Mechanical Behavior of a Composite Lightweight Slab, Consisting of a Laminated Wooden Joist and Ecological Mortar

The investigation reported in this paper is an evaluation of the mechanical behavior of full-scale ecological mortar slabs manufactured with a mixture of expanded clay and recycled concrete aggregates. The composite mortars form a compressive layer over laminated wooden joists to form a single construction unit. To do so, full-scale flexural tests are conducted of the composite laminated wood-ecological mortar slabs with different types of mortar designs: reference mortar (MR), lightweight mortar dosed with recycled concrete aggregates (MLC), and lightweight mortar dosed with recycled mixed aggregates (MLM). The test results showed that the mortar forming the compression layer and the laminated wooden joists worked in unison and withstood a higher maximum failure load under flexion than the failure load of the wooden joists in isolation. Moreover, the laboratory test results were compared with the simulated values of the theoretical model, generated in accordance with the technical specifications for structural calculations contained in the Spanish building code, and with the results calculated by a computer software package. From the analysis of the results of the calculation methods and the full-scale laboratory test results, it was concluded that the safety margin yielded by the calculations validated the use of those methods on this type of composite slab. In this way, a strong mixed wood–mortar slab was designed, contributing little dead-load to the building structure and its manufacture with recycled aggregate, also contributes to the circular economy of construction materials.


Introduction
At present, new urbanistic tendencies are oriented towards the recovery of the built environment, promoting the rehabilitation of classic buildings, historic city centers, and old degraded housing units [1][2][3]. European cities conserve buildings constructed between the 17th and the 18th century, with beautiful façades and interiors of incalculable historic value that are in need of conservation [4][5][6][7].
The horizontal structures of most of these historic buildings are made of wood, a noble material although sensitive to the maintenance conditions of the building, and subjected to working stresses close to their acceptable limitations. The old wooden structures often require reinforcement structures, because they present structural damage and are in need of conservation, due to humidity, xylophages, and excessive deformability under excessive loads [8][9][10][11][12].
Traditionally, various constructive solutions have been applied, to address these issues, such as the installation of lightly reinforced concrete floors over the pre-existing and previously treated structure,  [39], supplied by the firm Cementos Portland Valderribas (Navarra, Spain), and manufactured at its Mataporquera factory (Cantabria, Spain). It has a density of 3160 kg/m 3 and a Blaine specific surface of 340 m 2 /kg. Its chemical composition, obtained by X-ray fluorescence was mainly CaO (60.4%) and SiO 2 (21.3%). • Natural aggregates (NA): washed natural sand from an open-cast quarry situated in the locality of Cubillo del Campo (Burgos, Spain). Composed of SiO 2 (95.29%), its particle density was 2640 kg/m 3 , meeting the specifications of standard EN 1097-6 [40]. The granulometric curves of the aggregate employed in the mixtures are shown in Figure 1.
standard EN 413-1:2011 [39], supplied by the firm Cementos Portland Valderribas (Navarra, Spain), and manufactured at its Mataporquera factory (Cantabria, Spain). It has a density of 3160 kg/m 3 and a Blaine specific surface of 340 m 2 /kg. Its chemical composition, obtained by X-ray fluorescence was mainly CaO (60.4%) and SiO2 (21.3%). • Natural aggregates (NA): washed natural sand from an open-cast quarry situated in the locality of Cubillo del Campo (Burgos, Spain). Composed of SiO2 (95.29%), its particle density was 2640 kg/m 3 , meeting the specifications of standard EN 1097-6 [40]. The granulometric curves of the aggregate employed in the mixtures are shown in Figure 1. • Expanded clay (ExC): the expanded clay used in the mixtures was supplied by the firm Argex-Argila Expandida S.A. (Bustos, Portugal). Two types of commercial granulometries were employed under the following commercial brands: Argex ® 2-4 (ExC2/4) with an apparent dry density of 358 kg/m 3 , and Argex ® 3-8F (ExC3/8) with an apparent dry density of 300 kg/m 3 .

