limit analysis (RHS): • Contains Highly Active Clay – lots of swelling
capability • Contains over 50% clay – high proportion of
clay particles
Clay Strength analysis (below): • Low Residual Strength – once landslide starts
moving the strength reduces.
What is causing the Pissouri Landslide: Hydrology, Geology, Hydrogeology, Geotechnics
Other factors influencing foundations
Tree Roots
• During periods of dry weather tree roots extend in search for moisture. The resulting reduction in volume of soil can cause subsidence of adjacent structures.
• If a tree is removed, the soil within the root zone is likely to swell. This often occurs before construction.
• Exclusion zones exist for shallow foundation depending on the species and height of the tree.
Foundations in Soil and Rock
Frost action • Frost action can cause is an upwards swelling of soil during freezing conditions
caused by an increasing presence of ice as it grows towards the surface.
• Soils with a permeability similar to silt are most susceptible, clean sands are less susceptible.
Foundations in Soil and Rock
Other factors influencing foundations
Influence of geological features on foundation failures
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d fFeatures Effect on foundation
Rock type Strength and deformation characteristic - bearing capacity and settlement.
Creep rock - creep and time dependent failure.
Strata Layered structure - punching or shearing of rigid layer of rock above soft layer.
Fold Rock surface inclined due to folding - bearing surface may be inclined. Rockhead
contour - drastic change of rock surface and rock type.
Fault Day-lighting fault - slope failure with foundation.
Faulting of rock structure - drastic change of rock type.
Fault with infill-displacement due to compression of infill material.
Joint Open joints - failure by compression.
Closely spaced joints - general wedge failure.
Intersecting joint sets - forming wedge block and shear along the joints. Day-lighting
joint - sliding of rock block.
Weathering Weathered cavities - punching or shear a thin layer of roof rock. Weathering of rock -
may cause creep failure.
Karst Karstic surface – piled tip bending and the damage, failure of pinnacles. Solution
cavities –punching or shear of thin layer of roof rock.
Factors influencing the foundation depth
• Stability (Bearing pressure nearly always increases with depth).
• Suitability of strata (some layers may be weak or compressible).
• Consolidation settlement.
• Heave (foundations placed in or above the zone of seasonal moisture content fluctuations may suffer from expansion and contraction).
• Frost susceptibility (foundations should be placed below the zone of freezing and thawing in frost susceptible soils).
• Groundwater considerations (excavation below the water table may be difficult and costly).
• Cost (excavation and foundation costs increase with depth).
Foundations in Soil and Rock
Rock Foundations Design Parameters
Foundations in Soil and Rock
Mercia Mudstone Group and Penarth Group successions (late Triassic) — Aust Cliff, Avon. (P210568)
Granite Quarry, Vermont
Rock Foundations Design Parameters
Foundations in Soil and Rock
Note: Rock Mass Rating was introduced in Rock Classification Lecture
• This equation is for a very long footing where shearing is 2 dimensional
• Term 1 accounts of cohesion (c) in the soil.
• Term 2 accounts for surcharge (q) at the base of the foundation.
• Term 3 accounts for the size of the curved surface failure mechanism
Nc, N, Nq are bearing capacity factors and are related to the internal angle friction, φ’.
Term 1 Term 2 Term 3
𝑞𝑢𝑙𝑡 = 𝑐𝑁𝑐 + 𝑞𝑁𝑞 + 1
2 𝛾𝐵𝑁𝛾
Bearing Capacity Equations
Bearing Capacity Theory for a Strip Foundation
General Shear Failure of soil &
weak rock
Depth, z Surcharge, q
Term 2, (NqqSq) relates to the surcharge pressure of soil above the footing
Term 3, (0.5γBNγSγ) relates to soil in the curved failure plane, mainly beneath the footing
Width, B
Bearing Capacity Theory
Foundations in Soil and Rock
𝑞𝑢𝑙𝑡 = 𝑐𝑁𝑐 + 𝑞𝑁𝑞 + 1
2 𝛾𝐵𝑁𝛾
• cNc is due to cohesion and friction in the soil.
• qNq is due to surcharge and friction in the soil.
• 0.5BN is due to self weight and friction in the soil.
