anchored slab calculation

A 2.50 × 2.50 m reinforced-concrete slab is placed directly on a rockfill surface (the downstream of a dam) inclined at 42°.
The slab is subjected to a normal force and a downslope in-plane shear force from the structural model (components normal to plane and along slope), plus a small overturning moment.

Interface friction is limited (φ = 28°- to be discussed further), so friction alone is not sufficient; stability is ensured by rock anchors installed perpendicular to the slope, providing normal clamping force.

Anchors are Ø40/20 mm hollow steel, 6 m length as predimensioned, with field tests up to 25t and measured elongations/residual set.

Design is governed by sliding, while overturning and bearing are secondary checks.

Step 1 – Anchor design (global stability)

Dimension the anchors (number + working load) so that:

The system satisfies the required sliding safety factor under the resultant downslope action.

Each anchor is verified for:

steel tensile capacity,

bond capacity in rock for the available length,

realistic lock-off force considering seating / residual set from tests.

Output: required normal clamping force from anchors, anchor load per piece, and confirmation the Ø40–6 m anchors are adequate.

Step 2 – Slab design (structural capacity)

Dimension the slab so it can transfer anchor forces to the rock:

Determine minimum thickness for global bending and local effects near anchors.

Provide reinforcement for:

bending,

local anchorage/plate zone (splitting, bursting),

crack control.

Verify local bearing under anchor plates and confirm no uplift (eccentricity within base).

Output: slab thickness + rebar layout + local detailing around anchors.