Mechanics of rock and soil : powerpoint

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Ground mechanics

Dr. Robert Hack

ITC, University Twente

For credits and references is referred to ‘2018 PAO – Chapter 4 - Ground Mechanics – by Robert Hack’. 2

Ground Mechanics

In-situ (virgin) stress Stress around excavation Rock mass classification Numerical modeling

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Complicated loading of the ground

In the past:

Trial & error

Now:

Investigate, analyze and calculate

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Intact ground - groundmass

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Incipient vs mechanical discontinuities

Mechanicaldiscontinuities are ‘planes of mechanical weakness’ (i.e. the properties of the discontinuity make the ground weaker)

Incipientdiscontinuities are discontinuities that are not (yet) mechanical discontinuities (i.e. these do not make the ground weaker)

Incipient discontinuities may become mechanical due to weathering, stress configuration, water or gas pressure, etc.

Discontinuities are: faults, bedding planes, joints, schistosity, cleavage, fractures, etc.

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Intact rock – rock mass

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Intact soil - soil mass

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Ground vs groundmass

Isotropy versus anisotropy

Ground mass with discontinuities is (by definition) anistropic

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Geotechnical units

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Geotechnical units

Geotechnical units are defined based on: • Variation in geology

• Application • Risk

Geotechnical units are balanced again life, economical, and environment values

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The most important job of the engineer:

Rheological properties, viscosity, deformation,

strength, constitutive models

Rheology is the science of the deformation and flow of materials under stress and includes elasticity, plasticity, and viscosity.

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Intact ground

Stress-strain (normal)

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Stress-strain (shear)

G_𝑧𝑥= shear modulus in z direction due to shear stress in 𝑥

direction [𝑃𝑎]

𝜏_𝑧𝑥= shear stress in 𝑥 direction on plane with normal in z

direction [𝑃𝑎]

𝛾_𝑧𝑥= shear strain

∆𝑥 = shear deformation in 𝑥 direction [𝑚] 𝑧 = height of body [m]

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Stress-strain - creep

All rocks deform with time under constant load Creep may lead to failure

Reasons:

Solution and re-crystallization of minerals, or by the growth of micro cracks into larger cracks

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Consolidation, over-consolidation, and Compaction

Under pressure:

• Fluids and gasses are expelled

• Grain structure becomes tighter (partially elastic) • Changes occur in minerals that reduce volume Result: the ground becomes smaller irreversible

Over-consolidation: Ground has been loaded in the past more than it is at present, and thus will deform less because it has been deformed already before (loading due to glaciation, erosion, etc.)

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Unconfined and

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Unconfined Compressive Strength (UCS)

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Triaxial compressive strength

Tensile strength

Direct (DTS)and Brazilian (BTS)

𝜎𝑡 𝐵𝑟𝑎𝑧𝑎𝑙𝑖𝑎𝑛 =

2𝑃 𝜋𝐷𝑡

𝜎𝑡 𝐵𝑟𝑎𝑧𝑎𝑙𝑖𝑎𝑛 = Brazalian Tensile Strength 𝐵𝑇𝑆 [𝑃𝑎 ]

𝑃 = load on sample at failure [𝑁] 𝐷 = diameter [𝑚] 𝑡 = thickness [𝑚]

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Point Load Strength (PLS)

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Impact and rebound tests

Schmidt Hammer & Equotip

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Simple means’ field estimated for cohesive soil and

intact rock strength

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Discontinuities

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Isolated discontinuities vs discontinuity sets

Isolated discontinuities:

• Fault, or sets with a very large spacing (>> than the engineering structure, e.g. >> than tunnel diameter, etc.)

Discontinuities in sets:

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How to group discontinuities in sets?

Scanline

Group discontinuities in sets

Studied assessment and interpreted properties and parameters: • Visually inventory of the different discontinuity sets (based on

orientation, spacing, and the character of the discontinuity, e.g. infill and roughness)

• A mean orientation only of those discontinuities that belong to the discontinuity set

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Borehole cores

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Block size and form

Large is good; small is bad Cubic is good; flaky is bad

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Discontinuity shear strength

Discontinuity shear strength

Discontinuity shear strength depends on:

• Type of discontinuity (e.g. persistent, non-persistent, and abutting) • Roughness on different scales

• Material friction of discontinuity wall

• Condition of discontinuities (e.g. strength of asperities)

• Infill (cemented, non-softening, softening, gouge, flowing material) • History of discontinuity (fitting or non-fitting, and sheared or not

