Seismic retrofitting of masonry walls

Seismic retrofitting of masonry walls by means of SikaWrap®-350G Grid.

Introduction

Sika solution for masonry strengthening based on a TRM (textile reinforced mortar) solution comprises the following elements:

• SikaWrap®-350G Grid, a balanced bi-directional glass fiber grid, equipped with an alkali resistant coating.
• Sika® MonoTop®-722 Mur, high-ductility cementitious mortar.

The Sika TRM solution have been equally developed and tested for seismic retrofitting of walls, supplying the necessary shear and flexural strength to the masonry member for most of the in-plane and out-of-plane load combinations.

 

 

 

TECHNICAL DATA

Areal weight (glass fibre)

• Total: 295g/m2 ±5%
• Warp(longitudinal): 123g/m2 ±5% (47.31 mm2 ±5%
• Weft (transverse): 172g/m2 ±5%

 

Fibre density

2.6 g/cm3

 

Cross section:

• Warp(longitudinal): 47.31 mm2 ±5%
• Weft (transverse): 66.15 mm2 ±5%

 

Mechanical properties:

• Tensile strength: 2600 MPa (measured on roving).
• Tensile E-Modulus: 80 Gpa.
• Ultimate strain: >3%
• Characteristic debonding strain between TRM and masonry: 1.4%
• Design debonding strain between TRM and masonry: 0.9%-1.1%

 

CALCULATION PROCEDURE

INTRODUCTION

Masonry is commonly used in those applications where vertical load-bearing loads are expected. In buildings, masonry walls can serve as part of the lateral load-resisting system to resist wind and moderate horizontal loads.

However, unreinforced masonry structures show a significant vulnerability to major events such as earthquakes and severe wind, due to its limited strength under shear loads or flexure.

The use of external renders based on TRM (Textile Reinforced Mortars) supplies an additional mechanical capacity, which helps the wall to support the horizontal accelerations in case of seismic.

CASUISTIC

The collapse of the wall in case of horizontal forces can be originated by the rupture of the wall as consequence of one of the following mechanisms:

IN-PLANE LOADS: INSUFFICIENT SHEAR STREGTH

The shear capacity of the unreinforced masonry is limited by the “design value” under shear forces, which can be determined according to Eurocode 6 as follows:

??? = ??? ? ??

Where:

• fvd is the design shear strength of the masonry.
• t is the width of the wall.
• lc is the length of the wall under compression.

 

fvd is determined by dividing the characteristic shear strength of the masonry (fvk) by a safety factor (ym). In case of seismic retrofitting of existing structures, a secondary safety factor must be taken into account (CFKL) according to the existing knowledge about the structure (Eurocode 8).

Hence:

Where:

• fvk is the characteristic shear strength of the masonry.
• fvko is the initial characteristic shear strength of the masonry (no compression).
• σ is the average compressive stress corresponding to the compressed section of the wall (green area in the picture).

 

When strengthened, the horizontal yarns of the SikaWrap®-350G Grid take the shear forces in addition to the initial shear strength of the wall. In order to ensure the contribution of the existing masonry, the effective strain of the external strengthening must not exceed a certain value, in order to maintain the integrity of the masonry (e.g. 0.4% according to ACI 549.4R-13).

 

IN-PLANE LOADS: TOE CRUSHING + FLEXURAL CRACKING

Toe-crushing is a flexure-controlled failure mode, characterized by the formation of flexural cracks at the heel and crushing of the toe when the compressive stresses exceed the compressive strength of the masonry (left picture below).

The magnitude of the compressive and tension stresses can be easily determined by the equilibrium of forces&moments and strains compatibility in the section.

The mechanical performance of the masonry under compression can be determined according to the Eurocode 6, Part 1-1. Tipically, 0,35% can be assumed as the ultimate deformation of the fabric under compression.

The design strength of the masonry under compression can be obtained by dividing the characteristic strength by the corresponding safety factor (ym). In case of seismic retrofitting, the knowledge factor (CFKL) will also be taken into account as an additional reduction factor, according to Eurocode 8.