• c is cohesion
• q is the total overburden or surcharge pressure at foundation level around the
foundation = γ * footing depth. If footing base is at surface level, q = 0.
• γ is unit weight of soil
• B is the width of the foundation
Nc, N, Nq are bearing capacity factors and are related to the internal angle friction, φ’.
Bearing Capacity Theory
General Shear Failure of soil &
weak rock
Foundations in Soil and Rock
𝑞𝑢𝑙𝑡 = 𝑐𝑁𝑐 + 𝑞𝑁𝑞 + 1
2 𝛾𝐵𝑁𝛾
Nc, N, Nq are bearing capacity factors and are related to the internal angle friction, φ’.
Many researchers have proposed bearing capacity factors for soil and weak rock, e.g.
Terzaghi, Meyerhoff, Bell etc
Bearing Capacity Theory
( )
( )
+=
=
−=
+=
2 45tanN
NN
1NNN
1NN2N
2
2
q
20.5
γ
0.5
c
General Shear Failure of soil &
weak rock
Foundations in Soil and Rock
Bell’s Shape Factors & FOS Strip equation was derived for a very long footing where shearing was only 2 dimensional. However for less slender footings, shearing of rock/soil occurs all around the shape. In the case of a rectangle, the mechanism is similar to the strip but with an increased end effect. For a circular or square footing, a 3 dimensional failure mechanism will occur. These effects are reflected in the shape factors that modify the strip equation:
𝑞𝑎 = 𝐶𝑓1𝑐Nc + 𝑞Nq + 0.5𝐶𝑓2𝐵𝛾N𝛾
Fs
A factor of safety Fs is used to calculate the allowable bearing capacity qa from the ultimate bearing pressure qu. The value of Fs is usually taken to be 2.5 - 3.0. FOS used in foundation design are higher than in other areas of geotechnical design
Shape Cf1 Cf2
Strip (L/B > 6) 1.0 1.0
Rectangular (L/B = 2) 1.12 0.9
Rectangular (L/B = 5) 1.05 0.95
Square 1.25 0.85
Circular 1.2 0.7
Cf1 = shape factor Cf2 = shape factor Fs = factor of safety (typically 3) L = foundation length B = foundation breadth
Foundations in Soil and Rock
General Shear Failure of soil &
weak rock
Foundations in Soil and Rock
See Video AND note how shape affect the failure mechanism
Slender footing: Rectangle The mechanism is similar to a strip footing but with an increased end effect.
Less slender footing: Circle and Square For a circular or square footing, a 3 dimensional failure mechanism will occur
Bell’s Shape Factors & FOS
Bearing Capacity Theory in weak rock
𝑞𝑎 = 𝐶𝑓1𝑐Nc + 𝑞Nq + 0.5𝐶𝑓2𝐵𝛾N𝛾
Fs
• Bearing Capacity of Weak and Poor Rock Mass
• If the footing is at surface and foundation load is large (>>weight of rock mass), the equation can be
• simplified:
Shape Cf1 Cf2
Strip (L/B > 6) 1.0 1.0
Rectangular (L/B = 2) 1.12 0.9
Rectangular (L/B = 5) 1.05 0.95
Square 1.25 0.85
Circular 1.2 0.7
Cf1 = shape factor
Cf2 = shape factor
Fs = bulk factor of safety (typically 3)
L = foundation length
B = foundation breadth
𝑞𝑎 = 𝐶𝑓1𝑐Nc
Fs
Foundations in Soil and Rock
Example: Rectangular foundation
Ground level
1m
4m
A rectangular foundation, 2 m x 4 m is to be founded at the surface of a rock mass.
Site Investigation showed the rock has a RMR = 50. Determine qa
2m
𝑞𝑎 = 𝐶𝑓1𝑐Nc
Fs
Foundations in Soil and Rock
Shape Cf1 Cf2
Strip (L/B > 6) 1.0 1.0
Rectangular (L/B = 2) 1.12 0.9
Rectangular (L/B = 5) 1.05 0.95
Square 1.25 0.85
Circular 1.2 0.7
( )
( )
+=
=
−=
+=
2 45tanN
NN
1NNN
1NN2N
2
2
q
20.5
γ
0.5
c
Example: Rectangular foundation
Foundations in Soil and Rock
Assume Nc = 8
The relevant rock parameters are approximately: = 30 c = 0.24 MPa
Assume Nc = 8
Use equations for more accuracy
The relevant rock parameters are approximately: = 30 c = 0.24 MPa
From the chart of bearing capacity factors: Nc= 8
From Shape factors: Cf1 = 1.12
Example: Rectangular foundation
𝑞𝑎 = 𝐶𝑓1𝑐Nc
Fs =
1.12 ∗ 0.24 ∗ 8
3 = 0.7 𝑀𝑃𝑎
Note this is the allowable pressure the soil can withstand. It is a force.
