Ductile behaviour of reinforced and unreinforced masonry

Ductility is the ability of a structure to undergo large inelastic deformation without significant loss of strength before collapse. It is measured by the displacement ductility $\mu = \Delta_u/\Delta_y$, the ratio of ultimate to yield displacement.

Unreinforced masonry (URM)

• Masonry units and mortar are brittle with low tensile strength. After first diagonal cracking or toe crushing, strength drops quickly.
• Typical failure modes (diagonal shear, sliding, out-of-plane collapse) are brittle with small energy dissipation and ductility close to 1–1.5.
• URM can show limited ductility by rocking of squat walls under low axial load, but this is unreliable.

Reinforced masonry (RM)

• Vertical reinforcement in cells or cavities (grouted) and horizontal reinforcement in bond beams or bed joints carry tension after the masonry cracks.
• A flexural failure with yielding of steel is preferred to shear failure. Walls then show a wide hysteresis loop, absorb energy and can sustain large displacement.
• Shear failure remains brittle unless enough horizontal steel is given; the design should force flexure to govern ("strong shear, weak flexure").

 Load
  |       /\                URM: peak, then sudden drop
  |      /  \
  |     /    \____
  |    /   ________________ RM: ductile plateau
  |   /  _/
  |  / _/
  | /_/
  |/_____________________ Displacement

Confined masonry

Masonry walls enclosed by RC tie-columns and tie-beams cast after the wall are not reinforced masonry, but they show better ductility: the frame confines the wall after cracking and prevents collapse.

Improving ductility

1. Provide reinforced concrete or timber bands (plinth, lintel, roof) to tie the walls and control cracks.
2. Use vertical bars at corners, junctions and sides of openings, anchored in the foundation and the roof band.
3. Use bed-joint reinforcement or steel mesh; grout hollow blocks.
4. Use good bond between units and mortar, and avoid weak mortar or dry stone.
5. Keep walls at low axial stress, and limit slenderness and opening size.
6. Ensure box action by rigid floor diaphragms and tied roofs.

The code reduction (response reduction) factor $R$ is higher for reinforced masonry than for URM because of this ductility.