The Coupled Hydro-thermo-mechanical Process

in Soils and its Implications for Emerging

Geotechnical Engineering Practice

Xiong (Bill) Yu, Ph.D., P.E.

Associate Professor, Department of Civil Engineering, Case Western

Reserve University, 216-368-6247, xxy21@case.edu

Purdue Geotechnical Society Workshop

April 19, 2013

About myself

Purdue Graduate

Current program affiliation

Geotechnical engineering

Infrastructure engineering

EECS and other programs

Current research focus

Sensor technology

Field instrumentation

Durable and multifunctional civil engineering

materials

Sustainability

Energy geotechnology

Multiphysics stands for the coupling of multiple fields

Common observations in soil

Phase change of pore water involves energy significantly alter the soil

properties such as elastic modulus (hydraulic and mechanical).

Fluid transfer due to the temperature gradient (Philip, 1957; Cary,

1964). (Coupling between thermal and hydraulic)

Mechanical constraints: the mechanical field can only response partly

to the other field and thus in turn affect the other field (Mechanical on

thermal and hydraulic).

…

We are interested to explore the common scientific basis to the

multiphysics process in soils and other geomaterials

Multiphysics versus Single Field

Impacts on Engineering

Frozen soil covers 60% the earth surface

Climate effects on infrastructure

Geothermal energy

Green energy source

Gas hydrate

A huge potential energy source

Unconventional gas/oil

Utica shale in Ohio alone contains 15 trillion cubic

feet of natural gas Zhang et al. 1999

Johnson 2011 Ryder 2008

Observation 1: Thawing Soils

Volume Change Behaviors in Thawing Soils

Liu Y., Yu, et al. 2009

Thawing Soils: cont.

Component of volume change

Liu Y., Yu, et al. 2009

Observation 2: Desiccation Crack in Soil

Schematic drawing modified from internet resource

Observation 3: Plastic shrinkage of concrete

Commonly observed in fresh concrete

Accelerate deterioration

Relations between shrinkage and time for concretes stored at different

relative humidities (Troxell, Raphael, and Davis 1958). Examples of plastic shrinkage cracking (source Internet)

Shrinkage cracking mechanism (ACI 224R-01)

Chemically Treated Soils

Shrinkage Cracking Resulting from Problems with Cement-

Treated Base (internet image)

Cement treated soils

Cracks accelerate water infiltration into pavement base

Are There Common Mechanisms?

Freezing

Drying

Chemical hydration

These motivates us to explore the fundamental knowledge for porous

materials

Liquid water “consumption”?

Solid (Soil, Concrete, Ceramic, ...) Water Characteristic Curve

(SWCC)

Describes the change of matric suction with water

Decided by the pore structures

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

log(h) (unit of h: kPa)

Volu

metr

ic w

ate

r co

nte

nt

Base

Subgrade

Q1. Can SWCC explain the experimental observations?

Q2. If so, how to integrate into simulation modeling?

Pore space from CT scanning

Thermal (T,Ө)

Fourier’s eq.

Mechanical (u,T,Ө,h)

Navier’s eq.

Hydraulic (h,T,Ө)

Richards’ eq.

Өi

T

u

Ө

h

A multiphysical thermo-hydro-mechanical process.

i iw w( , ), ( , )C

iw( , , )K T

Ice-water balance

Clapeyron’s eq.

Freezing point

depression

Energy from phase change

iw( , )E

Volume change due to ice formation

Retention curve

th

Simulation of Freezing Soils

Three phase diagram of water

( From www1.lsbu.ac.uk )

Generalized Clapeyron equation:

(Williams and Smith, 1989)

f

w

LdP

dT V T i f

g

d L d

dT T dh

Freezing Point Depression

PDEs governing individual process Fourier’s equation, Richard’s equation, Navier’s equation

Boundary and constitutive relationships Newton’s low of cooling, Darcy’s law, mass balance, constitutive

relationships

Experimental correlations for porous media Soil water characteristic curve,

Hydraulic conductivity

Thermal conductivity

Phase transition Clapeyron’s equation for water-ice balance

Theoretical model–(PDEs-weak form)-solved numerically

Can’t go into details due to time constraints

Approach to the Problem

Lh Lh LT( ) 0K h K K T n

c emb( ) h ( )T T T n

Unsaturated uniform soil specimen subjected to surface freezing

Boundary condition

Example

0.00

0.05

0.10

0.15

0.20

0.25 0.30 0.35 0.40 0.45 0.50

0 hour

Heig

ht (m

)

