AASHTO LRFD:AASHTO LRFD:AASHTO LRFD:AASHTO LRFD: Structural Foundations and Earth Retaining Structural Foundations and Earth Retaining Structural Foundations and Earth Retaining Structural Foundations and Earth Retaining

StructuresStructuresStructuresStructures � Specification Background Specification Background Specification Background Specification Background What’s Happening Now!What’s Happening Now!What’s Happening Now!What’s Happening Now! � Limit States, Soil and Rock PropertiesLimit States, Soil and Rock PropertiesLimit States, Soil and Rock PropertiesLimit States, Soil and Rock Properties � Deep FoundationsDeep FoundationsDeep FoundationsDeep Foundations � Shallow FoundationsShallow FoundationsShallow FoundationsShallow Foundations � Earth Retaining StructuresEarth Retaining StructuresEarth Retaining StructuresEarth Retaining Structures Jerry DiMaggio, P. E., Principal Bridge Engineer (Geotechnical)Jerry DiMaggio, P. E., Principal Bridge Engineer (Geotechnical)Jerry DiMaggio, P. E., Principal Bridge Engineer (Geotechnical)Jerry DiMaggio, P. E., Principal Bridge Engineer (Geotechnical) Federal Highway Administration Office of Bridge Technology Washington D.C.

? New Legal Load

AASHTO Specification Background: Geotechnical AASHTO Specification Background: Geotechnical AASHTO Specification Background: Geotechnical AASHTO Specification Background: Geotechnical Engineering PresenceEngineering PresenceEngineering PresenceEngineering Presence

* TRB/ NCHRP Activities (A LOT!)* TRB/ NCHRP Activities (A LOT!)* TRB/ NCHRP Activities (A LOT!)* TRB/ NCHRP Activities (A LOT!) * * * * Geotechnical Engineering does NOT have a broad Geotechnical Engineering does NOT have a broad Geotechnical Engineering does NOT have a broad Geotechnical Engineering does NOT have a broad

based presence on AASHTO SubCommittees and based presence on AASHTO SubCommittees and based presence on AASHTO SubCommittees and based presence on AASHTO SubCommittees and Task Forces as do other technical specialties.Task Forces as do other technical specialties.Task Forces as do other technical specialties.Task Forces as do other technical specialties.

* SubCommittee on Construction (guide construction * SubCommittee on Construction (guide construction * SubCommittee on Construction (guide construction * SubCommittee on Construction (guide construction

specs) specs) specs) specs) * SubCommittee on Materials (specs on materials and * SubCommittee on Materials (specs on materials and * SubCommittee on Materials (specs on materials and * SubCommittee on Materials (specs on materials and

testing standards) testing standards) testing standards) testing standards) * SubCommittee on Bridges and Structures (specs on * SubCommittee on Bridges and Structures (specs on * SubCommittee on Bridges and Structures (specs on * SubCommittee on Bridges and Structures (specs on

materials/ systems, design, and construction) materials/ systems, design, and construction) materials/ systems, design, and construction) materials/ systems, design, and construction)

History of AASHTO: Design & Construction History of AASHTO: Design & Construction History of AASHTO: Design & Construction History of AASHTO: Design & Construction Specifications for Bridges and StructuresSpecifications for Bridges and StructuresSpecifications for Bridges and StructuresSpecifications for Bridges and Structures

* First structural * First structural * First structural * First structural “Guideline Specification” early 1930s (A code yet NOT A code!).(A code yet NOT A code!).(A code yet NOT A code!).(A code yet NOT A code!). * First “significant” Geotechnical content * First “significant” Geotechnical content * First “significant” Geotechnical content * First “significant” Geotechnical content 1989.1989.1989.1989. * First LRFD specification 1994 (Current * First LRFD specification 1994 (Current * First LRFD specification 1994 (Current * First LRFD specification 1994 (Current –––– 2004, 32004, 32004, 32004, 3rdrdrdrd

edition).edition).edition).edition). * * * * First REAL Geotechnical involvementFirst REAL Geotechnical involvementFirst REAL Geotechnical involvementFirst REAL Geotechnical involvement in Bridge in Bridge in Bridge in Bridge

SubCommittee activities @ SubCommittee activities @ SubCommittee activities @ SubCommittee activities @ 1996.1996.1996.1996. (Focus on mse (Focus on mse (Focus on mse (Focus on mse walls).walls).walls).walls).

