FRCM in Practice: what advantages do they give and what changes in the checks?

What is an FRCM fiber reinforcement?

FRCMs, an acronym for “Fiber Reinforced Cementitious Matrix” are part of the large family of composites and as such have similarities and differences with other systems of this type used in construction. Specifically, citing CNR-DT 215/2018 §2.1, they are described as composed of the combination of a tensile-resistant fibrous phase incorporated in a matrix capable of adhering the reinforcement system to the support to be consolidated.

The fibrous mesh is composed of high-strength steel, aramide, basalt, carbon, PBO and glass installed in the form of small strands in order to obtain corrugated surfaces that favor the adhesion between reinforcement and matrix, which is only inorganic and therefore lime or cement-based.

Generally, FRCM reinforcement systems have a thickness between 5 and 15 mm. In the case of several meshes, the thickness increases but can never be greater than 30 mm.

The high strength-to-weight ratio of FRCM systems enhances the mechanical performance of the reinforced structural element, essentially helping to resist tensile stresses without increasing its mass or significantly changing its stiffness.

FRCM reinforcements show, in general, a good chemical-physical compatibility with masonry and concrete substrates, a certain vapour permeability and can also be prepared and applied easily using basically traditional procedures, even on damp surfaces.

Mechanical properties of FRCM systems

The conventional limit voltage σ_lim,conv , for a specific FRCM system, represents the strength of the reinforcement system obtained by detachment tests from conventional supports and as such is dependent on the type of support. The conventional limit strain is equal to ε_lim,conv = σ_lim,conv /And_f.

In the checks governed by the same phenomena, but located in intermediate areas, the values to be used are the following: ε_conv=α ⋅ε_lim,conv and σ_lim,conv = E_f ⋅ ε_lim,conv.

The amplification coefficient α must be assumed to be equal to 1.5 for all FRCM systems except those for which the ordinate point σ_lim,conv falls in stage A of the average stress-strain curve mentioned above. For the latter, α = 1.0 must be assumed.

The calculation value X_d of the generic strength or strain property of an FRCM reinforcement system is expressed by means of a relation such as:

where η is an appropriate conversion factor that takes into account the conditions of exposure and γ_m is the corresponding partial factor. The latter is equal to 1.5 for Ultimate Limit States (ULS); to 1.0 for Serviceability Limit States (SLS).

Reinforcement and verification of load-bearing masonry structures

The reinforcement of masonry structures is one of the most important applications for FRCM systems. These reinforcements can be extended to the entire surface of the masonry element or be applied in strips of sufficient width to appropriately contain the tangential stress at the masonry-reinforcement interface.

Safety checks may be carried out against both the ULS and the SLD and, as a general rule, the increase in the calculation capacity of the FRCM-reinforced element may not be more than 50% higher than that of the non-reinforced element.if the resistance R_d,Rinf exceeds the R by 1.5 times_d,NRinf The verification is not met). The limitation does not apply to seismic actions.

Shear Design in the Plane

The shear strength of the reinforced wall (V_t,R ) is calculated as the sum of the contribution of the unreinforced masonry (V_t ), evaluated in accordance with the current legislation for unreinforced walls that go into crisis due to tensile shear, and that of reinforcement (V_t,f ). The latter is assessed with the following report:

The value of the ε_fd is obtained from the ε_lim,conv. The coefficient α_t it takes into account the reduced extensional strength of the fibers when stressed at shear and in the absence of proven experimental results it can be set equal to 0.80.

In the presence of reinforcement on only one side of the wall, the contribution V_t,f it must be reduced by at least 30% (the application of connectors must be provided that make the reinforcement integral with the wall). In the presence of fibers orthogonal to the direction of the cut and effectively anchored, it must also be verified that the acting cut does not exceed the following diagonal crushing value of the masonry:

The product n_f ⋅t_Vf ⋅ l_f represents the area of the equivalent cross-section of the effective shear reinforcement, arranged in a direction parallel to the shear force, intersecting a shear lesion inclined by 45°. Hence the limitation l_f ≤ H.

