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Acta Geotechnica

, Volume 14, Issue 2, pp 295–311 | Cite as

Simulation of long-term thermo-mechanical response of clay using an advanced constitutive model

  • Despina M. ZymnisEmail author
  • Andrew J. Whittle
  • Xiaohui Cheng
Research Paper

Abstract

There is extensive data to show that heating and cooling produces irrecoverable deformations in clays under fully drained conditions. The effects are most pronounced for normally and lightly overconsolidated clays that undergo significant compression. Most constitutive models have key limitations for predicting the thermo-mechanical response of clays through long-term (seasonal) cycles of heating and cooling. The Tsinghua ThermoSoil model (TTS; Zhang and Cheng in Int J Numer Anal Methods Geomech 41(4):527–554, 2017) presents a novel theoretical framework for simulating the coupled thermo-mechanical response of clays. The model uses a double-entropy approach to capture effects of energy dissipation at the microscopic particulate contact level on continuum behavior. This paper proposes a simple procedure for calibrating input parameters and illustrates this process using recent laboratory data for Geneva Clay (Di Donna and Laloui in Eng Geol 190:65–76, 2015). We then investigate capabilities of the TTS model in simulating familiar aspects of thermal consolidation of clays as well as the long-term, progressive accumulation of strains associated with seasonal heating and cooling processes for shallow geothermal systems installed in clays. The model predicts the existence of a long-term steady-state condition where there is no further accumulation of strain. This state depends on the consolidation stress and stress history but is independent of the imposed range of temperature, Tcyc. However, the value of Tcyc does affect the rate of accumulation of strain with thermal cycles. Simulations for normally consolidated Geneva Clay find steady-state strain conditions ranged from 2.0 to 3.7% accumulating within N = 10–50 thermal cycles.

Keywords

Constitutive modeling Cyclic thermal loading Irrecoverable deformations Long-term response Thermo-mechanical response 

List of symbol

Lower case

a

TTS model input constant that controls rate effects

c

TTS model input constant related to cohesion

c

TTS model input constant related to the critical state friction angle

e

Void ratio

h

TTS model input constant that controls hysteretic strains

m1

TTS model input constant that controls elastic strain evolution

m2

TTS model input constant that controls elastic strain evolution and location of reload curve

m3

TTS model input constant that controls the contribution of volumetric and deviatoric strains on granular temperature production

m4

TTS model input constant that controls the rate of granular temperature production

m5

TTS model input constant that controls the amount of thermal volumetric strains produced due to heating and cooling

p

Mean total stress

p

Mean effective stress

q

Shear stress

w

Water content

Upper case

B0

TTS model input constant that controls the location of the VCL

B1

TTS model input constant that controls the slope of the VCL

Cc

Compressibility index

Gs

Specific gravity of soil

\(\dot{I}_{\text{g}}\)

Granular entropy conversion rate

K0

In situ coefficient of earth pressure at rest

Ke

Secant elastic bulk modulus of the solid skeleton

LT

TTS model input constant that controls the shift of the VCL due to increase in temperature

M

Slope of critical state line

T

Temperature

Tcyc

Imposed range of temperature during cyclic heating and cooling

Tg

Granular temperature

Greek

αbf

Input constant for TTS model that controls the conversion of bound to free water during heating

β

Thermal expansion coefficient

εs

Deviatoric strain

εv

Volumetric strain

ξ

TTS model input constant that controls the coefficient of earth pressure at rest K0

ρ

Mass density

ρd

Dry density of soil medium

σh

Horizontal effective stress

σoct

Mean effective stress

σp

Preconsolidation pressure

σv

Vertical effective stress

φ

Porosity

ωe

Elastic potential energy density function

Superscripts

D

Irreversible

e

Elastic

h

Hysteretic

Subscripts

0

Reference initial state

20

At temperature 20°C

bw

Bound water

fw

Free water

NC

Normally consolidated

OC

Overconsolidated

s

Soil skeleton or solid particles

w

Water

Abbreviations

CSL

Critical state line

NC

Normally consolidated

OC

Overconsolidated

OCR

Overconsolidation ratio

SSA

Specific surface area

SQD

Specimen Quality Designation

TTS

Tsinghua ThermoSoil Model

VCL

Virgin consolidation line

Notes

Acknowledgements

The Authors are grateful for the support provided by the Low Carbon Energy University Alliance (LCEUA), which enabled three-way collaborations with colleagues at Tsinghua University and the University of Cambridge. The first Author (DMZ) also received a Robert A. Brown, Onassis Foundation, Exponent and Martin Foundation Fellowships for her Ph.D. studies.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Despina M. Zymnis
    • 1
    Email author
  • Andrew J. Whittle
    • 2
  • Xiaohui Cheng
    • 3
  1. 1.Department of Civil and Environmental EngineeringMITCambridgeUSA
  2. 2.Edmund K. Turner Professor of Civil and Environmental EngineeringMITCambridgeUSA
  3. 3.Civil EngineeringTsinghua UniversityBeijingChina

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