* Technical advances to Standard Specifications * Technical advances to Standard Specifications * Technical advances to Standard Specifications * Technical advances to Standard Specifications STOPPED STOPPED STOPPED STOPPED in 1998in 1998in 1998in 1998 to encourage LRFD use (secret).to encourage LRFD use (secret).to encourage LRFD use (secret).to encourage LRFD use (secret).

* Major rewrites needed to walls and foundations * Major rewrites needed to walls and foundations * Major rewrites needed to walls and foundations * Major rewrites needed to walls and foundations sections (NOW COMPLETE).sections (NOW COMPLETE).sections (NOW COMPLETE).sections (NOW COMPLETE).

“Geotechnical Scope”:“Geotechnical Scope”:“Geotechnical Scope”:“Geotechnical Scope”: AASHTO Design & AASHTO Design & AASHTO Design & AASHTO Design & Construction Specifications for Bridges and Construction Specifications for Bridges and Construction Specifications for Bridges and Construction Specifications for Bridges and StructuresStructuresStructuresStructures

* * * * Topics Included:Topics Included:Topics Included:Topics Included: Subsurface Investigations, soil and Subsurface Investigations, soil and Subsurface Investigations, soil and Subsurface Investigations, soil and rock properties, shallow foundations, driven piles, rock properties, shallow foundations, driven piles, rock properties, shallow foundations, driven piles, rock properties, shallow foundations, driven piles, drilled shafts, rigid and flexible culverts, abutments, drilled shafts, rigid and flexible culverts, abutments, drilled shafts, rigid and flexible culverts, abutments, drilled shafts, rigid and flexible culverts, abutments, WALLS (cantilever, mse, crib, bin, anchor).WALLS (cantilever, mse, crib, bin, anchor).WALLS (cantilever, mse, crib, bin, anchor).WALLS (cantilever, mse, crib, bin, anchor).

* * * * Topics NOT addressedTopics NOT addressedTopics NOT addressedTopics NOT addressed: integral abutments, micropiles, : integral abutments, micropiles, : integral abutments, micropiles, : integral abutments, micropiles, augercast piles, soil nails, reinforced slopes, and ALL augercast piles, soil nails, reinforced slopes, and ALL augercast piles, soil nails, reinforced slopes, and ALL augercast piles, soil nails, reinforced slopes, and ALL SOIL and ROCK EARTHWORK FEATURES. SOIL and ROCK EARTHWORK FEATURES. SOIL and ROCK EARTHWORK FEATURES. SOIL and ROCK EARTHWORK FEATURES.

Standard and LRFD AASHTO SpecificationsStandard and LRFD AASHTO SpecificationsStandard and LRFD AASHTO SpecificationsStandard and LRFD AASHTO Specifications

* Currently AASHTO has 2 separate * Currently AASHTO has 2 separate * Currently AASHTO has 2 separate * Currently AASHTO has 2 separate specifications: Standard specs 17specifications: Standard specs 17specifications: Standard specs 17specifications: Standard specs 17thththth edition and edition and edition and edition and LRFD, 2004 3rd edition.LRFD, 2004 3rd edition.LRFD, 2004 3rd edition.LRFD, 2004 3rd edition.