In the V_t,c only the properties of unreinforced masonry intervene as FRCM reinforcement does not contribute to the compressive strength of the masonry.

In a simplified way, the calculation of the capacity of reinforced masonry can be carried out by flat-rate increase, by means of appropriate multiplication coefficients, the stress parameter of the average shear strength of the unreinforced masonry in the absence of normal stresses of the coefficient present in Table 4.1 of CNR-DT 215/2018 in compliance with the details reported.

The values shown in Table 4.1 of CNR-DT 215/2018 have been taken from tests performed in the laboratory, without taking into account the exposure conditions referred to in Table 3.1 of CNR-DT 215/2018. Therefore, the results obtained by them must be suitably reduced, multiplying them by the factor η_at of Table 3.1 of CNR-DT 215/2018 corresponding to the competent exposure condition.

N.B. the reinforcement will therefore be less and less effective as the plan size of the wall increases, precisely because of the limitation l_f ≤ H. Where possible, the shear strength can be assumed to be the greater of the “simplified” resistive shear with increment and the rigorous calculation (possibly limited by the formula [4.1b]). It can be observed that the resistant cut on the masonry side is always calculated with the Turnsek-Cacovik formula [C8.7.1.16]. In the event that the reinforcement is applied to a single face, the effect of the shear reinforcement is reduced by 30%, it is not possible to apply the simplified method referred to in table 4.1 of CNR-DT 215/2018, the coplanar bending checks are carried out without reduction and the orthogonal bending and shear checks are not carried out.

In-plane Flexural Pressure Design

In order to increase the pressure bending capacity in the plane of wall panels, the application of FRCM reinforcements can be envisaged in which there are fibers arranged in the direction of the axis of the structural element (preferably on both sides of the panel, usually covering almost the entire surface). The resisting moment associated with a given normal stress N_SD compression, M_Rd (N_SD), can be calculated assuming the following assumptions as valid:

• Conservation of flat sections;
• Perfect adherence between FRCM reinforcement and support.

The constitutive bond σ −ε of masonry for uniaxial stress states can be schematized as follows:

• Traction: zero resistance;
• Compression: linear behavior up to the design strength, f_MD, which is responsible for the value ε_m of deformation; zero tension for deformations greater than the last one, ε_mu; constant voltage, equal to f_MD, for deformations in the range ε_m ≤ε ≤ ε_mu .

In the absence of experimental data, the ultimate design deformation, ε_mu, can be assumed to be equal to 3.5‰.

The constitutive bond σ−ε of the reinforcement for tensile stresses is linear elastic up to the limit strain ε_fd starting from conventional deformation ε_lim,conv . The reinforcement is free of stiffness and compressive strength, so in the event that the neutral axis cuts the section of the reinforcement it is divided by the neutral axis itself into two parts, one of which is tensioned and one non-reacting.

The verification is fulfilled if M_SD ≤ M_Rd being M_SD and M_Rd respectively the moments of stressing and resistant calculation, the latter evaluated as a function of the concomitant normal calculation effort associated with M_SD.

The value of M_Rd It is calculated considering 3 possible stress-deformation configurations:

• Configuration I: masonry in the elastic field and reinforcement at the maximum limit of deformation reached. The check to be carried out for this stage is therefore ε ≤ ε_my;

• Configuration II: elasto-plastic masonry with ultimate deformation not reached and reinforcement at the maximum limit of deformation reached. The check to be carried out for this stage is therefore ε_my ≤ ε ≤ ε_mu;

• Configuration III: elasto-plastic masonry with ultimate deformation reached and reinforcement at the maximum limit of deformation not reached. The check to be carried out for this stage is therefore ε_fmax ≤ ε_fd.

Shear and Pressure-Bending Design Out of Plane

The value of the specific resisting moment, M_Rd, of the reinforced masonry section can be expressed as a function of the mechanical characteristics of the masonry and the FRCM composite, the thickness t, the wall, the value of the concomitant specific normal calculation stress, associated with M_SD. The panel subjected to seismic actions out of the plane typically has maximum moment in the center of the panel and negligible stresses at the ends.

