Timber-Based Strategies for Seismic Collapse Prevention and Energy Performance Improvement in Masonry Buildings

Abstract

This study investigates the effectiveness of a range of timber-based solutions for the seismic and energy retrofitting of existing masonry buildings. These solutions are designed not only to prevent structural collapse during earthquakes but also to create integrated interventions that enhance thermo-physical performance and reduce emissions in existing buildings. Various case scenarios were considered and both mechanical and energetic behaviour post-intervention were evaluated. Timber-engineered products serve as foundational components for the retrofit approach, encompassing one-dimensional vertical elements (strong-backs) and various types of panels (cross-laminated timber panels, laminated veneer lumber panels, and oriented strand board panels). The analyzed retrofit techniques share a common principle involving the attachment of these timber-based elements to the building’s wall surfaces through mechanical point-to-point connections. The proposed solutions integrate strong-backs and timber panels with membranes and insulation layers, yielding cohesive, and highly effective interventions. Finite element modeling was employed to analyze the mechanical and thermal responses of the retrofitted walls. A comprehensive comparative analysis of various techniques was conducted to determine the most effective solution for each specific scenario.

1. Introduction

In recent decades, Europe’s construction sector has undergone a profound transformation, shifting its focus from the construction of new buildings to the enhancement of existing building stock. With many buildings nearing the end of their design lifespan, the need to address energy inefficiencies and structural vulnerabilities has become increasingly evident. Retrofitting initiatives have gained prominence, offering a crucial means to not only enhance the overall performance of existing structures but also to fortify sustainability and resilience within the built environment [1,2].

Seismic safety holds paramount importance, especially in regions across Europe prone to earthquakes. The seismic vulnerability of existing masonry structures has emerged as a pressing concern, with profound implications for human safety, infrastructure resilience, and cultural heritage preservation. Many masonry buildings were constructed before modern seismic design standards and exhibit inherent vulnerabilities that pose risks during seismic events. Those vulnerabilities become particularly evident in regions prone to seismic activity where ground motions can lead to extensive damage, economic losses, and, tragically, the loss of lives [3,4,5]. Moreover, these events threaten cultural heritage by placing historical masonry buildings at risk, and therefore necessitate careful consideration of retrofitting and preservation strategies.

Simultaneously, thermal comfort and energy-saving measures are mandated by European legislation [6]. These requirements significantly impact occupant well-being, construction costs, and environmental sustainability. Existing buildings, particularly historical ones, contribute substantially to Europe’s energy consumption and carbon emissions. Improving their performance can dramatically mitigate environmental effects and operational costs, and enhance the decarbonization (reduction of CO₂ emissions) of the building sector to reach the goal of Net Zero Emissions (NZE) by 2050 [7]. Additionally, rising energy prices increase the risk of energy poverty. Refurbishment of these highly inefficient buildings could therefore help to tackle this problem and improve the lives of their inhabitants.

When designing a retrofit intervention, structural, energetic, and architectural aspects must be considered simultaneously to obtain a cost-optimal renovation. The present study investigates the effectiveness of timber-based coating retrofit solutions aimed at reducing the seismic vulnerability of existing unreinforced masonry (URM) structures while improving the energy performance. The mechanical retrofit is provided by timber products fixed to the masonry wall using dry fasteners spreading along the walls surface which guarantee fast execution and reversibility of the intervention. Insulation layers and membranes were added to improve the hygro-thermal performance and the durability of the system.

Timber-based retrofit solutions for existing masonry buildings have emerged as a promising and innovative approach to address the seismic vulnerability of these historical structures while preserving their cultural heritage, offering a compelling alternative to conventional retrofitting techniques [8]. In recent decades, timber has reemerged as a sustainable and versatile material, garnering attention for its potential uses. Timber’s inherent properties, including high strength-to-weight ratio, flexibility, and renewable nature, make it an ideal choice for retrofitting interventions that seek to fortify existing masonry buildings against seismic forces. The first step in such a direction could be that of using timber to strengthen those structural components in traditional buildings that often are already made of timber, such as roof and floor diaphragms [9]. Mirra and Ravenhorst [10] have shown that adopting a plywood overlay to strengthen existing diaphragms can remarkably enhance the seismic performance of URM buildings. As alternatives to plywood overlays, additional layers of diagonal timber boards/planks [11] and CLT panels [12] have also proven to be effective in increasing the in-plane strength and stiffness of timber diaphragms and positively influencing the building response to earthquakes [13,14]. In the case of strong seismic hazards, even when the diaphragms and their connection to the walls have been improved, favouring the so-called “box-like behaviour”, the full capacity of the masonry walls may be exceeded, and consequently, wall strengthening is due.

Various authors in the literature on this topic have examined the mechanical performance of diverse timber-based retrofit solutions. Research contributions include experimental investigations of the properties of timber-to-masonry wall connections performed by Riccadonna et al. [15] and Rizzi et al. [16] considering dry and adhesive connections, respectively. Additionally, Giongo et al. [17] conducted full-scale onsite testing of masonry walls retrofitted with cross-laminated timber (CLT) panels, measuring 6 cm in thickness and fixed using the dry fasteners previously examined by Riccadonna et al. [15]. Further insights into the effectiveness of this CLT-based coating have been provided by Cassol et al. [18,19] by means of parametric simulations considering the behaviour of the retrofit applied on masonry piers, walls with openings, and buildings. Further insight into the experimental and numerical behaviour of masonry walls retrofitted with timber panels has also been provided by Borri et al. [20], Pozza et al. [21], Lucchini et al. [22], Iuorio et al. [23], and Sustersic and Dujic [24].