* Standard Specifications use a combination of * Standard Specifications use a combination of * Standard Specifications use a combination of * Standard Specifications use a combination of

working stress and load factor design platform.working stress and load factor design platform.working stress and load factor design platform.working stress and load factor design platform. * LRFD uses a limit states design platform with * LRFD uses a limit states design platform with * LRFD uses a limit states design platform with * LRFD uses a limit states design platform with

different load and resistance factors (than LFD).(than LFD).(than LFD).(than LFD).

LRFD IMPLEMENTATION STATUSLRFD IMPLEMENTATION STATUSLRFD IMPLEMENTATION STATUSLRFD IMPLEMENTATION STATUS

Geotechnically, most States still use a working stress Geotechnically, most States still use a working stress Geotechnically, most States still use a working stress Geotechnically, most States still use a working stress approach for earthworks, structural foundations, and approach for earthworks, structural foundations, and approach for earthworks, structural foundations, and approach for earthworks, structural foundations, and earth retaining structures. Several States have totally earth retaining structures. Several States have totally earth retaining structures. Several States have totally earth retaining structures. Several States have totally adopted LRFD.adopted LRFD.adopted LRFD.adopted LRFD.

Many State Geo/Structural personnel and consultants Many State Geo/Structural personnel and consultants Many State Geo/Structural personnel and consultants Many State Geo/Structural personnel and consultants

ARE NOT FAMILARARE NOT FAMILARARE NOT FAMILARARE NOT FAMILAR with the content of LRFD 3with the content of LRFD 3with the content of LRFD 3with the content of LRFD 3rdrdrdrd edition. edition. edition. edition.

“AASHTO and FHWA have agreed that all state “AASHTO and FHWA have agreed that all state “AASHTO and FHWA have agreed that all state “AASHTO and FHWA have agreed that all state

DOTs will use LRFD for NEW structure design DOTs will use LRFD for NEW structure design DOTs will use LRFD for NEW structure design DOTs will use LRFD for NEW structure design by 10/07.”by 10/07.”by 10/07.”by 10/07.”

What are UNIQUE Geotechnical issues related to What are UNIQUE Geotechnical issues related to What are UNIQUE Geotechnical issues related to What are UNIQUE Geotechnical issues related to LRFD?LRFD?LRFD?LRFD?

* Strong influence of construction on design.* Strong influence of construction on design.* Strong influence of construction on design.* Strong influence of construction on design. * GEOTECHs strong bias toward performance based * GEOTECHs strong bias toward performance based * GEOTECHs strong bias toward performance based * GEOTECHs strong bias toward performance based

specifications.specifications.specifications.specifications. * Natural variability of GEO materials.* Natural variability of GEO materials.* Natural variability of GEO materials.* Natural variability of GEO materials. * Variability in the type, and frequency of tests, and * Variability in the type, and frequency of tests, and * Variability in the type, and frequency of tests, and * Variability in the type, and frequency of tests, and

method to determine design property values of soil method to determine design property values of soil method to determine design property values of soil method to determine design property values of soil and rock.and rock.and rock.and rock.

* Differences between earthwork and structural * Differences between earthwork and structural * Differences between earthwork and structural * Differences between earthwork and structural foundation design model approaches.foundation design model approaches.foundation design model approaches.foundation design model approaches.

* Influence of regional and local factors.* Influence of regional and local factors.* Influence of regional and local factors.* Influence of regional and local factors. * * * * General lack of data on limit state conditions.General lack of data on limit state conditions.General lack of data on limit state conditions.General lack of data on limit state conditions.

What Should I Know and Do?What Should I Know and Do?What Should I Know and Do?What Should I Know and Do? * Become familiar with BOTH the AASHTO standard * Become familiar with BOTH the AASHTO standard * Become familiar with BOTH the AASHTO standard * Become familiar with BOTH the AASHTO standard

specifications and LRFD specs.specifications and LRFD specs.specifications and LRFD specs.specifications and LRFD specs. * Develop an understanding of your agency’s current * Develop an understanding of your agency’s current * Develop an understanding of your agency’s current * Develop an understanding of your agency’s current

design practice with your structures office.design practice with your structures office.design practice with your structures office.design practice with your structures office. * Develop and compare results for SEVERAL example * Develop and compare results for SEVERAL example * Develop and compare results for SEVERAL example * Develop and compare results for SEVERAL example

problems with LRFD and YOUR standard design problems with LRFD and YOUR standard design problems with LRFD and YOUR standard design problems with LRFD and YOUR standard design practice.practice.practice.practice.