0.00

0.05

0.10

0.15

0.20

0.25 0.30 0.35 0.40 0.45 0.50

12 hours

Heig

ht (m

)

0.00

0.05

0.10

0.15

0.20

0.25 0.30 0.35 0.40 0.45 0.50

24 hours

Total volumetric water content

Heig

ht (m

)

0.00

0.05

0.10

0.15

0.20

0.25 0.30 0.35 0.40 0.45 0.50

50 hours

Total volumetric water content

Heig

ht (m

)

Volumetric total water content after 0,12,24,50 hours

Results: thermally driven moisture migration

0.00

0.05

0.10

0.15

0.20

-4 -3 -2 -1 0 1 2 3 4 5 6 7

0 hour

He

ight (m

)

0.00

0.05

0.10

0.15

0.20

-4 -3 -2 -1 0 1 2 3 4 5 6 7

12 hours

He

ight (m

)

0.00

0.05

0.10

0.15

0.20

-4 -3 -2 -1 0 1 2 3 4 5 6 7

24 hours

Temperature (oC)

He

ight (m

)

0.00

0.05

0.10

0.15

0.20

-4 -3 -2 -1 0 1 2 3 4 5 6 7

50 hours

Temperature (oC)

He

ight (m

)

Temperature after 0,12,24,50 hours

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60 70

0 hour

Heig

ht (m

)

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60 70

12 hours

Heig

ht (m

)

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60 70

24 hours

Pressure head (m)

Heig

ht (m

)

0.00

0.05

0.10

0.15

0.20

0 10 20 30 40 50 60 70

50 hours

Pressure head (m)

Heig

ht (m

)

Pore pressure head after 0,12,24 50 hours

Soil Freezing: Interesting Phenomena

Vertical deformation VS time Vertical internal stress

• Two important phenomena reproduced by the simulation.

1.0

0.8

0.6

0.4

0.2

0.00 10 20 30 40 50 60 70 80 90 100

Time (minute)A

xis

dis

pla

ce

me

nt

(mm

)

The similarity between freezing and Drying

Water

Vapor

Water

Ice

Drying Freezing

a w i wAP P P P

Koopmans (1966) and Spaans (1996)

CT imaging

Water content in drying process Unfrozen water content in freezing process (measured by TDR)

SWCC from Freezing Process?

f ln273.15

TL

Clapeyron equation (Groenevelt, 1974)

u f

% 100%t fw w

w w

wa

d

1w K a

b

a,t a,f

a,u a,f

% 100%K K

K K

22

L

L

v

cK a

a

Matric suction in drying process Temperature in freezing process (measured by thermal couples)

21

Traditional

New method

Computer

PICO TDR

Thermo-

TDR

Refrigerator (-18 degC)

Demonstration

TDR

Zhang and Yu 2009

Example Results: 1

(a) Soil # 1, Specimen #1 (b) Soil #1, Specimen #2

0.01 0.1 1 10

Stable SFC

Suction (Mpa)

Measured SWCC

0.0

0.2

0.4

0.6

0.8

1.0

Satu

ration

Modified Stable SFC

0.01 0.1 1 10

0.0

0.2

0.4

0.6

0.8

1.0

Stable SFCSa

tura

tio

n

Suction(Mpa)

Measured SWCC

Measured SFC by new method and SWCC by traditional filter paper method

23

Example Results: 2

1E-5 1E-4 1E-3 0.01 0.1 1 10 100

0.0

0.2

0.4

0.6

0.8

1.0

Stable SFC

Satu

ration

Suction (Mpa)

Measured SWCC

2 4 6 8 10 12 14 16 18

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Measured SFC of bean curd

Genuchten fit

Satu

ration

Suction (MPa)

Model Genuchten

Equation y=1/(1+(a*x)^n)^m

Parameter Fitted Value Standard Error

m 0.69123 0.23977

n 1.9782 0.28557

a 0.98565 0.27371

Figure 2 SFC and SWCC of soil #2 SFC of a slab of firm bean curd

24

Is SWCC the Ultimate Goal?

Solid, air and liquid interface

Young–Laplace equation Young’s equation

Is SWCC the Ultimate Goal? (cont.)