Mortar Mixtures
Three different mortar dosages were used for manufacturing the compression layer of the slab framework: • Reference mortar (MR): prepared with Natural Aggregate (NA), with a 1:4:w (cement: aggregate: water) dosage by weight of raw materials. • Lightweight mortar MLC: 75% of the NA was substituted in this mortar by expanded clay (ExC), specifically, 56.25% by ExC2/4 and 18.75% by ExC3/8. The remaining 25% was substituted by recycled concrete aggregates (RCA). • Lightweight mortars MLM: 75% of the NA was substituted in this mortar by expanded clay (ExC), specifically, 56.25% by ExC2/4 and 18.75% by ExC3/8. The remaining 25% was substituted by recycled mixed aggregates (RMA).
The relation of components by weight of the ecological mortar designs are shown in Table 1. • Expanded clay (ExC): the expanded clay used in the mixtures was supplied by the firm Argex-Argila Expandida S.A. (Bustos, Portugal). Two types of commercial granulometries were employed under the following commercial brands: Argex ® 2-4 (ExC2/4) with an apparent dry density of 358 kg/m 3 , and Argex ® 3-8F (ExC3/8) with an apparent dry density of 300 kg/m 3 .

Mortar Mixtures
Three different mortar dosages were used for manufacturing the compression layer of the slab framework: The relation of components by weight of the ecological mortar designs are shown in Table 1. The mortars designed with recovered construction waste and expanded clay have been studied in earlier investigations [37,38], in accordance with the specifications of the European standard. Their characteristics, both in the fresh and in the hardened state, are shown in Table 2.

Laminated Wood
The wood used for the manufacture of the composite laminated wood-ecological mortar slab was supplied by the firm "Arte y Madera, S.A." (Burgos, Spain). The slab consisted of the following materials ( Figure 2):

•
Wooden laminated (Gulam) joists of Douglas Fir GL24c with a width and height of (100 × 160) mm 2 and a length of 1500 mm. The Gulam joist is composed of five even layers, each with a thickness of 32 mm. Their mechanical properties and characteristics are shown in Table 3.

•
Agglomerated wooden board with dimensions of (500 × 1500) mm 2 and a thickness of 15 mm. The board is used as a sort of lost formwork for pouring the mortar. Its characteristics were not computed in the theoretical calculations.

•
Connectors between the joist and the construction mortar layer: bichromate-plated self-tapping flat-topped round screws with a diameter of 8 mm and a length of 200 mm.
thickness of 32 mm. Their mechanical properties and characteristics are shown in Table 3. • Agglomerated wooden board with dimensions of (500 × 1500) mm 2 and a thickness of 15 mm. The board is used as a sort of lost formwork for pouring the mortar. Its characteristics were not computed in the theoretical calculations.

•
Connectors between the joist and the construction mortar layer: bichromate-plated self-tapping flat-topped round screws with a diameter of 8 mm and a length of 200 mm.

Composite Framework: Wood-Mortar Section
The composite slab section design in this investigation consisted of a laminated wooden (Gulam) joist, next to a compression layer of cement mortar manufactured with recovered construction waste and expanded clay, as shown in Figure 3.

Composite Framework: Wood-Mortar Section
The composite slab section design in this investigation consisted of a laminated wooden (Gulam) joist, next to a compression layer of cement mortar manufactured with recovered construction waste and expanded clay, as shown in Figure 3.
where, Em Elasticity modulus of the wood (see Table 3) Ec Elasticity modulus of the mortar (Equation (2)) The elasticity modulus (Em) of the mortar was calculated with the specifications from the Structural Concrete standard EHE-08 [49] as a function of the average compression strength obtained from the tests, with the expression where, Materials 2020, 13, 2575 6 of 20 E m -Elasticity modulus of the wood (see Table 3) E c -Elasticity modulus of the mortar (Equation (2)) The elasticity modulus (E m ) of the mortar was calculated with the specifications from the Structural Concrete standard EHE-08 [49] as a function of the average compression strength obtained from the tests, with the expression E c = 8500 3 f cm (2) where, f cm is the average compression strength of the mortar (f cm = 35 MPa for the MR mortar, and an average value of f cm = 17 MPa for the MLC and the MLM mortars).
The mechanical properties for the study of the composite section, considering the effective rigidity of the laminated wood-cement mortar composite are shown in Table 4. The objective is to determine the maximum theoretical failure load for the constructive laminated wood-mortar component with each mortar as a compression layer, in order to compare it with the failure load from the full-scale test. Likewise, the stress state in the upper fiber of the (mortar) construction component and in the lower fiber (laminated wood joist) will be determined.

