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Study on Shear–Softening Constitutive Law of Rock–Concrete Interface

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Abstract

To study fracture properties and establish a shear–softening constitutive law for rock–concrete interfaces, direct tension, three-point bending, and single shear push-out tests were conducted on composite rock–concrete specimens with different degrees of interface roughness. The relationships between tensile strength (ft), average shear strength (τav), initial fracture toughness (Kini 1C), mode I fracture energy (GIf) and interfacial roughness were determined based on experimental results. A shear–softening constitutive law for rock–concrete interface was developed by measuring strain variations on rock surfaces under loading stages during single shear push-out tests and defined based on shear strength (τmax) and mode II fracture energy (GIIf). For practical applications, the relationships between τmax and ft and between GIf and GIIf were determined by statistically fitting the experimental data in such a way that shear–softening constitutive law could be conveniently determined simply by measuring ft and GIf parameters of rock–concrete interface. Also, numerical simulations were carried out to investigate crack propagation in rock–concrete interfaces under mixed mode I–II fractures. Predicted load versus crack mouth opening displacement (CMOD) curves agreed well with experimental findings and verified the shear–softening constitutive law for rock–concrete interfaces obtained in this study.

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Data Availability

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Code Availability

Not applicable.

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All authors consent for publication.

Abbreviations

FPZ:

Fracture process zone

FCM:

Fictitious crack model

COD:

Crack opening displacement

CSD:

Crack slip displacement

ENF:

End-notched flexure

ELS:

End loaded split

SSP:

Single shear push-out

DT:

Direct tension

TPB:

Three-point bending

CMOD:

Crack mouth opening displacement

PVC:

Polyvinyl chloride

SIFs:

Stress intensity factors

w :

Crack opening displacement

w s :

Crack slip displacement

σ :

Tension stress

τ :

Shear stress

E :

Young’s modulus

v :

Poisson’s ratio

f t :

Uniaxial tensile strength

f c :

Uniaxial compressive strength

\(K_{{1{\text{C}}}}^{{{\text{ini}}}}\) :

Initial mode I fracture toughness

\(K_{{2{\text{C}}}}^{{{\text{ini}}}}\) :

Initial mode II fracture toughness

G If :

Mode I fracture energy

P max :

Peak load

A :

Interfacial area

τ av :

Interfacial average shear strength

δ x :

Relative crack displacements along horizontal x directions

δ y :

Relative crack displacements along vertical y directions

K 1 :

Interfacial SIFs of mode I

K 2 :

Interfacial SIFs of mode II

\(K_{{1}}^{{{\text{ini}}}}\) :

Interfacial SIFs of mode I caused by the initial cracking load

\(K_{{2}}^{{{\text{ini}}}}\) :

Interfacial SIFs of mode II caused by the initial cracking load

R a :

Roughness degrees

t :

Rock block thickness

L :

Bonding length between rock and concrete

q :

Linear load applied on the top of rock block

σ y :

Stress along y-axis

σ x :

Stress along x-axis

τ xy :

Shear stress along x–y plane

Ф :

Stress function

F y :

Forcing function

ε y :

Strain along y-axis

γ xy :

Shear strain along x–y plane

τ max :

Average peak shear stresses

ΔL :

Distance between the midpoints of two adjacent strain gauges

δ s :

Average slip displacement

δ s1 :

Crack slip displacement at the intersection point of bilinear relationship

δ s0 :

Stress-free crack slip displacement

δ e :

Elastic deformation

δ p :

Plastic deformation

w s :

Fracturing displacement

w s0 :

Stress-free crack slip displacement

w s,ini :

Crack opening displacement corresponding to shear stress initiation

G IIf :

Mode II fracture energy

l ch :

Characteristic length for mode I fracture

l ch-II :

Characteristic length for mode II fracture

K IC :

Critical fracture toughness of mode I

K IIC :

Critical fracture toughness of mode II

\(K_{1}^{P} ,K_{2}^{P}\) :

SIFs of modes I and II caused by external loading

\(K_{{{1}}}^{{{{\sigma ,\tau }}}}\),\(K_{{{2}}}^{{{{\sigma ,\tau }}}}\) :

SIFs of modes I and II caused by cohesive tensile stress σ and shear stress τ

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Acknowledgements

The authors gratefully acknowledge the financial support of National Natural Science Foundation of China under Grant Numbers NSFC 51478083 and NSFC 51878117.

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Authors and Affiliations

  1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, People’s Republic of China

    Wei Dong, Zhimin Wu & Ji She

  2. Department of Civil Engineering and Environmental Management, School of Computing, Engineering and Built Environment, Glasgow Caledonian University, Glasgow, G4 0BA, Scotland, UK

    Binsheng Zhang

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  1. Wei Dong
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  2. Zhimin Wu
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  4. Ji She
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Contributions

WD: Validation, Writing-original draft, Supervision, Project administration, Funding acquisition. ZW: Conceptualization, Methodology. BZ: Data curation, Writing-review and editing. JS: Formal analysis, Investigation.

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Correspondence to Wei Dong.

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Dong, W., Wu, Z., Zhang, B. et al. Study on Shear–Softening Constitutive Law of Rock–Concrete Interface. Rock Mech Rock Eng 54, 4677–4694 (2021). https://doi.org/10.1007/s00603-021-02536-6

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  • DOI: https://doi.org/10.1007/s00603-021-02536-6

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