The flexural cracking as a consequence of the vertical tension (right picture) is expected in the case of unreinforced masonry, as its strength under vertical tension is almost negligible. In case of retrofitted walls, the external strengthening must be able to assume the vertical tensile forces with no contribution from the masonry.

 

OUT-OF-PLANE LOADS: HORIZONTAL BENDING

As previously indicated, the bending capacity of the un-reinforced masonry member is extremely limited, due to the inability to assume tensions. Hence, the section of the wall must essentially stay working under compression.

In the case of masonry panels restrained at both top and bottom, and subjected to horizontal forces as a consequence of the seismic acceleration, a failure is expected due to the formation of 3 hinges (bottom, top and intermediate).

In the case of an unreinforced panel, the resulting distribution of stresses must avoid the existence of tensions in the extreme fibre of the section. When strengthened, the vertical yarns of the external SikaWrap®-350G Grid will assume those vertical stresses. In that case, the design must verify that:

 

a) The deformation of the TRM under tension must not exceed the strain corresponding to the debonding from the substrate.

b) The compressive stress will not exceed the design value corresponding to the design strength of the wall under compressive forces fd as indicated previously.

 

OUT-OF-PLANE LOADS: SIMPLE OVERTURNING

The overturning is expected around a hinge located at the bottom of the panel, usually expected in the outer surface of the wall.

Overturning is feasible for those elements not restrained at top or not properly connected to orthogonal walls.

A simple solution is to display a band of horizontal TRM displayed at the top of the wall, properly anchored or extended to the orthogonal walls at both sides.

The performance of the fibre mesh will not be limited by its ultimate strength, but by the debonding from the anchorage points (orthogonal walls), hence the debonding stress of the TRM will be used for the design.

The performance of the TRM (force developed by the TRM can be determined by the moment equilibrium with respect to the location of the hinge at the bottom of the panel.

The external forces to be considered are:

• Nd (axial force on the top of the panel).
• Pd (panel self-weight).
• αs (ratio between the horizontal and vertical loads).
• Fd (Force exerted on the masonry panel by the TRM band on top).

 

The moment equilibrium with respect to the bottom hinge is achieved when:

 

CALCULATION EXAMPLES:

• Solid bricks group 1, compressive strength 15MPa, mortar strength M10, Class CC1.
• Panel density: 1800 kg/m3
• Characteristic compressive strength: fk=6.20 Mpa.
• ym=max (1.5; 2/3 x 1.5)= 1.5 according to Eurocode 8, part 1.
• Knowledge level (Eurocode 8, part 3): KL1. Hence, knowledge factor CFKL1=1.35
• Design compressive strength fd=6.20MPa/(1.5 x 1.35)= 3.06MPa.
• Maximum compressive strain: 0,35%
• Parabola stress block, defined by the equation:
   where x corresponds to the compressive strain (0 ≤ x ≤ 0.0035).
• Tensile strength of the masonry are neglected for the calculations.
• Panel dimensions:

 

OUT-OF-PLANE: HORIZONTAL BENDING.

The next example is based on the additional assuptions:

a) The calculations are based on 1 meter length of the panel.

b) The contribution of the masonry under tension in negligible.

c) SikaWrap®-350 Grid will be displayed horizontally, full cover (3strips x 1m). The influence of the TRM in the compressed face of the panel will not be taken into account (however, the TRM should be displayed on both sides as the seismic acceleration will lead to compress any of both sides indistinctly).

 

Unreinforced masonry.

Under these circumstances, the panel will be able to work under eccentric compression, but limited to those combinations of axial loads and bending moments within the section is still under compression.

When a panel is subjected to a small bending moment (i.e., when the eccentricity is small), the entire element will stay under compression, but the stress will be higher on one side than on the other. The maximum compressive strain in the wall will be 0.35% and failure will occur either by the crushing of the compressed masonry or by the decompression of the panel on the opposite side.

As the axial load applied to the wall is changed, the moment that the panel can resist will change. Hence, the influence of the axial load is extremely important as it will modify the maximum acceptable bending moment. Hence, several combinations (axial-bending) are possible.

All this combinations can be calculated according to the compatibility of strains and equilibrium of forces and moments, and finally determined as an interaction diagram. The inner surface of the diagram will show the different combinations of axial loads and bending moments that can be supported by the panel.