In parallel, the behaviour of masonry walls retrofitted with timber strong-backs (vertical timber elements) to improve the wall out-of-plane response has been tested by Giaretton et al. [25] and Cassol et al. [26]. Damiani et al. [27], Guerrini et al. [28], and Miglietta et al. [29] tested the effectiveness on the in-plane behaviour of a strengthening strategy that sees vertical timber strong-backs supplemented with horizontal timber blocking elements to create a frame that is then sheathed by oriented timber-based sheets (OSB panels). The experimental campaigns included in-plane quasi-static cyclic tests performed on masonry piers and shake-table tests performed on full-scale building prototypes, tested in bare and retrofitted conditions, respectively.

Further numerical simulations were performed by Busselli et al. [30] and Cassol et al. [31] to evaluate both the seismic and the thermo-physical properties of various aforementioned timber-based retrofit solutions, with the aim of designing integrated retrofit interventions. In this context, an alternative solution named Nested Building Approach was studied by Valluzzi et al. [32]. The analyzed solution consisted of removing the building internal elements and inserting a new inner structure realized with CLT panels coupled with insulation and finishing layers. In this case, both the improvement of the seismic and hygrothermal performances were numerically investigated.

2. Retrofit Solutions

The retrofit solutions studied herein consist of connecting timber-based products (panels and strong-backs) to the surface of the walls of a building using mechanical point-to-point connections, with the aim of improving the in-plane and the out-of-plane capacity of the URM walls. Insulation layers, membranes, and finishing layers were added to guarantee the durability of the timber elements and to improve the thermophysical performance of the retrofits. Four solutions were analyzed with the structural retrofit provided by cross laminated timber (CLT) panels, laminated veneer lumber (LVL) panels, or by two different combinations of timber strong-backs and oriented strand boards (OSB) panels (referred to as “frame and sheathing” solutions). Two configurations of the non-structural layers were designed for each solution, acknowledging that the intervention could be applied to either the internal or external side of the masonry walls (see Figure 1). The selected thicknesses of the timber panels were compatible with those used for the in situ campaigns performed by [15,16,17], while the timber strong-back cross-sections were selected based on the experimental campaigns reported in [25,26].

For the internal solutions, expanded rigid polyurethane foam (PIR) panels were employed for the insulation, a vapor barrier was applied close to the inner finishing layer (plasterboard sheets), and a breathable and waterproof membrane was installed on the masonry wall surface to avoid imbibition of the timber elements. For the external installations, PIR panels, covered on both sides by saturated fibreglass facers, were used to create an external thermal insulation composite system (ETICS). A breathable, waterproof, and reflective membrane was applied to the outer surface of the timber elements to hinder the passage of sunrays while a waterproof membrane was installed between the masonry wall and the timber elements, similarly to what was conducted for the internal solutions. Both internal and external retrofit solutions considered either vapor barriers or breathable membranes in order to increase the timber durability as suggested by [33]. A maximum value of 125 mm was assumed as the limit for the retrofit thickness in the case of internal application, with the aim of limiting the reduction of internal volume due to the intervention. This value acknowledges previous research on the seismic performance of timber-based retrofits for masonry. Cassol et al. [18] have shown in a parametric study that 60 mm thick CLT panels can significantly improve the in-plane capacity of walls from 250 mm to 600 mm thick (increments up to ≈70%), while Guerrini et al. [28] have used a 60 mm thick timber frame sheathed with 18 mm OSB sheets (for a total thickness of 78 mm) to successfully increase the lateral strength (by 35%) and the displacement capacity (by 167%) of 100 mm thick calcium silicate brick walls. The thickness of the insultation layers of the external solutions was calculated analytically based on the maximum thermal transmittance (U = 0.28 W m⁻² K⁻¹) allowed by the Italian regulation [34] for existing buildings, considering the climatic zone E.

The effectiveness of the integrated retrofit interventions was evaluated considering the improvement of both mechanical and energy performance. In particular, as regards the seismic behaviour, increases in lateral capacity and displacement capacity in the plane direction of the reinforced walls were assessed through nonlinear static analysis. The effectiveness of the various retrofits in improving the out-of-plane wall response was not directly investigated in this study, however, it can be inferred from the out-of-plane performance of the strong-back technique tested in [26]. The “frame and sheathing” solutions studied here see the strong-backs as integral components of the retrofit. Regarding the “panel-based” techniques, the timber-to-masonry connection has comparable performance to that used for the strong-backs, and the out-of-plane inertia of the panels is consistent, when not larger, than that of all the strong-backs applied to the wall. The enhancement of the wall thermo-physical properties was evaluated in terms of the reduction of steady-state thermal transmittance (U) for winter performance and periodic thermal transmittance (Yie), as well as the increase in phase shift (Δt) for summer performance using FEM simulations. Additionally, the response factor curves of each analyzed configuration were provided.