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Persistence

Persistent(movement can take place without further displacement) Abutting(before movement is possible abutting blocks have to move) Non-persistent(before movement can take place the discontinuity has to extend and intact rock broken

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Discontinuity shear strength

Roughness contribution to shear strength depends on: • Overriding

• Shearing asperities • Deformation of asperities

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Different scale roughness

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Discontinuity strength of asperities

Roughness also depending on the strength of asperities:

• Discontinuity asperities often weaker than intact rock, due to, for example, weathering

• Occasionally stronger than intact rock due to, for example, coating with a strong mineral

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Stepped discontinuity

If

φ + i-angle ≥ 90°(e.g. material friction + roughness ≥ 90°)

then

No movement is possible without shearing of asperities (which gives ‘cohesion’ in the Mohr-Coulomb shear criterion)

Three-dimensionality of discontinuity surfaces

In real rocks only ONEperfect fit; any displacement leads to a reduction of shear strength

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Discontinuity infill

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Infill description for estimating shear strength of

discontinuities

Infill material in discontinuity:

• Cemented infill (both sides of discontinuity are cemented, ‘glued’, together by an agent)

• Non-softening – softening infill (not cemented) (e.g. does it facilitate, ‘lubricate’, movement, for example clay does, quartz grains do not • Thickness of the infill

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Thickness of infill

• If there are points of contact between the discontinuity walls, the shear strength is mainly determined by the properties of the discontinuity walls.

• If the infill thickness in the discontinuity is less than about the grain size of the intact rock grains or minerals in the discontinuity walls or of the grain size of the infill material, the shear strength of the

discontinuity is that of the infill but influenced by the discontinuity wall material.

• If the infill thickness is larger than the grain size of the discontinuity wall and the grain size of the infill, the shear strength is that of the infill material

History of discontinuity

(fitting or non-fitting, and

sheared or not sheared

asperities)

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Fitting – non-fitting of discontinuity walls

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History of discontinuity

History important because any displacement may give: • Sheared asperities (hence less rough surfaces) • Overridden asperities (non-fitting surface) • Breaking of cemented infill

• Re-molding or squeezing out of infill material (respectively reduces and increases shear strength)

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Fluid and gas

pressure in

discontinuity

Aperture, openness, and permeability of a

discontinuity

Aperture often used, but what does it mean?

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Testing discontinuity shear strength

• Laboratory (already discussed in intact ground) • Field

• Tilt test

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Tilt test

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‘Sliding criterion’ (SSPC) roughness determination

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Sliding criterion vs tilt test

Sliding criterion comparable to tilt test:

• Tilt test: maximum angle for stability of a block in hand sample (maximum 0.10 m height)

• Sliding criterion: maximum angle for stability of a block on a

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Barton JRC concept

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Ground mass

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Anisotropy of permeability

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Deformation ground mass

Deformation rock mass virtually always:

• Plastic (due to movements along discontinuities) • Anisotropic

• Time dependent

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Deformation

ground mass

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Anisotropy of deformation

Simple orthotropic symmetry

𝜀𝑥 𝜀𝑦 𝜀𝑧 𝛾𝑥𝑦 𝛾𝑦𝑧 𝛾𝑧𝑥 = 1 𝐸𝑥 −𝜐𝑦𝑥 𝐸𝑦 −𝜐𝑧𝑥 𝐸𝑧 0 0 0 −𝜐𝑦𝑥 𝐸𝑥 1 𝐸𝑦 −𝜐𝑧𝑦 𝐸𝑧 0 0 0 −𝜐𝑧𝑥 𝐸𝑥 −𝜐𝑧𝑦 𝐸𝑦 1 𝐸𝑧 0 0 0 0 0 0 1 𝐺𝑥𝑦 0 0 0 0 0 0 1 𝐺𝑦𝑧 0 0 0 0 0 0 1 𝐺𝑧𝑥 𝜎𝑥 𝜎𝑦 𝜎𝑧 𝜏𝑥𝑦 𝜏𝑦𝑧 𝜏𝑧𝑥

𝜀𝑎= strain in 𝑎 direction 𝛾𝑎𝑏= shear strain due to shear stress 𝜏𝑎𝑏

𝜎𝑎= stress in 𝑎 direction [𝑃𝑎]

𝜏𝑏𝑎= shear stress in 𝑎 direction on plane with normal in 𝑏 direction [𝑃𝑎]

𝐸𝑎= elastic Young′s modulus of deformation in 𝑎 direction [𝑃𝑎]

𝜐𝑏𝑎= Poisson′s ratio of expanding in 𝑎 direction due to stress in 𝑏 direction

𝐺𝑏𝑎= shear modulus in 𝑏 direction due to shear stress in 𝑎 direction [𝑃𝑎]

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Strength (failure) of ground mass

What is strength in ground mas?

