Concrete cone failure

Concrete cone is one of the failure modes of anchors in concrete, loaded by a tensile force. The failure is governed by crack growth in concrete, which forms a typical cone shape having the anchor's axis as revolution axis.

Concrete Cone Model[1]

Mechanical models

ACI 349-85

Under tension loading, the concrete cone failure surface has 45° inclination. A constant distribution of tensile stresses is then assumed. The concrete cone failure load ${\displaystyle N_{0}}$ of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by[2]:

${\displaystyle N_{0}=f_{ct}{A_{N}}[N]}$

Where:

${\displaystyle f_{ct}}$ - tensile strength of concrete

${\displaystyle A_{N}}$ - Cone's projected area

CCD (Concrete Capacity Design) Approach for Fastening to Concrete

Under tension loading, the concrete capacity of a single anchor is calculated assuming an inclination between the failure surface and surface of the concrete member of about 35°. The concrete cone failure load ${\displaystyle N_{0}}$ of a single anchor in uncracked concrete unaffected by edge influences or overlapping cones of neighboring anchors is given by[2]:

${\displaystyle N_{0}=k{\sqrt {f_{cc}}}{h_{ef}}^{1.5}[N]}$,

Where:

${\displaystyle k}$ - 13.5 for post-installed fasteners, 15.5 for cast-in-site fasteners

${\displaystyle f_{cc}}$ - Concrete compressive strength measured on cubes [MPa]

${\displaystyle {h_{ef}}}$ - Embedment depth of the anchor [mm]

The model is based on fracture mechanics theory and takes into account the size effect, particularly for the factor ${\displaystyle {h_{ef}}^{1.5}}$ which differentiates from ${\displaystyle {h_{ef}}^{2}}$ expected from the first model. In the case of concrete tensile failure with increasing member size, the failure load increases less than the available failure surface; that means the nominal stress at failure (peak load divided by failure area) decreases. [3]

Overlapping Areas in case of group of anchors[1]

Current codes take into account a reduction of the theoretical concrete cone capacity ${\displaystyle N_{0}}$ considering: (i) the presence of edges; (ii) the overlapping cones due to group effect; (iii) the presence of an eccentricity of the tension load. [4]

Difference between models

The tension failure loads predicted by the CCD method fits experimental results over a wide range of embedment depth (e.g. 100 - 600 mm).[2] Anchor load bearing capacity provided by ACI 349 does not consider size effect , thus an underestimated value for the load-carrying capacity is obtained for large embedment depths.[2]

Influence of the head size

For large head size, the bearing pressure in the bearing zone diminishes. An increase of the anchor's load-carrying capacity is observed . Different modification factors were proposed in technical literature.[5][6]

Un-Cracked and Cracked concrete

Anchors, experimentally show a lower load-bearing capacity when installed in a cracked concrete member. The reduction is up to 40% with respect to the un-cracked condition, depending on the crack width.[7] The reduction is due to the impossibility to transfer both normal and tangential stresses at the crack plane.

References

1. Cook, Ronald; Doerr, G T; Klingner, R.E. (2010). Design Guide For Steel To Concrete Connections. University Of Texas Austin.
2. Fuchs, Werner; Eligehausen, Rolf (1995). "Concrete Capacity Design (CCD) Approach for Fastening to Concrete". ACI Structural Journal. 109 (January): 1–4. ISSN 0889-3241.
3. Ožbolt, Joško; Eligehausen, Rolf; Reinhardt, Hans-Wolf (1999). "Size effect on the concrete cone pull-out load". International Journal of Fracture. 95: 391–404. ISSN 0376-9429.
4. ACI (2004). "ACI 349.2 Guide to the Concrete Capacity Design ( CCD ) Method — Embedment Design Examples". Concrete (Ccd): 1–77.
5. Ožbolt, Joško; Eligehausen, Rolf; Periškić, G.; Mayer, U. (2007). "3D FE analysis of anchor bolts with large embedment depths". Engineering Fracture Mechanics. 74 (1–2): 168–178. doi:10.1016/j.engfracmech.2006.01.019. ISSN 0013-7944.
6. Nilforoush, R.; Nilsson, M.; Elfgren, L.; Ožbolt, J.; Hofmann, J.; Eligehausen, R. (2017). "Tensile capacity of anchor bolts in uncracked concrete: Influence of member thickness and anchor's head size". ACI Structural Journal. 114 (6): 1519–1530. doi:10.14359/51689503. ISSN 0889-3241.
7. Mallèe, Rainer; Eligehausen, Rolf; Silva, John F (2006). Anchors In Concrete Structures. Ernst&Shon. ISBN 978-3433011430.

See also

• Fracture mechanics
• Concrete fracture analysis
• Size effect