The specific resisting moment, M_Rd, can be calculated from the following relationship:

being M_0d the specific moment of design of the unreinforced wall section, M_1d that of the reinforced section and γ_Rd is a partial model factor to which the value 2.00 is attributed, to the state of current knowledge.

It must also be verified that the value of the specific stressing shear, V_SD, in the concomitant load condition, does not exceed in any section the resistant one:

being f_vd the design shear strength of the unreinforced masonry, evaluated in accordance with current regulations, as a function of the average normal stress calculated as the ratio between the resultant of the compressive stresses and the surface area between the extreme compressed edge and the neutral axis, y_n.

N.B. In the out-of-plane flexural pressure design, as for the in-plane design, the constitutive bonds referred to in par 11.1.2 NTC2018 are used – right triangle for masonry, linear tensile strength only for fabric. Also for the out-of-plane verification, 3 stress-deformation stages are considered. The calculation of M_0d is carried out with [7.8.2] as described in par 7.8.2.2.3 NTC2018. In the Out-of-plane shear design, the shear strength reported in chapter 11.10.4 NTC2018 is considered and σN is calculated considering the resulting compression in the masonry.

Practical example with PRO_SAP and comparison with manual calculations

The purpose of the example is to calculate the ultimate stresses of a masonry male to which FRCM fiber reinforcements are applied. The masonry tap chosen is 40.00 cm thick, 270.00 cm long and 420.00cm high, belonging to a regular structure in plan and height that is spread over 2 levels. The structure, with use class II, is located in Ferrara (FE) with subsoil category C. The behavior factor used is 2.00 while the FC confidence factor is 1.35 (LC1).

The basic material of the structure is solid brick and lime mortar, with the following mechanical properties:

The application of FRCM on masonry is similar to that of FRPs:

• First of all, it is necessary to define the reinforcement archive with the command Structuredata > Consolidation interventions > FRCM masonry reinforcements. For the description of the parameters required in the table, please refer to the previous paragraphs and to the PRO_SAP manual;
• The second thing to do is specify which material will be reinforced within the material repository. If only a portion of the building is reinforced, it is possible to copy the material in use and indicate the reinforcement only in the copy;
• The third and last thing is to select the portions of the structure to be reinforced and assign the reinforced material.

The properties of the fiber reinforcements used are shown below:

On the basis of linear dynamic analyses, we carry out the calculations on an intermediate strip at the male under examination and we derive through the macro actions the average membrane normal stress Ned = 0.5*[1.227+1.236]*10^4 =1.2315*10^4 daN, which we will need for the manual calculation of the ultimate stresses via Excel sheet.

After planning and testing the existing building, the last values shown in the general control window of the element are obtained:

The values obtained by Excel spreadsheet are now reported using the same parameters for masonry and fiber reinforcements previously illustrated.

Check in the plan:

Out-of-plan check:

The comparison between the results obtained in PRO_SAP and those obtained in manual calculations give errors of the order of 0.1‰.

In Conclusion

As can be seen from the tables above, the ultimate values of shear and pressure-bending strength have significantly increased thanks to the application of fiber reinforcement. Specifically:

• For shear strength, the resistance component given by the mesh is added;
• For pressure bending there is a transition from a no-tension behavior to a compound section behavior where the fiber reinforcement reacts to the tensile stresses that unreinforced masonry is normally unable to absorb.

The direct advantage obtained is therefore a greater resistance of the fiber-reinforced elements belonging to the structure, not only in seismic conditions: even in static conditions, in fact, existing buildings, where the masonry tends to have poor mechanical properties, sometimes have walls with pressure bending verification problems that can be solved thanks to the application of FRCM fiber reinforcement, always recalling the limit imposed by chapter 4 CNR-DT 215/2018 according to which for static CMBs “the increase in the calculation capacity of the FRCM-reinforced element cannot be greater than 50% compared to that of the non-reinforced element”.