### Abstract

The ASTM standard C 78 for determining the modulus of rupture f_{r} (or flexural strength) provides a constant value of a measure of tensile strength which is currently used for designing pavements of all thicknesses, as well as concrete structural members, of all sizes. However, accumulated test data on f_{r}, as well as analytical studies and numerical simulations, clearly indicate that f_{r} is not constant but significantly decreases as the structure size increases. This evidence of size effect has so far been ignored. The consequence for thick pavements is increased cracking and thus poorer durability and serviceability, and for large structures even a significant increase of failure probability. The size dependence determined from test data follows a simple equation, which represents a gradual transition between a deterministic (energetic) size effect caused by stress redistribution at small sizes, and the power-law size effect of the classical Weibull statistical theory of strength, which is approached for large sizes. The transition is explained and modeled by the non-local Weibull theory. In this paper, modifications to the current standards that incorporate a simple procedure to obtain the size dependence f_{r} are proposed. Furthermore, the cohesive fracture mechanics, which is a more fundamental way to predict the effect of pavement thickness, resting on a given subsoil, is described. The energy release calculated according to cohesive fracture mechanics is shown to give the initial crack spacing, which may later increase due to instability of interacting parallel cracks. This is and important design consideration, since crack spacing controls the crack opening, and thus the ingress of water and corrosive agents, as well as transmission of shear stresses. Discussion and examples are limited to the formation of secondary cracks in between stress-relieving notches. This summary paper presents a general apercu of the problem, explains the fracture mechanics approach, and concludes by comparisons with test data.

Original language | English (US) |
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Title of host publication | Pavement Cracking: Mechanisms, Modeling, Detection, Testing and Case Histories |

Pages | 137-144 |

Number of pages | 8 |

State | Published - 2008 |

Externally published | Yes |

Event | 6th RILEM International Conference on Cracking in Pavements - Chicago, IL, United States Duration: Jun 16 2008 → Jun 18 2008 |

### Other

Other | 6th RILEM International Conference on Cracking in Pavements |
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Country | United States |

City | Chicago, IL |

Period | 6/16/08 → 6/18/08 |

### Fingerprint

### ASJC Scopus subject areas

- Civil and Structural Engineering
- Building and Construction
- Architecture

### Cite this

*Pavement Cracking: Mechanisms, Modeling, Detection, Testing and Case Histories*(pp. 137-144)

**Consequences of fracture mechanics for size effect, crack spacing and crack width in concrete pavements.** / Hoover, Christian; Bažant, Z. P.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Pavement Cracking: Mechanisms, Modeling, Detection, Testing and Case Histories.*pp. 137-144, 6th RILEM International Conference on Cracking in Pavements, Chicago, IL, United States, 6/16/08.

}

TY - GEN

T1 - Consequences of fracture mechanics for size effect, crack spacing and crack width in concrete pavements

AU - Hoover, Christian

AU - Bažant, Z. P.

PY - 2008

Y1 - 2008

N2 - The ASTM standard C 78 for determining the modulus of rupture fr (or flexural strength) provides a constant value of a measure of tensile strength which is currently used for designing pavements of all thicknesses, as well as concrete structural members, of all sizes. However, accumulated test data on fr, as well as analytical studies and numerical simulations, clearly indicate that fr is not constant but significantly decreases as the structure size increases. This evidence of size effect has so far been ignored. The consequence for thick pavements is increased cracking and thus poorer durability and serviceability, and for large structures even a significant increase of failure probability. The size dependence determined from test data follows a simple equation, which represents a gradual transition between a deterministic (energetic) size effect caused by stress redistribution at small sizes, and the power-law size effect of the classical Weibull statistical theory of strength, which is approached for large sizes. The transition is explained and modeled by the non-local Weibull theory. In this paper, modifications to the current standards that incorporate a simple procedure to obtain the size dependence fr are proposed. Furthermore, the cohesive fracture mechanics, which is a more fundamental way to predict the effect of pavement thickness, resting on a given subsoil, is described. The energy release calculated according to cohesive fracture mechanics is shown to give the initial crack spacing, which may later increase due to instability of interacting parallel cracks. This is and important design consideration, since crack spacing controls the crack opening, and thus the ingress of water and corrosive agents, as well as transmission of shear stresses. Discussion and examples are limited to the formation of secondary cracks in between stress-relieving notches. This summary paper presents a general apercu of the problem, explains the fracture mechanics approach, and concludes by comparisons with test data.

AB - The ASTM standard C 78 for determining the modulus of rupture fr (or flexural strength) provides a constant value of a measure of tensile strength which is currently used for designing pavements of all thicknesses, as well as concrete structural members, of all sizes. However, accumulated test data on fr, as well as analytical studies and numerical simulations, clearly indicate that fr is not constant but significantly decreases as the structure size increases. This evidence of size effect has so far been ignored. The consequence for thick pavements is increased cracking and thus poorer durability and serviceability, and for large structures even a significant increase of failure probability. The size dependence determined from test data follows a simple equation, which represents a gradual transition between a deterministic (energetic) size effect caused by stress redistribution at small sizes, and the power-law size effect of the classical Weibull statistical theory of strength, which is approached for large sizes. The transition is explained and modeled by the non-local Weibull theory. In this paper, modifications to the current standards that incorporate a simple procedure to obtain the size dependence fr are proposed. Furthermore, the cohesive fracture mechanics, which is a more fundamental way to predict the effect of pavement thickness, resting on a given subsoil, is described. The energy release calculated according to cohesive fracture mechanics is shown to give the initial crack spacing, which may later increase due to instability of interacting parallel cracks. This is and important design consideration, since crack spacing controls the crack opening, and thus the ingress of water and corrosive agents, as well as transmission of shear stresses. Discussion and examples are limited to the formation of secondary cracks in between stress-relieving notches. This summary paper presents a general apercu of the problem, explains the fracture mechanics approach, and concludes by comparisons with test data.

UR - http://www.scopus.com/inward/record.url?scp=79952136858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79952136858&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:79952136858

SN - 0415475759

SN - 9780415475754

SP - 137

EP - 144

BT - Pavement Cracking: Mechanisms, Modeling, Detection, Testing and Case Histories

ER -