3. Seismic Analyses

3.1. Numerical Model

The numerical models were realized using the finite element software Abaqus/Standard [35]. A simplified micro modelling approach was adopted for simulating the masonry wall. In this approach, the size of the masonry units (i.e., bricks) is expanded to incorporate the mortar joints. The expanded masonry units are modelled as continuum elements and the interaction between such elements is reproduced by selecting proper interface properties. The expanded masonry units (EMU) were modelled with an equivalent, homogeneous, and isotropic material. The EMU elastic modulus E_EMU was determined considering the elastic modulus, the thickness of the bricks (E_b and h_b), and the mortar joints (E_m, h_m), as indicated in Equation (1). The EMU nonlinear behaviour was described by the concrete damage plasticity (CDP) constitutive model. This model was developed by Lubiner et al. [36] and was further elaborated by Lee and Fenves [37]. It allows for the simulation of the post cracked behaviour of quasi brittle materials such as masonry. The tensile and compressive behaviours of the EMU under axial loading were implemented using bilinear and parabolic stress–strain relations, respectively. The EMU compressive strength f_c,EMU was calculated as indicated in Eurocode 6 [38] (see Equation (2)), while the EMU tensile strength f_t,EMU was defined as equal to the brick tensile strength f_t,b. The fracture energy values governing the post cracked behaviour of the EMU were calculated as recommended by Lourenço and João [39].

$$E_{EMU}=\frac{{(h_b+h_m)·E}_b·E_m}{h_b·E_m+h_m·E_b}$$

(1)

$$f_{c,EMU}=0.45·{f_{c,b}}^{0.7}·{f_{c,m}}^{0.3}$$

(2)

The horizontal mortar joints (i.e., bed joints) and the vertical mortar joints (i.e., head joints) are characterized by different properties and, consequently, their contribution was accounted for by adopting different approaches. The interfaces simulating the head joints were provided with a hard-contact interaction property which allows for compression stress transfer only. The head joints were assumed to be cracked (e.g., due to shrinkage), which meant that both the cohesive and the friction contributions from these interfaces were neglected. The modelling approach adopted for the bed joints can simulate both the tensile and the shear-cracking failure modes. Contact properties such as traction separation, cohesive, and tangential friction were used to model the joint interfaces. The uncoupled stiffness coefficients for the normal direction (k_n) and tangential directions (k_s and k_t) were determined considering the mortar and brick elastic moduli and dimensions as indicated in Equations (3) and (4). The quadratic traction stress criterion [35] was used to define damage initiation, as shown in Equation (5) where the Macauly brackets indicate that, in the normal direction, only the tensile stresses were considered. The maximum normal strength (t_n,max) and shear strengths (t_s,max and t_t,max) were assumed to be equal to the tensile strength (f_m,t) and the cohesion (c) of the masonry joints. The post cracked behaviour was defined assuming a linear damage evolution based on the energy dissipated during the crack propagation. The tensile and shear fracture energy values were calculated as recommended by Lourenço and João [39]. The mixed mode damage evolution was modelled according to the Benzeggagh–Kenane (BK) law, which is suitable for representing the damage evolution when the shear behaviour is the same along the two reference directions of the shear plane, assuming a BK exponent equal to two. The viscosity coefficient for the damage stabilization was assumed equal to 0.02. In the tangential direction, a further contribution due to friction was considered. The friction coefficient was assumed equal to 30° and a limit to the maximum value of the shear stress f_v,lim was fixed (f_v,lim = 0.065 f_c,b [40]).

$$k_n=\frac{E_b·E_m}{h_m·(E_b-E_m)}$$

(3)

$$k_s=k_t=\frac{G_b·G_m}{h_m·(G_b-G_m)}$$

(4)

$${\left(\frac{〈t_n〉}{t_{n,max}}\right)}^2+{\left(\frac{t_s}{t_{s,max}}\right)}^2+{\left(\frac{t_t}{t_{t,max}}\right)}^2=1$$

(5)

Timber was modelled as an orthotropic material where inelastic phenomena, such as compression crushing at the panel’s toe, were simulated using a plastic constitutive model. The CLT panels were modelled as three-layer solids, while the LVL panels and the OSB sheets were simulated using equivalent orthotropic materials. The point-to-point connections between the timber elements and the masonry wall, as well as the anchoring connections and the timber-to-timber connections, were modelled using one-dimensional wire elements. The properties of such elements were calibrated on the outcomes of different experimental campaigns, while the wire extremities were fixed to the timber and the masonry using coupling constraints with adequate influence radii. A regular mesh pattern with eight nodes and three-dimensional elements (C3D8R) was used. The selected mesh size (30 mm) is the maximum size that allows describing of the behaviour of the EMU with adequate accuracy (for the validation process, please refer to Section 3.2). The horizontal and the vertical loads were applied as uniform pressures, and the geometric nonlinearities were considered. Quasi-static analyses were performed to improve the convergence and reduce the computational cost of the simulations.

3.2. Model Validation

The models reproducing the unreinforced masonry (URM) condition and the retrofitted condition with the retrofit provided by the application of a CLT panel were validated on the results from in situ full-scale semi-cyclic shear-compression testing of triple-leaf clay brick masonry walls performed by Giongo et al. [17]. The specimens, which measured 1800 mm × 1800 mm × 340 mm, were isolated from the internal walls of a clay-brick vertical addition constructed in the 1920s on top of a three-story masonry hotel, originally built in the nineteenth century in northern Italy (Comano Terme bath area in the Trentino province) and now decommissioned. Before starting the lateral loading, a vertical stress of ≈0.2 MPa was applied on top of the specimens to simulate the stress level at the base of the walls of 2- or 3-story buildings and to ensure activation of the pier shear failure. The retrofit scheme comprised a three-layer CLT panel that was 60 mm thick and was fixed to the masonry surface using twenty-five double-threaded screw anchors (≈8 fasteners/m²). The specimens were characterized by a composite failure mode with an initial phase of rocking followed by diagonal shear failure. The application of the retrofit produced an increase of 41% in the load-bearing capacity, while the initial stiffness of the wall appeared not to be modified. Figure 2 presents the comparison between the experimental and numerical results. Two numerical models were used: a simplified model (M1), which was realized adopting equivalent masonry units six times the size of a brick to reduce the computational effort of the simulations, and a detailed model (M2) implemented considering the actual brick pattern and size. It can be observed that the numerical outcomes are consistent with the experimental data in terms of failure mechanism, initial stiffness, and lateral load capacity.