Bearing capacity of footing on a slope
Foundations in Soil and Rock
( )
s
γq2cq1
F
N5.0N BCcC q
ff
a
+ =
c
H =
o N
stability number:
W y
ll ie
, D
. C
., 1
9 9
9 . F
o u
n d
a ti
o n
s o
n R
o ck
: E
n g
in e
e ri
n g
P ra
ct ic
e .
2 n
d e
d .
Lo n
d o
n :
E &
F N
S p
o n
P re
ss .
p p
.4 0
1 .
Note Nc and Nγ have changed from previous Equation
Bearing Capacity Design Issues
Foundations in Soil and Rock
• Based on past experience • Relate to rock quality and geologic
structure • Rock quality can deteriorate with time
due to weathering • Bearing capacity can usually be
adjusted by increasing footing size • Most difficult bearing capacity
problems in karstic terrain.
Bearing Capacity Design Issues - Karst
Foundations in Soil and Rock
Development of karstic features
Joint sets
Typical Bearing Capacity Values
Foundations in Soil and Rock
Bearing Capacity Design Issues
Foundations in Soil and Rock
Eurocode EN1997-1:2004 Annex G
The design of spread foundations on rock shall take account of the following features: — the deformability and strength of the rock mass and the permissible settlement of the
supported structure;
— the presence of any weak layers, for example solution features or fault zones, beneath the foundation;
— the presence of bedding joints and other discontinuities and their characteristics (for example filling, continuity, width, spacing);
— the state of weathering, decomposition and fracturing of the rock;
— disturbance of the natural state of the rock caused by construction activities, such as, for example, underground works or slope excavation, being near to the foundation.
Bearing Capacity Design Issues
Foundations in Soil and Rock
Eurocode EN1997-1:2004 Annex G
• Spread foundations on rock may normally be designed using the method of presumed bearing pressures.
• For strong intact igneous rocks, gneissic rocks, limestones and sandstones, the presumed bearing pressure is limited by the compressive strength of the concrete foundation.
• The settlement of a foundation may be assessed on the basis of comparable experience related to rock mass classification.
Eccentric Loading
Foundations in Soil and Rock
For combined direct stress and bending stress the middle third rule ensures that there is no tension under the foundation
Eccentric Loading
Foundations in Soil and Rock
For combined direct stress and bending stress the middle third rule ensures that there is no tension under the foundation. This Slide is from Engineering Principles
Shallow foundations subject to combined vertical,
horizontal and moment loads
Foundations in Soil and Rock
Examples of combined V, H, M loads: • offshore platforms • wind turbines • retaining walls
Shallow foundations subject to combined vertical,
horizontal and moment loads
Foundations in Soil and Rock
Shallow foundations subject to combined vertical,
horizontal and moment loads
Foundations in Soil and Rock
Where: Vmax is the max vertical force V is the vertical force H is the horizontal force M is the moment th = tan δ (failure by sliding at zero M and low vertical loads) tm = failure by sliding at zero M and low vertical loads C is a coefficient