* Translate your current practice to an LRFD format with * Translate your current practice to an LRFD format with * Translate your current practice to an LRFD format with * Translate your current practice to an LRFD format with your structural office.your structural office.your structural office.your structural office.

* Communicate findings of your example problem * Communicate findings of your example problem * Communicate findings of your example problem * Communicate findings of your example problem comparisons to AASHTO’s SubCommitteee members.comparisons to AASHTO’s SubCommitteee members.comparisons to AASHTO’s SubCommitteee members.comparisons to AASHTO’s SubCommitteee members.

What Happening Now?What Happening Now?What Happening Now?What Happening Now? * FHWA sponsored a complete rewrite of Section 10 during 2004. * FHWA sponsored a complete rewrite of Section 10 during 2004. * FHWA sponsored a complete rewrite of Section 10 during 2004. * FHWA sponsored a complete rewrite of Section 10 during 2004.

The rewrite was prepared by National subject matter experts The rewrite was prepared by National subject matter experts The rewrite was prepared by National subject matter experts The rewrite was prepared by National subject matter experts and had broad input from a number of Key State Dots, and had broad input from a number of Key State Dots, and had broad input from a number of Key State Dots, and had broad input from a number of Key State Dots, (including T(including T(including T(including T----15 member States), and the Geotechnical 15 member States), and the Geotechnical 15 member States), and the Geotechnical 15 member States), and the Geotechnical community (ASCE community (ASCE community (ASCE community (ASCE ---- GI, DFI, ADSC, PDCA).GI, DFI, ADSC, PDCA).GI, DFI, ADSC, PDCA).GI, DFI, ADSC, PDCA).

* During the Proposed spec development @ 2000 comments * During the Proposed spec development @ 2000 comments * During the Proposed spec development @ 2000 comments * During the Proposed spec development @ 2000 comments

were addressed. The Proposed spec was then distributed to were addressed. The Proposed spec was then distributed to were addressed. The Proposed spec was then distributed to were addressed. The Proposed spec was then distributed to all States for review. An additional @ 1000 comments were all States for review. An additional @ 1000 comments were all States for review. An additional @ 1000 comments were all States for review. An additional @ 1000 comments were addressed.addressed.addressed.addressed.

* The revised Proposed Specification was advanced and * The revised Proposed Specification was advanced and * The revised Proposed Specification was advanced and * The revised Proposed Specification was advanced and

approved by the AASHTO’s Bridge and Structures Subapproved by the AASHTO’s Bridge and Structures Subapproved by the AASHTO’s Bridge and Structures Subapproved by the AASHTO’s Bridge and Structures Sub----Committeee in June 2005. Committeee in June 2005. Committeee in June 2005. Committeee in June 2005.

The revised Proposed Specification is used in the NHI LRFD The revised Proposed Specification is used in the NHI LRFD The revised Proposed Specification is used in the NHI LRFD The revised Proposed Specification is used in the NHI LRFD Substructure course which currently available.Substructure course which currently available.Substructure course which currently available.Substructure course which currently available.