3.3. Results

The effectiveness of the proposed retrofit solution was further investigated using the modelling approaches described in the previous sections. The timber retrofits were applied to two double-leaf clay brick masonry walls characterized by different aspect ratios (i.e., b/h 0.58 and 1.08) and failure modes (i.e., rocking and shear). Such walls were 3000 mm high and 250 mm thick. The bricks’ dimensions were 240 × 120 × 75 mm, and the bed joints were 15 mm thick. The overburden was applied as a uniform pressure of 0.1 MPa, a conservative value representing the vertical load typically encountered in a three-story URM building. The horizontal load was applied to the side of the masonry walls at an average height from the base of 2565 mm, targeting the blocks within the third, fourth, and fifth rows from the top. The adopted masonry properties are shown in

Table 1. Masonry properties.

Material	E [MPa]	G [MPa]	fc [MPa]	ft [MPa]	c [MPa]
Clay bricks	3000	1200	20.00	2.00	-
Mortar	300	120	1.30	0.05	0.15

. The retrofit was provided by a single timber panel as long as the wall for the slender wall (wall 1) and by three side-by-side panels for the stocky and longer wall (wall 2). The panel-to-panel side connection for the solutions where CLT and LVL panels were used was realized by inserting fully threaded timber screws at an angle of 45° to the joint line (8 mm diameter screws spaced at 200 mm). The layout of the masonry-to-timber connections was the same for all the investigated retrofit configurations matching that of the experimental campaign reported in [17] (≈4 fasteners/m², horizontal spacing = 500 mm, vertical spacing = 540 mm). The timber strong-backs and the horizontal timber “blocking” elements were fixed to the masonry wall by adopting the same fastener spacing used for the solutions with the timber panels. The OSB sheets were connected to the timber frames with nailed connections (fastener spacing = 100 mm) and, if multiple OSB sheets were used, the sheet-to-sheet joints were realized in correspondence with the strong-back location. Tensile anchors (i.e., hold-downs) were fixed next to the wall’s corner while a single shear anchor (angle bracket) for each timber panel was used. The timber properties were determined assuming a timber grade C24 for the boards of the CLT panels [41] and a timber grade C18 for the strong-backs [41]. The properties of the equivalent materials used to simulate the LVL panels and OSB sheets were defined as indicated in [42] (LVL-X) and [43] (OSB 3). The timber-to-masonry connection properties were calibrated on the experimental outcomes reported in [15], the properties of the anchors were defined based on the experimental results reported in [44], the timber panel-to-panel side connections were modelled as recommended by [45], and the OSB panels-to-timber connections were implemented considering the experimental results reported in [46].

Figure 3 shows the lateral load-displacement curves of the retrofitted masonry walls. All the analyzed retrofit solutions increased the load bearing and displacement capacities of the masonry walls considerably. The ultimate displacement of the walls was evaluated as the displacement corresponding to a strength degradation of 20% of the maximum lateral capacity [47]. In the case of rocking behaviour (wall 1), the failure of the retrofitted walls occurred when the ultimate strength of the tensile anchors was reached and, consequently, the four analyzed solutions provided the same load bearing capacity (71 kN, with an increase of 145%). The stiffness of the retrofit is responsible for the displacement required to engage the maximum load-bearing capacity and the displacement capacity of the solutions. The response of the timber panel retrofit solutions (CLT and LVL) was very similar due to the comparable stiffness of the timber panels. Such solutions reached the maximum load-bearing capacity at a drift of 1.15%, while the increase in displacement capacities was 70% (at a drift of 2.25%). Expectedly, the solutions with the strong-backs and the OSB sheets (SB90 and SB45) proved more deformable than the panel solutions due to the reduced stiffness of the retrofit. The maximum load-bearing capacity was engaged at a drift of 1.83% (SB45) and 2.14% (SB90), while the increase in the displacement capacity was 115% (SB45) and 133% (SB90). In the case of shear behaviour (wall 2), the failure of the walls retrofitted with timber panels (CLT and LVL) was determined by the capacity of the timber-to-masonry connections being exceeded. The CLT and LVL solutions allowed an increase in the load-bearing capacity of 52% and in the displacement capacity of 226% (drift = 2.50%). The SB45 and SB90 solutions were less effective than the timber panel ones due to the reduced stiffness of the timber retrofit and the limited strength of the OSB panel-to-strong-back nailed connections. The solutions with the strong-backs and the OSB sheets, when applied to squat masonry walls (wall 2), improved only the displacement capacity with increases of 265% (SB45) and 300% (SB90), and drift values of 2.80% (SB45) and 3.07% (SB90). SB45 appeared to be slightly more effective than SB90 due to the bigger inertia modulus of the SB45 strong-backs in the direction parallel to the wall.