In the case of pure axial load, the maximum design load corresponds to the entire section (110mm x 1000mm=110000mm2) working under the design compressive strength (fd=3.06MPa).

Hence: 3.06 N/mm2 x 110000mm2=336.6kN (in the case of 0,0 kNm bending moment).

In the case of pure bending, the inability of assuming tensions avoids the possibility of resisting any bending moment (hence, for no axial load no bending moment is feasible 0 kN = 0 kNm) (*).

(*) The un-cracked fabric can show a very limited strength under tension. However, in the case of seismic this situation may not be expected, hence it´s recommendable not to expect any contribution to tensile forces.

In case of axial load, some bending strength can be expected, as the compressive stresses that stem from the axial loads will balance the tensions resulting to the bending. The balanced situation will comprise the extreme fiber of the section working at its maximum compressive strain, and the opposite side of the section showing to compression or tension (zero strain). This situation can be calculated by means of strain compatibility and forces/moment equilibrium (to be adjusted by trial and error), providing the next result:

According to those limitations, the interaction diagram (axial+bending) for a section of 1m panel, can be determined as follows:

 

Strengthened masonry.

Even when the external TRM will not influence the performance of the panel in those situations where the ultimate strength is compression-controlled, the influence of the SikaWrap®-350G Grid will be very significant under tension-controlled situations, as a consequence of bending moments caused by horizontal accelerations.

The mechanical contribution of the SikaWrap®-350G Grid will be limited by the debonding from the brick wall, which can vary significantly according to the properties of the substrate. For this example, the reduced debonding strain between TRM and masonry for the design will be taken as 1 %.

Under those circumstances, the force developed by the TRM will depend on the transverse section (66.15mm2 per 1m panel) and its modulus (80 GPa).

So, following the same procedure (forces & moment equilibrium and strains compatibility), the expected results corresponding to different axial + bending combinations can be calculated as follows:

According to those parameters, the new interaction diagram for the strengthened wall is obtained:

OUT-OF-PLANE: SIMPLY OVERTURNING

This example follows will determine the ratio between horizontal and vertical loads (assumed to be equal to the horizontal acceleration) for the sample wall, with the next assumptions:

The volume of the wall is: 0,11m x 3m x 4m = 1.32 m3

Its weight can be determined is given as: Pd=1.32m3 x 1800kg/m3 = 2376 kgf ~23,3 kN.

The uniform load on the wall equals 30kN/m : Nd= 4m x 30kN=120 kN.

 

The calculation takes into account 3x1m strip of SikaWrap®-350G Grid displayed horizontally on the exterior surface of the wall.

As the calculation is limited by the debonding of the TRM, the maximum force that can be exerted by the TRM strengthening (considering it´s bonded on both lateral transverse walls) can be determined as:

• Design debonding strain: 1%
• Design debonding stress: 1% x 80.000 MPa = 800MPa.

 

The cross-section of the SikaWrap®-350G grid for these 3 strips is:

3 x 47.31 mm2 = 141.93 mm2

Hence, the maximum force exerted by the TRM (limited by the debonding of the TRM from the transverse walls) is:

2Fd= 2 x ((800MPa- 0MPa)/2 x 141.93mm2))= 2 x 56.77 kN = 113.54 kN.

 

The maximum horizontal/vertical loads ratio (αs) can be obtained due to the moment equilibrium with respect to the hinge at the bottom:

 

113.54 kN x 2m + (120kN +23.3kN) x 0.055mm = αs x (120kN x 3m + 23.3 kN x 1.5m)

 

This condition is satisfied for a horizontal/vertical load ratio of: αs = 0.59

 

 

 

 

 

 

 

 

IN-PLANE LOADS: TOE CRUSHING + FLEXURAL CRACKING

For the same panel (4x3x0.11 m. wall), self-weight (23.3kN) and uniform vertical load of 70kN/m (total=70kN/m x 4m=280kN), and considering a horizontal/vertical ratio αs = 0.43, the internal distribution of stresses can be determined as a consequence of the strain compatibility of the materials and static equilibrium.

