Utilities¶
Two support tools included in Rock Mechanics NX: estimating the impact force of a rock block on a structure and assessing susceptibility to collapse triggered by a seismic event.
Impact force of a rock block¶
The impact force of a rock block on a masonry or concrete structure is evaluated based on the work of McCarty & Carden (1962), Kar (1978) and Knight (1980), as revisited by Paronuzzi (1989).
Quantities involved¶
| Symbol | Quantity |
|---|---|
| \(F\) | impact force (t) |
| \(P\) | weight of the block (kg) |
| \(m = P/g\) | mass of the impacting block |
| \(g\) | gravitational acceleration |
| \(V\) | impact velocity of the block (m/s) |
| \(T\) | impact duration (ms) |
| \(z\) | penetration of the block into the structure (cm) |
| \(\sigma\) | compressive strength of the structure (kPa) |
| \(E_m\) | elastic modulus of the block (kPa) |
| \(E_s\) | elastic modulus of the structure (kPa) |
| \(d\) | maximum diameter of the block (cm) |
| \(N\) | shape factor: 1 for a pointed block, 0.72 for a flat block |
Procedure¶
The impacting mass is derived from the weight of the block:
The impact force \(F\) is a function of the block's momentum (\(m\,V\)) dissipated over the impact duration \(T\). In turn, \(T\) depends on the penetration \(z\) of the block into the structure, and \(z\) is obtained from a variable \(Z\) that is a function of the structure's strength \(\sigma\), the elastic moduli \(E_m\) and \(E_s\), the diameter \(d\) and the shape factor \(N\).
The following rule applies to the penetration/diameter ratio:
- if \(z/d > 2\) then \(z = z\) is assumed;
- if \(z/d \leq 2\) then \(z\) is corrected according to Paronuzzi's relation.
Finally, the maximum stress transmitted to the structure is obtained. The complete formulation follows Paronuzzi (1989) — see Bibliography.
Sizing the defenses
For the actual design of rockfall protection works (rigid and flexible rockfall barriers) you can use the dedicated applications in Geoapp.
Collapse prediction for a seismic event¶
Seismic events, even of low magnitude, are recognized among the triggering causes of collapse phenomena. Susceptibility to seismic actions was studied by Harp & Noble (1993), who propose classifying the rock mass with a methodology derived from Barton's Q.
Starting from the geostructural surveys, a value of modified Q is computed:
where RQD is obtained from the number of joints per cubic metre \(J_v\) (see RQD), \(J_n\), \(J_r\), \(J_a\) are the joint parameters of Barton's classification (\(J_n\) · \(J_r\) · \(J_a\)) and \(A_F\) is the aperture factor of the discontinuities.
Aperture factor A~F~¶
| Aperture of the discontinuities | \(A_F\) |
|---|---|
| All joints are closed | 1.0 |
| Mostly closed, some open up to 2 cm | 2.5 |
| Mostly closed, some open up to 5 cm | 5.0 |
| More than 20% of the joints with apertures up to 20 cm | 7.5 |
| More than 60% of the joints with apertures up to 20 cm | 10.0 |
| Joints open more than 20 cm | 15.0 |
If the rock mass contains free blocks, \(A_F\) must be increased by 1; likewise if a persistent joint is dip-slope oriented.
Susceptibility classification¶
From the value of Q computed in this way, the authors propose the following classification of collapse susceptibility for a seismic event of magnitude > 5:
| Q | Collapse susceptibility |
|---|---|
| < 0.1 | Very high |
| 0.1 – 1 | High |
| 1 – 9.99 | Medium |
| > 10 | Low |
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