4. Energy Performance Analyses

A numerical model of the analyzed components was developed in COMSOL Multiphysics^® [48] to assess the thermal performance of the retrofit solutions both in winter and summer seasons. At first, a steady-state heat transfer model was created for the different configurations. This allowed the calculation of solutions’ thermal transmittances considering the structure’s minor thermal bridges. Then, a time-dependent heat transfer model was created to simulate a typical temperature pattern occurring during the summer season. This analysis allows for the evaluation of the periodic thermal properties often used in regulatory requirements. Finally, the response factors [49,50,51,52,53,54,55] of the retrofit solutions were simulated in order to obtain the thermal response in terms of specific heat flux on the internal side after the application of a triangular temperature excitation. Response factors underlie the calculation methods used by many building energy simulation software (e.g., EnergyPlus™ [56], TRNSYS [57]). Thus, an experimental assessment of such factors could result in a more accurate simulation of the real behaviour of walls. Moreover, recent experimental techniques [58] show how the exploitation of triangular pulses applied on one side of a wall can be adopted in the assessment of the U-value of the wall, both under controlled conditions and in situ, by significantly reducing the test time. Preliminary results show good agreement between U-values obtained with the pulse method and the U-value calculated with the standard stationary procedure suggested by [59,60].

4.1. Numerical Model

4.1.1. Geometry and Materials

The bi-dimensional geometry of the masonry wall and of the eight retrofit solutions was first created in order to build the model in COMSOL Multiphysics^®. Figure 4 shows the different geometric models of the nine configurations that were modelled, obtained by replicating the retrofit stratigraphy seen in Figure 4. To each closed element, a material was associated. Thermophysical properties of the adopted materials are the ones reported in

Table 2. Thermophysical properties of the materials.

Materials	Thickness [mm]	ρ [kg/m3] 1	λ [W/(mK)] 2	cp [J/(kgK)] 3
Clay brick masonry	250	1800	0.800	840
CLT panel	60	420	0.120	1600
LVL panel	40	530	0.130	2720
OSB panel	15	650	0.130	1700
PIR	40–60–90	36	0.022	1453
PIR (ETICS application)	40–80–90	35	0.028–0.026	1464
Plaster	12	1000	0.250	2000
Fibre-cement board	15	950	0.300	1000
Skim-coating	10	950	0.310	950
Plasterboard	12–24	1800	0.900	910
Vapour barrier	0.02	500	0.390	1700
Breathable membrane	0.03	250	0.300	1800
Breathable and reflective membrane	0.05	300	0.300	1800

¹ Density. ² Conductivity. ³ Mass specific heat at constant pressure.

.

4.1.2. Model Description

The governing heat transfer mechanisms consisted of (i) heat conduction across the wall and (ii) heat convection on the surfaces. The Newton–Robin boundary condition on the two vertical surfaces was set by defining the heat transfer coefficient and the air’s temperature (see Equation (6)).

$$q_0=h\cdot (T_{AIR}-T_s)$$

(6)

where q₀ [W m⁻²] is the boundary convective heat flux, h [W m⁻² K⁻¹] is the heat transfer coefficient, T_AIR [°C] is the air’s temperature, and T_s [°C] is the temperature of the wall surface. For the internal side, the heat transfer coefficient was set equal to h_int =7.69 W m⁻² K⁻¹, while for the external side h_ext was set equal to 25 W m⁻² K⁻¹, according to the Standard EN ISO 6946:2018 [61]. Conversely, the two horizontal surfaces were set as adiabatic. The air’s temperature was defined according to the study being performed, either stationary or periodic, as described in the following sections.

4.1.3. Steady-State Regime

A stationary analysis was run to determine the thermal transmittance of the different retrofit solutions. As a matter of fact, constant air temperatures at the internal and external sides were set, namely T_AIR,i = 20 °C and T_AIR,e = 0 °C, with a thermal gradient of 20 K. The steady-state study was run considering a relative tolerance of the solver equal to 0.001.

Starting from numerical results, it was possible to calculate the thermal transmittance. At first, the thermal resistance of the wall R_wall [m² K W⁻¹] was determined according to Equation (7). Then the thermal transmittance U of each retrofit solution, expressed in W m⁻² K⁻¹, was assessed through Equation (8).

$$R_{wall}=\frac{T_{si}-T_{se}}{\dot{q}}$$

(7)

$$U=\frac{1}{R_{si}+R_{wall}+R_{se}}$$

(8)

where T_si [°C] and T_se [°C] are the internal and external surface temperatures calculated as the line average on each surface, respectively. $\dot{q}$ [W m⁻²] is the specific heat flux obtained as the line average on each one of the vertical surfaces.

4.1.4. Periodic Regime

A dynamic periodic study is required to analyze the summer performance. The selected regime was a periodic one, in which the internal air’s temperature was set constantly equal to T_AIR,i = 16 °C, while the external T_AIR,e was forced to follow a sinusoidal function with 10 K of semi-amplitude, 16 °C of average temperature, and a period of 24 h (Equation (9)).

$$T_{AIR,e}=16 °\mathrm{C}+10\cdot \sin \frac{2 \pi \cdot \tau }{T}$$

(9)

where τ [s] is the time expressed in [s] and T is the 24 h period of solicitation. The initial condition in the solid domain was taken equal to the wall’s average temperature, which was 16 °C. In this way, the transient period of the simulation was reduced.