The wall is assumed to be strengthened by means of SikaWrap®-350G Grid displayed horizontally on both sides of the wall (3 strips x 1 metro at both sides).

The vertical tensions will be assumed by the vertical yarns of the grid.

The corresponding SikaWrap®-350G Grid section for 1 meter wall will be 2×66.15mm2=132.30 mm2.

The design strain for the SikaWrap®-350G Grid is 1%, corresponding to a stress of 800MPa.

The equilibrium of forces and moments is achieved for a position of the neutral axis equal to 1.48m (that is: 1.48m of the wall will be supporting tensions, and 2.52m will be acting under vertical compressions).

The toe-crushing is not expected (the effective compressive stress for the masonry is 2.044MPa (fd=3.06Mpa).

The effective deformation of the TRM under vertical tension will be 0.087% (which is lower than the design strain corresponding to the debonding from the substrate, 1%).

 

 

 

 

 

 

 

 

 

 

 

IN-PLANE LOADS: INSUFFICIENT SHEAR STREGTH

For the last example, it´s possible to determine the in-plane shear strength of the wall. The shear capacity of the strengthened wall can be evaluated as VRd, strengthened =VRd + VRd,TRM where VRd is the masonry contribution to shear strength:

??? = ??? ? ??

and:

• fvd is the design shear strength of the masonry.
• t is the width of the wall (110mm).
• lc is the length of the wall under compression (2520mm).

 

fvd is calculating by reducing the characteristic shear strength (fvk)by a safety factor (ym). In the case of seismic retrofitting of existing structures, a secondary safety factor must be taken into account (CFKL) according to the existing information about the structure.

Hence:

where :

• fvk is the characteristic shear strength of the masonry, and equals min( (???? + 0,4?); 0.065?? )), where:
• fk is the characteristic compressive strength of the masonry (6.20MPa).
• fvko is the initial characteristic shear strength of the uncompressed masonry (0.20 MPa).
• σ is the average compressive stress corresponding to the compressed section of the wall (310140N/(110x2520mm)=1.18MPa).

According to this:

The contribution of the TRM (VRd,TRM) displayed on both sides of the wall, can be determined according to ACI549.2R-13:

VRd, TRM = 0.75 ∙ 2 ∙ n ∙ Af ∙ L ∙ ffv

where:

• ffv is the design tensile strength of the mesh under shear forces (effective limited to 0,4% by ACI549.2R-13, hence ffv=0.004 x 80000MPa = 320MPa).
• Af is the area of the mesh reinforcement by unit width (Af=47.31mm2/1000mm=0.04731mm2/mm).
• N is the number of plies of mesh displayed in the face of the support (n=1).
• L is the length of the wall in the applied shear force (L=4m=4000mm).

VRd, TRM = 0.75 ∙ 2 ∙ 1 ∙ 0.04731 ∙ 4000 ∙ 320 = ??. ?? ??

Finally, the in-plane shear strength for the panel can be calculated as:

VRd, strengthened =VRd + VRd,TRM = 55.17kN + 90.83kN= 146kN

 

REMARKS

The calculation of seismic strengthening for shear walls may lead to complex calculations, as different guidelines/codes may be used simultaneously. The previous examples showed this complexity, working with a combination of different ACI and European codes.

The user must take into account that the parameters for the calculation may be indicated either in local or international codes; some of the most significant international codes are:

Concerning the design of masonry structures:

• Eurocode 6: Design of masonry structures.
• ACI 530/530.1-13: Building Code Requirements and Specification for Masonry Structures.

 

Concerning seismic evaluation and design of existing structures:

• Eurocode 8: Design of structures for earthquake resistance.
• ACI 530/530.1-13: Building Code Requirements and Specification for Masonry Structures.

Concerning the FRP strengthening of masonry walls:

• ACI 440.7R-10 Guide for the Design and Construction of Externally Bonded Fiber-Reinforced Polymer Systems for Strengthening Unreinforced Masonry Structures.
• ACI 549.4R-13 Guide to Design and Construction of Externally Bonded Fabric-Reinforced Cementitious Matrix (FRCM) Systems for Repair and Strengthening Concrete and Masonry Structures.
• CNR-DT 200 R1 (2013) Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Existing Structures, from Italy.