Water Characteristic Curve

SWCC Key concept of porous geomaterials

Pore-size Distribution CT, ultrasonics

Contact Angle Tensiometer

2/4/2012

Application: Holistic Simulation of Climate Effects on Pavement

Ohio Instrumented Road: air temperature, precipitation; initial and final temperature, material properties of different layers; monitored temperature and water content by sensors

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

Simulated:

Dec 3

Dec 11

Dec 22

Volu

metr

ic M

ois

ture

conte

nt

Depth (m)

Measured:

Dec 3

Dec 11

Dec 22

0 1 2 3 4 5 6 7 8 9 10-6

-4

-2

0

2

4

6

8

10

12

14

16

18

Simulated:

S1

S3

S5

AirT

Te

mp

era

ture

(d

eg

C)

Time (day)

Measured:

S1

S3

S5

0 5 10 15 20 25 3020.20

20.24

20.28

20.32

20.36

20.40

Vert

ica

l str

ess (

MP

a)

Time (day)0 5 10 15 20 25 30

35

40

45

50

55

60

65

Ve

rtic

al str

ess (

MP

a)

Time (day)0 5 10 15 20 25 30

2

3

4

5

6

7

8

Ve

rtic

al str

ess (

MP

a)

Time (day)

Application: Frost Effects on Pipe Fracture

Max vertical stress VS time

Frost front reach the crown of the pipe

Arch

Case I Case II Case III

Case I Case II Case III

(cont.)

Sinusoidal

1 hour

0 3 6 9 12 15 18 21 24 27 302.8x107

3.0x107

3.2x107

3.4x107

3.6x107

3.8x107

4.0x107

Maxim

um

tensile

str

ess (

Pa)

Time (day)

Seasonly frost (upper)

Unfrozen (lower)

Permafrostd e m o d e m o d e m o d e m o d e m o

d e m o d e m o d e m o d e m o d e m o

d e m o d e m o d e m o d e m o d e m o

d e m o d e m o d e m o d e m o d e m o

d e m o d e m o d e m o d e m o d e m o

d e m o d e m o d e m o d e m o d e m o

d e m o d e m o d e m o d e m o d e m o

0 0.5 1 1.5 2

x 1010

0

5

10

15

20

25

30

35

Number of stress cycle

Depth

of cra

ck (

mm

)

Permafrost

Seasonal frost

Unfrozen

Service life decreases

0 4 8 12 16 200.0

0.2

0.4

0.6

0.8

1.0

Satu

ration

Distance from bottom (m)

HydrateResSim

MH21

STARSOIL

STARSSOLID

STOMPHYD

UNIVHOSTON

NewModel

0 4 8 12 16 200.2

0.3

0.4

0.5

0.6

0.7

0.8

Sa

tura

tio

n

Distance from bottom (m)

HydrateResSim

MH21

STARSOIL

STARSSOLID

STOMPHYD

UNIVHouston

NewModel

Application: Methane Hydrate Exploration and Geohazards

1 Day 100 Day

Bottom Top

20 m

NETL Gas Hydrate Simulation Comparison Program: Problem 1

0 10 20 30 40 50 60 70 80 90 100-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Su

bsid

en

ce

(m

)

Time (day)

Subsidence

Liu and Yu 2012

Summary

Multiphysics process in soils

An emerging frontier in soil mechanics

A “unified” theory might be possible

Improving engineering design could result from understanding and

simulating the fundamentals

We are continuing to explore into the fundamentals as well as many

exciting applications

It is a team effort

Acknowledgements

Funding Agencies

National Science Foundation, The Ohio Department of Transportation/FHWA, TRB, Minnesota

Department of Transportation, Cleveland Water Department, Industry sponsors (GRL/PDI, WPC

Inc., Durham Geo Enterprises, MWH Inc., DLZ Ohio Inc., etc)

Graduate Students

Past: Xinbao Yu (UT Arlington), Bin Zhang (Mike Baker), Yan Liu (GRL)

Current: Zhen Liu, Junliang Tao, Ye Sun, Chih-Chien Kung, Guangxi Wu, Jianying Hu, Quan

Gao

Undergraduate Researchers

Pete Simko, John Holman, Yuan Gao, Andrew Bittleman, Pete Simko, Cassandra McFadden,

Paul Mangola, Jingsi Lang, Donald Cartwright, Alex Potter-weight, Randall Beck, Vanessa

Penner,Peter Frank, Ben Ma, Rebecca Ciciretti, Joseph Brenner, Javanni Gonzalez, Vanessa

Penner, Grant Mott, et al.)

Department engineer Jim Berrila

Thank you