The relative and absolute tolerances of the time-dependent solver were stricter than the stationary study and were set equal to 10⁻⁴ and 10⁻⁵, respectively. Those values were necessary in order to obtain accurate results in the time-dependent study. Simulations were run for a period of 10 days with 1 min time-step, and the Runge–Kutta method was chosen as the resolution method, which is extremely suitable for oscillatory problems.

Periodic thermal parameters were calculated starting from the numerical results, in terms of temperatures and specific heat fluxes, analyzing them in a 24 h period in the stabilized regime, thus, after the transient time. The periodic thermal transmittance Y_ie [W m⁻² K⁻¹] was calculated by taking the ratio of the semi-amplitude of the specific heat flux function over the semi-amplitude of the external air’s temperature function, both considered in the same period of one day. The decrement factor f [-] was calculated by taking the periodic thermal transmittance Y_ie and dividing it by the U-value. The phase shift Δτ_ie, expressed in hours, was determined as the difference between the moments at which the maximum values of the specific heat flux and of the external air’s temperature occur.

4.1.5. Dynamic Regime

Among dynamic studies, it is also possible to analyze the thermal behaviour of the retrofit solutions by applying a temperature impulse on the external side and investigating the response in time in terms of internal heat flux. This is known as response factor [49,50,51,52,53,54,55]. In particular, the external air’s temperature was forced to follow a triangular function, as shown in Equation (10), while the internal air’s temperature was kept equal to 16 °C. The initial condition was set equal to 16 °C in the whole solid domain.

$$\left\{ \begin{array}{c}{T}_{AIR,E}=16+10\cdot t, 0<t\le 1 \mathrm{h} \\ T_{AIR,E}=26-10\cdot \left(t-1\right), 1<t\le 2 \mathrm{h} \\ T_{AIR,E}=16, 2<t\le 96 \mathrm{h}\end{array}\right.$$

(10)

Notwithstanding, the theory [49,50,51,52,53,54,55] defines response factors as responses to a unitary temperature solicitation of 1 K, however the simulation was run by setting the temperature increment to 10 K. Indeed, a unit change in temperature would produce heat fluxes that are not graphically appreciable, especially for the retrofit solutions. Heat fluxes were then divided by 10 K with the aim of obtaining a unitary response X (W m⁻² K⁻¹), and values were reported for each hour over a period of 4 days (as seen in Equation (11)). This range of time is also the simulation time selected for the analysis, and it was obtained by considering the analyzed component that had shown the longest thermal response in order to not neglect significant terms in the series.

$$X_j=\frac{\dot{q_{s,¡}}}{\mathsf{\Delta }T}$$

(11)

where j is the time-index (with j = 1, 2, …, N), $\dot{q_{s,¡}}$ is the specific heat flux on the internal side (W m⁻² K⁻¹), and ΔT [K] is the temperature magnitude equal to 10 K. The response factor series starts from 1, which is the moment at which the peak of the temperature excitation occurs.

4.1.6. Mesh Selection

To numerically solve the heat transfer problem, it was necessary to discretize the domain into non-overlapping triangles. However, to assess the effect that different discretization levels of the geometry have on the results, a sensitivity analysis of the mesh was performed for each retrofit configuration. By running the stationary study and changing the user-defined mesh from normal (i.e., maximum size = 7.04 cm, minimum size = 0.03 cm) to extremely fine (i.e., maximum size = 1.05 cm, minimum size = 0.002 cm), changes in the results were analyzed.

Table 3. Percentage variation of the steady-state specific heat flux as a function of the mesh size and of the retrofit solution (beyond the URM wall).

Configuration		Mesh Size
		Normal	Fine	Finer	Extra Fine	Extremely Fine
	URM	-	0.00%	0.00%	0.00%	0.00%
Internal Retrofit	CLT	-	0.00%	0.00%	0.00%	0.00%
	LVL	-	0.00%	0.00%	0.00%	0.00%
	SB90	-	0.00%	0.00%	−0.01%	−0.02%
	SB45	-	0.00%	0.00%	−0.01%	−0.02%
External Retrofit	CLT	-	0.00%	0.00%	0.00%	0.00%
	LVL	-	0.00%	0.00%	0.00%	0.00%
	SB90	-	0.00%	0.00%	0.00%	−0.01%
	SB45	-	0.00%	0.00%	0.00%	−0.01%

shows the percentage differences of the specific heat flux across the different configurations obtained as the difference in the result considering successive meshes. It can be noticed that the mesh does not have any influence on the simulation results. Only the two timber-frame retrofits (internal and external) showed a slight difference between meshes, which can be explained by the non-planar geometry in correspondence with the strong-back. Nevertheless, differences are negligible (−0.02% to −0.01%). For this reason, domains were discretized with a normal mesh, with the advantage of reducing the computational time.

4.2. Results and Discussion

Results of the complete energetic analysis, both in terms of thermal transmittance and in terms of periodic thermal parameters of the different retrofit solutions and the URM wall, are shown in

Table 4. Results of the energetic analysis.