Fundamentals of LRFDFundamentals of LRFDFundamentals of LRFDFundamentals of LRFD Principles of Limit State DesignsPrinciples of Limit State DesignsPrinciples of Limit State DesignsPrinciples of Limit State Designs

* Define the term “Limit State” * Define the term “Limit State” * Define the term “Limit State” * Define the term “Limit State” * Define the term “Resistance”* Define the term “Resistance”* Define the term “Resistance”* Define the term “Resistance” * Identify the applicability of each of the four primary limit * Identify the applicability of each of the four primary limit * Identify the applicability of each of the four primary limit * Identify the applicability of each of the four primary limit

states.states.states.states. * Understand the components of the fundamental LRFD * Understand the components of the fundamental LRFD * Understand the components of the fundamental LRFD * Understand the components of the fundamental LRFD

equation.equation.equation.equation.

A Limit State is a A Limit State is a A Limit State is a A Limit State is a defined conditiondefined conditiondefined conditiondefined condition beyond which a beyond which a beyond which a beyond which a structural component, ceases to satisfy the structural component, ceases to satisfy the structural component, ceases to satisfy the structural component, ceases to satisfy the

provisions for which it is designed.provisions for which it is designed.provisions for which it is designed.provisions for which it is designed.

Resistance is a Resistance is a Resistance is a Resistance is a quantifiable value that definesquantifiable value that definesquantifiable value that definesquantifiable value that defines the the the the point beyond which the particular limit state under point beyond which the particular limit state under point beyond which the particular limit state under point beyond which the particular limit state under

investigation for a particular component will be investigation for a particular component will be investigation for a particular component will be investigation for a particular component will be exceeded.exceeded.exceeded.exceeded.

Resistance can be defined in terms of:Resistance can be defined in terms of:Resistance can be defined in terms of:Resistance can be defined in terms of:

* Load/Force (static/ dynamic, dead/ live)* Load/Force (static/ dynamic, dead/ live)* Load/Force (static/ dynamic, dead/ live)* Load/Force (static/ dynamic, dead/ live) * Stress (normal, shear, torsional)* Stress (normal, shear, torsional)* Stress (normal, shear, torsional)* Stress (normal, shear, torsional) * Number of cycles* Number of cycles* Number of cycles* Number of cycles * Temperature* Temperature* Temperature* Temperature * Strain* Strain* Strain* Strain

Limit StatesLimit StatesLimit StatesLimit States

* Strength Limit State* Strength Limit State* Strength Limit State* Strength Limit State * Extreme Event Limit State* Extreme Event Limit State* Extreme Event Limit State* Extreme Event Limit State * Service Limit State * Service Limit State * Service Limit State * Service Limit State * Fatigue Limit State* Fatigue Limit State* Fatigue Limit State* Fatigue Limit State

L

I

S

T

Strength Limit State

Extreme Event Limit State

Service Limit State

Service Limit State

Rn / FS ≥≥≥≥ ΣΣΣΣQ

ΣηΣηΣηΣηiγγγγiQi ≤ Rr = φφφφRn

ηi =

γi =

Qi =

Rr =

φ =

Rn =

Load modifier (eta)

Load factor (gamma)

Force effect

Factored resistance

Resistance factor (phi)

Nominal resistance

ΣηΣηΣηΣηiγγγγiQi ≤ Rr = φφφφRn

f(γγγγ,φφφφ)

Qn

Rn

Q

R

γ Qn

φ Rn

Q or R

Pro

babili

ty o

f O

ccurr

ence

η

Subsurface MaterialsSubsurface MaterialsSubsurface MaterialsSubsurface Materials

* Soil

* Rock

* Water

* Organics

10.4 SOIL AND ROCK PROPERTIES 10.4.1 Informational Needs 10.4.2 Subsurface Exploration 10.4.3 Laboratory Tests 10.4.3.1 Soil Tests 10.4.3.2 Rock Tests 10.4.4 In-situ Tests 10.4.5 Geophysical Tests 10.4.6 Selection of Design Properties 10.4.6.1 Soil Strength 10.4.6.1.1 Undrained strength of Cohesive Soils 10.4.6.1.2 Drained Strength of Cohesive Soils 10.4.6.1.3 Drained strength of Granular Soils 10.4.6.2 Soil Deformation 10.4.6.3 Rock Mass Strength 10.4.6.4 Rock Mass Deformation 10.4.6.5 erodibility of rock