As shown in the Failure envelope. Surface footings are quite vulnerable to horizontal and moment loading, with failure often occurring when H ~ Vmax/8 and M/B ~Vmax/11 Failure envelope
Shallow foundations subject to combined vertical,
horizontal and moment loads
Foundations in Soil and Rock
Shallow foundations subject to V, H, M loading: calculation of Vmax
Foundations in Soil and Rock
For a surface footing, the bearing capacity in pure vertical loading may be calculated using the general bearing capacity equation to find qult
Vmax (kN) =qult *B*L (kN)
B is breath or width of foundation L is length qult is ultimate bearing capacity shown in previous slides
Example: offshore platform foundation design
Calculate size of the square pad foundations for FOS = 3
Ignore pore water pressure in soil
Note: no cohesion, c = 0
Foundations in Soil and Rock
Note: structure has four legs/foundations in planform, and loading is assumed perpendicular to one slide of the platform
φ’ = 30֯ γ = 20 kN/m3
th = 0.4
Example: offshore platform foundation design
Foundations in Soil and Rock
φ’ = 30֯ γ = 20 kN/m3
th = 0.4
Calculate size of the square pad foundations for FOS = 3
• Steady component of vertical load on each foundation pad is:
V= 52MN / 4 = 13MN
• 8MN wind/wave loading is shared equally between the four pads giving:
H= 8MN / 4 = 2MN
• 8MN also exerts a moment of 8MN * 98m = 784 MNm about the seabed. This causes an increase in the vertical load of ΔV on the two right hand pads, and a corresponding decrease on the left hand pads, where ΔV *56 = 874/2 i.e. ΔV =7MN (per pad)
Two possible loading cases:
LHS pads, (V–ΔV ) = 6MN; H=2MN
RHS pads, (V+ ΔV ) =20MN; H=2MN
Example: offshore platform foundation design
Foundations in Soil and Rock
Calculate Vmax for the two possible loading cases. Use the VHM Parabola to calculate Vmax
th = 0.4
Case 1: 2/0.4 = 6*(Vmax-6)/Vmax Vmax = 36MN
Case 2: 2/0.4 = 20*(Vmax-20)/Vmax Vmax = 27MN
LHS pads are more critical – need Vmax = 36MN
.
𝐻
𝑡ℎ = 𝑉
𝑉𝑚𝑎𝑥 − 𝑉
𝑉𝑚𝑎𝑥
φ’ = 30֯ γ = 20 kN/m3
th = 0.4
Example: offshore platform foundation design
Calculate qa assuming a FOS = 3
Ignore pore water pressure in soil
Note: no cohesion, c = 0
Assume shape factor Sγ = 1.3
Nγ = 15.7
Sγ = 0.8
Foundations in Soil and Rock
𝑞𝑢𝑙𝑡 = 𝐶𝑓1𝑐Nc + 𝑞Nq + 0.5𝑆γ𝐵𝛾N𝛾
𝑞𝑎 = 𝑞𝑢𝑙𝑡/3 = 0.5𝑆γ𝐵𝛾N𝛾 / 3
φ’ = 30֯ γ = 20 kN/m3
th = 0.4
𝑞𝑎 = 0.5 ∗ 0.8 ∗ 𝐵 ∗ 20 ∗ 15.7/ 3
𝑞𝑎 = 0.5 ∗ 0.8 ∗ 𝐵 ∗ 20 ∗ 15.7/ 3
𝑞𝑎 = 42 ∗ 𝐵 kPa
𝑉𝑚𝑎𝑥 = 𝐵2 ∗ 𝑞𝑎 = 42 ∗ 𝐵 3𝑘𝑁
𝑉𝑚𝑎𝑥 = 36 𝑀𝑁 = 0.042 ∗ 𝐵3 𝑀𝑁
𝐵3 = 857 𝑚3 𝑜𝑟 𝑩 = 𝟗.𝟓 𝒎
Shape Factors & FOS Ignoring pore water pressure
𝑞𝑢𝑙𝑡 = 𝐶𝑓1𝑐Nc + 𝑞Nq + 0.5𝐶𝑓2𝐵𝛾N𝛾
A factor of safety Fs is used to calculate the allowable bearing capacity qa from the ultimate bearing pressure qu. The value of Fs is usually taken to be 2.5 - 3.0. FOS used in foundation design are higher than in other areas of geotechnical design
Shape Cf1 Cf2
Strip (L/B > 6) 1.0 1.0
Rectangular (L/B = 2) 1.12 0.9
Rectangular (L/B = 5) 1.05 0.95
Square 1.25 0.85
Circular 1.2 0.7
Cf1 = shape factor Cf2 = shape factor Fs = factor of safety (typically 3) L = foundation length B = foundation breadth
Foundations in Soil and Rock
𝑞𝑢𝑙𝑡 = 0.5𝐶𝑓2𝐵𝛾N𝛾