Compression: not existing? Practical:

Failure is more deformation than allowed

Tensile strength: not existing

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Weathering

Exposure of weathered granodiorite (an intrusive, igneous rock comparable to granite); zones of fresh, hard, and strong grano diorite (bluish-grey colored) occur in between zones with granodiorite fallen apart in smaller blocks and zones completely decomposed into loose soil material (brownish colored). Note the general increase of decay upwards to the original topographical surface (vegetated). (Road T710, Falset-Gratallops, Catalunya, Spain; photograph courtesy of Verwaal 2002).

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Weathering

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Weathering

Weathering is:

▪ Chemical and physical change due to surface processes (mostly water & air)

Mostly leads to disintegration of the rock material and rock mass Sometimes to hardening (for example, due to cementation)

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Weathering effects and time

Effects: _Time:

Ground Pressure – virgin stress field

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Mn-made stress field

Local stress and strain (active & passive ground

pressure)

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Time effects and creep

Four different time effects:

I)

No strain can be instant (would require infinite velocity of mass)

(If stress is applied, shock waves of stress-strain will travel trough the rock and rock mass. It will take some time before stress and strain will be in equilibrium throughout the rock and rock mass.)

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Time effects and creep

II)

All rocks show some (for some rocks limited) effects of time dependent deformation. This is often described as creep. The effect is responsible for the delay in, for example, collapses of underground excavations. When a rock mass is loaded with a new stress environment due to the excavation and if the stress levels do not exceed immediately the strength of the rock mass, the excavation will not fail immediately. However, small micro cracks may develop in the rock if the stresses at the wall are more than half the UCS strength (rule of the thumb). The number of cracks will increase over time and after some time the rock will fail.

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Time effects and creep

III)

All rocks show a long-term creep effect. The rock deforms and after some time the rock will fail even if the rock is stressed well below half of the UCS strength. The mechanisms for this effect are largely unknown, but it is thought that re-crystallization under stress may play a role.

IV) Long-term creep is likely responsible for some collapses of excavations after very long time spans, sometimes up to 2000 years

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Stress around underground excavation (arching)

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Stress around underground excavation (arching)

Ground carries itself

Ground is not carried by the support

Support only to keep ground material at bay

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Rock mass classification

Rock mass classification

Virtual impossible to calculate analyticalwith a discontinuous rock mass Numericalcalculations also problematic

Therefore:

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Rock mass classification

Rock mass classification relates the stability or design of an application (tunnel, slope, etc.) empirically to a set of (easily) obtainable properties of the rock mass (such as ‘simple means intact rock strength’, block size, shear strength of discontinuities by tilt test or visual observation, etc.)

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Bieniawski’s Rock Mass Rating (RMR)

Barton’s Q-system

𝑅𝑄𝐷 = Rock Quality Designation 𝐽𝑛= Joint Set number 𝐽𝑟= Joint Roughness number

𝐽𝑎= Joint Alteration number 𝐽𝑤 = Joint Water reduction factor

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Barton’s Q-system

Geological Strength

Index (GSI)

𝜎1′, 𝜎3′ = major respectively minor principal stress

𝜎𝑐𝑖 = Unconfined Compressive Strength (𝑈𝐶𝑆)

mb, s, a groundmass constants

depending on lithology,

the GSI value from the figure, and damage due to the method of excavation

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Excavation based on deformation

New Austrian Tunneling Method (NATM)

Lunardi’s Analysis of Controlled Deformations (ADECO-RS) methodology - new Italian Tunneling Method (NITM)

Lunardi’s Analysis of Controlled Deformations

(ADECO-RS) methodology

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Numerical modelling

Numerical analyses

1 Distinct block model

The rock mass is modelled as blocks. Each discontinuity is modelled independent, and the intact blocks are modelled as a continuous material in a distinct element program (for example, UDEC, 3DEC)

2 Continuous- finite element program (or similar)

The discontinuities are modelled in a constitutive model, and this constitutive model is used within a continuous numerical calculation program (for example, FLAC, 3DFLAC, Plaxis)

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Numerical analyses

3 Particle Flow Code’ (PFC)

Materials are modelled with spherical particles that may be shaped in objects of any form by bounding (cementing) particles together. PFC is particularly suited for problems where many objects interact, flow features, and objects that fracture in many blocks

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Continuous

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