Configuration		Stationary	Periodic
		U (W m−2 K−1)	Yie (W m−2 K−1)	f (-)	$\mathsf{\Delta }{\mathsf{\tau }}_{\mathbf{i}\mathbf{e}}$ (h)
	URM	2.072	0.894	0.432	7.4
Internal Retrofit	CLT	0.354	0.052	0.148	12.9
	LVL	0.282	0.037	0.131	13.2
	SB90	0.297	0.052	0.176	11.9
	SB45	0.270	0.035	0.129	13.2
External Retrofit	CLT	0.244	0.023	0.094	13.0
	LVL	0.257	0.023	0.089	12.9
	SB90	0.316	0.038	0.119	12.3
	SB45	0.319	0.030	0.095	13.0

.

The heat flow by heat transmission across opaque components is known to be one of the main shares of the total thermal load of a building. The quantity of energy transferred between internal and external environments depends on both the component type and the temperature differential. In winter design scenarios, this heat flow is assessed under steady-state conditions, where temperature remains constant over time. Thus, the thermal parameter associated with the winter thermal performance is the thermal transmittance. According to Table 4, it can be noticed that all the retrofit solutions, both internal and external, show improvements in the thermal insulation with respect to the URM wall (with U-value equal to 2.072 W m⁻² K⁻¹). On average, all U-values are lower than the initial case, and in these specific examples, best winter performances were obtained for the CLT-ext and the LVL-ext, which resulted being very effective with values equal to 0.244 and 0.257 W m⁻² K⁻¹, respectively. It can be noticed that for the CLT and LVL structural layers, passing from internal to external insulation, the U-value decreases, which can be explained by the greater total thickness, despite the higher value of thermal conductivity adopted in the external configuration (i.e., 0.026–0.028 W m⁻² K⁻¹ for the PIR ETICS). On the contrary, in the timber-frame structure, both SB90 and SB45, an increase in U-value is noticed by placing the insulation layer on the external side instead of the internal one. This is because, on average, thermal transmittances of external timber-frame solutions have a less thermal resistant insulation layer. As a result of comparing analytical U-values rather than the numerical ones, it can be noticed that CLT and LVL retrofit solutions do not significantly change (errors lower than 0.05%), while a relevant difference was obtained for timber-frame solutions. As a matter of fact, U-values increase by 30% to 40% for the SB90 (internal and external) and by 17% to 21% for the SB45 retrofit solutions (internal and external) when considering numerical U-values, instead of analytical ones. This increase is due to the thermal bridges caused by the strong-backs. Almost all solutions exceed the U-value prescribed by the standard when taking into account thermal bridge effects, except for the SB45-int, CLT-ext, and LVL-ext.

When it comes to cooling periods, external climatic conditions such as air temperature can undergo remarkable changes, differently from those assumed in winter seasons. For this reason, the thermal behaviour of opaque components must be evaluated under non-stationary conditions. Following the results of Table 4, it can be seen that the retrofit solutions exhibit a significantly better performance than the URM. In fact, Figure 5 shows the specific heat flux on the internal side for the URM wall (in black) and the other retrofit solutions (in grey) as a function of the time. On the right, the external solicitation in terms of air temperature is reported. It is evident that both attenuation and phase shift are enhanced. The goal of the retrofit solution, from the energetic point of view, is to obtain lower values of periodic thermal transmittance, as well as of the decrement factor, while, in terms of phase shift, the higher the value, the better the solution.

On average, installing the insulation layer on the external side is more effective in attenuating and shifting the heat flux. The best performance was obtained for the CLT-ext and the LVL-ext. The massive presence of either cross-lam or laminated veneer lumber gives a lower thermal diffusivity to the configuration than the timber-frame solutions. This can also be noticed in Figure 6, which represents the internal specific heat flux (W m⁻²) as a function of the time for the external retrofit solutions. On the right side, the external air temperature function expressed in °C is reported over a period of 24 h. In regards to the timber-frame solutions, the SB45 configuration attenuates more the heat flux than the SB90 one. Despite the slightly lower total thickness of the SB45 (i.e., 36 cm vs. 38 cm), both of the 4 cm insulation layers installed with a layer of OSB in the middle can greatly dump and shift the external solicitation in comparison to a single 9 cm layer of PIR ETICS.

On the other hand, when the insulation layer is applied on the internal side of the masonry wall, a different behaviour is noticed. The most effective solutions become the LVL-int and the SB45-int, as seen in Figure 7. The only difference between the two is in terms of attenuation, while the phase shift is comparable.

Smaller performance enhancements were obtained for the SB90-int solutions, where the highest oscillation in terms of internal heat flux and the lowest phase shift was noticed (11.9 h). The presence of 90 mm of PIR insulation, which is characterized by higher thermal diffusivity than bulk layers like either CLT or LVL, leads to higher values of periodic thermal transmittance (Y_ie) and decrement factor (f), and lower phase shift (Δτ_ie).

By considering all the retrofit solutions, it can be stated that the most effective solutions in terms of energy retrofit (both in winter and summer seasons) are the CLT-ext and the LVL-ext with external insulation. The external configuration can be convenient during a retrofit, especially because it does not affect the indoor space of the building. While, if restrictions on the external façade are present, it is suggested to adopt either the LVL-int or the SB45-int retrofit solutions in order to enhance the thermal performance. Both configurations show higher attenuation and longest phase shifting among internal retrofit solutions.