Overview of Soil and Rock MaterialsOverview of Soil and Rock MaterialsOverview of Soil and Rock MaterialsOverview of Soil and Rock Materials

* * * * Apply the principle of effective stress to Apply the principle of effective stress to Apply the principle of effective stress to Apply the principle of effective stress to computation of vertical effective stresscomputation of vertical effective stresscomputation of vertical effective stresscomputation of vertical effective stress

* Use the Mohr* Use the Mohr* Use the Mohr* Use the Mohr----Coulomb equation to determine Coulomb equation to determine Coulomb equation to determine Coulomb equation to determine the shear strength of soils. the shear strength of soils. the shear strength of soils. the shear strength of soils.

* Understand the difference between drained and * Understand the difference between drained and * Understand the difference between drained and * Understand the difference between drained and undrained strengthundrained strengthundrained strengthundrained strength

* Know what field or laboratory test should be * Know what field or laboratory test should be * Know what field or laboratory test should be * Know what field or laboratory test should be performed to obtain the required soil or rock performed to obtain the required soil or rock performed to obtain the required soil or rock performed to obtain the required soil or rock properties.properties.properties.properties.

* Understand the difference between the intact * Understand the difference between the intact * Understand the difference between the intact * Understand the difference between the intact properties of rock and the rock mass properties of rock and the rock mass properties of rock and the rock mass properties of rock and the rock mass properties.properties.properties.properties.

Soil Characteristics

* Composed of individual grains of rock

* Relatively low strength

* Coarse grained (+ #200)

* High permeability

* Fine grained (- #200)

* Low permeability

* Time dependant effects

Rock Characteristics

* Strength

* Intermediate geomaterials, qu = 50-1500 psi

* Hard rock, qu > 1500 psi

* Rock mass properties

% F

ine

r b

y W

eig

ht

% F

ine

r b

y W

eig

ht

Uniform

Well Graded

Gravel Sand Silt Clay

Grain Diameter (mm) Grain Diameter (mm)

100

100 10 1 0.1 0.01 0.001

US Standard Sieves 3” 2” 1” 3/4” 3/8” 4 6 10 20 40 60 100 200

80

60

40

20

0

Atterberg Limits

The water content at which a soil changes state

PI = LL - PL

Solid Semi-Solid Plastic Liquid

SL PL LL PI

Increasing water content

Effective Stress – Spring Analogy

∗ σ∗ σ∗ σ∗ σ’ = σσσσ – u

∗ σ∗ σ∗ σ∗ σ’ = effective

stress

∗ σ∗ σ∗ σ∗ σ = total stress

* u = pore pressure

X

σσσσ’

σσσσ

u

P

Soil Shear Strength

τ’ = c’ + σn’ tan φf’

σσσσ’a

σσσσ’a

σσσσ’r σσσσ’r

ττττ’

σσσσ’n φφφφ’

σσσσ’n

ττττ’f

σσσσ’

ττττ’

c’

Strength envelope

Undrained Strength of Cohesive Soils, su

Unconfined Compression su = qu/2

Vane Shear Test

su

σσσσ qu

φφφφ=0

Typical Values su = 250 - 4000 psf

Drained Strength of Cohesive Soils, c’ and φφφφ’f

Triaxial Compression CU Test

Typical Values c’ = 100 - 500 psf

φ’f = 20o - 35o

Drained Strength of Cohesionless Soils, φφφφ’f

Standard Penetration Test (SPT)

Typical Values φ’f = 25o - 45o

Friction angle is correlated to SPT results.