Figure 8, Figure 9 and Figure 10 summarize the results in terms of specific heat flux after the impulsive temperature excitation. Figure 8 represents all the heat fluxes comprising the behaviour of the URM wall. Figure 9 and Figure 10 give instead the heat fluxes obtained on the internal side, separately for external and internal retrofit solutions, respectively. Results on the left side are displayed for a period of 96 h, while the temperature profile spans just 24 h for the sake of clarity. The temperature was maintained constant at 16 °C after the temperature impulse until the end of the simulation. Figure 11 and Figure 12 represent the response factor on the non-excited side on the wall after the application of a unitary temperature excitation on the opposite side, obtained by dividing the internal specific heat flux by the magnitude of the temperature excitation (i.e., 10 K) and then by sampling the data series every hour.

In order to verify the accuracy of simulation results related to the dynamic regime, a summation of the response factor series over time was performed for each analyzed component. The result was compared to the U-value obtained from the stationary simulation [54], as seen in Equation (12).

$$\sum _{j=0}^{j=96 \mathrm{h}}{X}_j=U$$

(12)

According to the response factor theory [54], and since the response factor is defined as a time-series, it is infinite, thus, the summation must be performed for an infinite period. However, after some time, values become extremely small and no longer significantly influence the summation. In this study, the sum was conducted for a period of 96 h (i.e., simulation period). As a result of this study, negligible differences (about <5%) with respect to the steady-state thermal transmittance were found, as visible in

Table 5. The sum of the 96 terms of the response factor series for each analyzed component and their percentage differences with respect to the stationary U-value.

Configurations		Response Factor
		$\sum _{96\mathbf{h}}{\mathbf{X}}_{\mathbf{j}}$ (W·m−2·K−1)	Error (%)
	URM	2.072	−0.02%
Internal Retrofit	CLT	0.351	−0.29%
	LVL	0.279	−1.25%
	SB90	0.296	−0.35%
	SB45	0.268	−0.77%
External Retrofit	CLT	0.235	−4.02%
	LVL	0.244	−5.27%
	SB90	0.309	−2.18%
	SB45	0.310	−2.95%

. Larger differences are registered for the external retrofit solutions than the internal ones (i.e., −5.29% for the LVL-ext and −0.29% for the CLT-int). This is explained by the longer thermal response obtained in retrofit solutions with external insulation rather than internal. However, these values are far below the uncertainty of the thermal transmittance measurements (approximately 10%), thus, the analysis is considered correct. The determination of the U-value through the response factor theory can bring advantages especially in situations in which boundary conditions cannot be kept constant, such as, in situ. This result is extremely useful in retrofit analysis where the current energetic state of the building must be evaluated in order to find retrofit solutions.

5. Conclusions

The retrofit solutions studied herein were designed and analyzed considering both structural and energetic aspects, with the aim of realizing integrated interventions characterized by low impact and fast execution. The outcomes obtained for the various techniques were compared to individuate the best performing solution for any given scenario. The following conclusions were drawn:

• The timber panel retrofits (i.e., CLT and LVL panels) proved to be more effective than the solutions with the timber frame and the OSB sheathing (i.e., SB90 and SB45) in improving the in-plane mechanical behaviour of double-leaf masonry brick-walls. Increases in lateral load-carrying capacity of 145% and 52% and in displacement capacities of 70% and 226% were obtained for the timber panel retrofits in the cases of rocking and shear failure modes, respectively.
• In the case of rocking behaviour, the solutions with the timber frame and the OSB sheathing exhibited the same load carrying capacity as the panel-based retrofits (as the wall capacity was limited by the strength of the tension anchors at the base) even though the maximum capacity was engaged at larger drift values (>1.80%), exceeding the limits typically adopted for masonry structures. In the case of shear failure, the solutions SB45 and SB90 produced a considerable increase in the wall displacement capacity (increases > 265%, up to drift values of ≈3%), with limited impact on the load-carrying capacity.
• The energy performance of the masonry walls was noticeably improved by the application of the retrofit solutions. Reductions in the thermal transmittance (U) up to 87% and of the periodic thermal transmittance (Y_ie) up to 97% were noticed.
• The most effective solutions in terms of energy retrofit (both in winter and summer seasons) are the external solutions CLT-ext and the LVL-ext. However, if the retrofit is applied on the internal side, it is suggested to adopt either the LVL-int or the SB45-int solutions. As expected, the thickness of the insulation layer plays a major role in determining the effectiveness of the solutions. Consequently, if a limitation to the total thickness of the intervention is considered (i.e., for the internal solutions), the possibility of inserting the insulation layers between the timber elements allows larger improvements in the wall thermophysical properties.
• The adoption of the response factor theory, specifically utilizing a triangular air temperature profile, presents a promising approach to evaluate U-values, particularly in experimental settings where stationary boundary conditions cannot be kept, for example, for in situ measurements. This result is extremely useful in retrofit analysis where the current energetic state of the building must be evaluated. Deviations from the stationary U-values are minimal for less massive walls, such as the internal retrofit solutions, while they get more pronounced in the case of external retrofit due to the longer response time. However, these deviations consistently remain below the threshold of measurement uncertainty.
• The retrofit solution with the LVL panels appeared to be the best performing, improving both the mechanical and the thermophysical properties of the URM walls considerably. However, all the analyzed solutions can be considered quite promising and worthy of further study.

In summary, the comprehensive evaluation of retrofit solutions presented in this study evidences the significance of integrating structural and energetic considerations for achieving interventions that offer minimal impact and swift implementation. The findings, highlighting the superior performance of timber panel retrofits in enhancing mechanical behaviour and energy efficiency, signify promising directions for future research and practical applications. These results emphasize the importance of integrated approaches in retrofitting, paving the way for more resilient and energy-efficient structures.