φφφφ’f

σσσσ’

q’

c=0

For N160 = 10, select φ’f = 30o

(modified after Bowles, 1977)

N160 φf

<4 25-30

4 27-32

10 30-35

30 35-40

50 38-43

Soil Deformation

0

-2

-4

-6

-8

-10

-12 1 10 100 1000 10000

Time (days)

Sett

lem

en

t (i

n)

Initial elastic settlement (all soils)

Primary consolidation Secondary consolidation

Fine-grained (cohesive) soils

Consolidation Properties

Log10 σv’

Void

Ratio (

e)

σp’ = Preconsolidation Stress

Cs

Cr

Cc

0.1 1 10 100

0.5

1

eo

One log cycle ∆e=Cα=0.06

0.1 1 10 100 1000 10000

Elapsed Time (min)

Void

ratio (

e)

2.65

2.6

2.55

2.5

2.45

2.4

2.35

2.3

2.25

Stress Range, 40 – 80 kPa

tp

Typical Consolidation Properties

Property Typical Value

Cc 0.1 to 1.0

Cr 10 % of Cc

Cs Approximately Cr

Cα 4% to 6% of Cc

Cv 0.01 to 1.0 ft2/day

Elastic Properties of Soil

Young’s Modulus, Es

� Typical values, 20 – 2000 tsf

Poisson’s Ratio, υ � Typical values, 0.2 – 0.5

Shear Modulus, G � Typical values, Es / [2 (1 + υ)]

Determination by correlation to N160 or su, or in-situ tests

Rock Properties

Laboratory testing is for small intact rock specimens

Rock mass is too large to be tested in lab or field

Rock mass properties are obtained by correlating intact rock to large-scale rock mass behavior – failures in tunnels and mine slopes

Requires geologic expertise

Intact Rock Strength

Point Load Test

Unconfined Compression, qu

Typical Values qu = 1500 - 50000 psi

Rock Quality Le

ng

th, L

0.8 ft

0.7 ft

0.8 ft

0.6 ft

0.2 ft

0.7 ft

Sound

Not sound, highly weathered

Not sound, centerline pieces < 4 inches, highly weathered

Sound

Not sound

Sound

Core Run Total = 4 ft

CR = 95% RQD = 53%

CSIR Rock Mass Rating System

This system is based on qu, RQD, joint spacing, joint condition and

water condition.

Rock Mass Strength

C1’

Sh

ear

str

ess,

ττ ττ

Effective Normal Stress, σσσσ’

σσσσtm σσσσ3 σσσσ1 σσσσ

ττττ

φφφφ’i

ττττ = (cot φφφφ’i – cos φφφφ’i)mqu/8

φφφφ’i = tan-1(4 h cos2[30+0.33sin-1(h-3/2)]-1)-1/2

h = 1 + 16(mσσσσ’n+squ)/(3m2qu)

Rock-Mass Quality and Material Constants

Values of the parameters m and s are determined based on empirical

correlation to rock type and RMR

Intact Rock Deformation, Ei

Typical values range from 1000 to 13000 ksi

Poisson’s Ratio, υυυυ

Typical values range from 0.1 to 0.3

Rock Mass Deformation

Eα = 2 RMR - 100

( )40

10RMR

M 10145,000E−

×=90

70

50

30

10

In s

itu m

odulu

s of

defo

rmation, E

M (

GPa)

10 30 50 70 90

12

10

8

6

4

2

(psi x 106)

Rock mass rating RMR

GEC 5GEC 5GEC 5GEC 5 FHWAFHWAFHWAFHWA----IFIFIFIF----02020202----034034034034

Jerry A. DiMaggio P. E.Jerry A. DiMaggio P. E.Jerry A. DiMaggio P. E.Jerry A. DiMaggio P. E. Principal Bridge Engineer Principal Bridge Engineer Principal Bridge Engineer Principal Bridge Engineer TEL: (202) 366TEL: (202) 366TEL: (202) 366TEL: (202) 366----1569156915691569 FAX: (202) 366FAX: (202) 366FAX: (202) 366FAX: (202) 366----3077307730773077

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