Preparation of Specimens
Six constructive units were prepared for the industrial test in the laboratory, two for each of the mortars used as the compression layer (MR, MLC, and MLM), as per the following process, in accordance with the scheme shown in Figure 3:

•
In the first place, the agglomerated wooden board was attached to the laminated wooden joist of Douglas Fir by six pairs of connectors (in total, 12 metal screws), at intervals of 26 cm from pair to pair, positioned at an angle of 45 • and at an approximate height of 50 mm over the upper surface of the board ( Figure 4).

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Subsequently, boarding was positioned around the perimeter that functioned as shuttering for the compression layer of mortar. This formwork consisted of three-layer cross-laminated wooden boards.

•
As reinforcement, an electro-welded mesh formed of 5 mm diameter bars with a mesh span of (200 × 300) mm 2 was used. With the objective of guaranteeing an upper cover of 25 mm, the reinforcement was supported upon small mortar blocks ( Figure 5).
Materials 2020, 13, x FOR PEER REVIEW 6 of 20 The objective is to determine the maximum theoretical failure load for the constructive laminated wood-mortar component with each mortar as a compression layer, in order to compare it with the failure load from the full-scale test. Likewise, the stress state in the upper fiber of the (mortar) construction component and in the lower fiber (laminated wood joist) will be determined.

Preparation of Specimens
Six constructive units were prepared for the industrial test in the laboratory, two for each of the mortars used as the compression layer (MR, MLC, and MLM), as per the following process, in accordance with the scheme shown in Figure 3:

•
In the first place, the agglomerated wooden board was attached to the laminated wooden joist of Douglas Fir by six pairs of connectors (in total, 12 metal screws), at intervals of 26 cm from pair to pair, positioned at an angle of 45° and at an approximate height of 50 mm over the upper surface of the board ( Figure 4).

•
Subsequently, boarding was positioned around the perimeter that functioned as shuttering for the compression layer of mortar. This formwork consisted of three-layer cross-laminated wooden boards.

•
As reinforcement, an electro-welded mesh formed of 5 mm diameter bars with a mesh span of (200 × 300) mm 2 was used. With the objective of guaranteeing an upper cover of 25 mm, the reinforcement was supported upon small mortar blocks ( Figure 5).
Having positioned the reinforcements in place, the mortar designed with recovered construction waste and expanded clay was mixed. The components that were used and their dosages are shown in Table 5.
A Mark T-Mech electric mixer with a capacity of 70 L was used for mixing the components, introducing in the first place the aggregates and 50% of the required volume of water, mixing the mass of concrete for 2 min. Subsequently, the cement was added and the remaining 50% of the water, mixing for 2 min to achieve an even mixture.
The mortar compression layer was done by pouring two 4-cm-thick mortar layers, compacted with a water vibrator. The excess mortar was removed using a metallic rod, levelling off the mixture at the level of the upper board of the formwork, leaving a smooth, flat and even top surface ( Figure 6).     The six construction slab components remained in the laboratory for 28 days at a temperature of 20 °C and a relative humidity of 50%. The mortar was covered with plastic for the first seven days of curing, to minimize water evaporation. Over the first few days, water was softly pulverized over the surface to humidify it, thereby avoiding loss of mix water due to the increased hydration heat, in order to ensure proper setting and hardening of the mortar. After 7 days, the plastic was removed and the samples remained in the laboratory until the 28 days of curing was over.

Full-Scale Flexural Test of the Composite Slab
Following 28 days, the mortar had properly set and hardened and the flexural test could be performed using a hydraulic press in the laboratory with a load capacity of 100 t, connected to a five-channel electronic measurement unit. The press is an MTS brand, model 201.70 HF, with the following characteristics: a tension force of 965 kN and a compression force of 1460 kN. Equipped with an MTS transducer model 661.31F-01, it had a capacity of 1000 kN (Figure 7).
It can apply continuous and variable loads, with the objective of achieving a uniform displacement of the transducer. The application of a variable downward load in the test was decided upon at a velocity of 0.01 mm/s. Having positioned the reinforcements in place, the mortar designed with recovered construction waste and expanded clay was mixed. The components that were used and their dosages are shown in Table 5. A Mark T-Mech electric mixer with a capacity of 70 L was used for mixing the components, introducing in the first place the aggregates and 50% of the required volume of water, mixing the mass of concrete for 2 min. Subsequently, the cement was added and the remaining 50% of the water, mixing for 2 min to achieve an even mixture.
The mortar compression layer was done by pouring two 4-cm-thick mortar layers, compacted with a water vibrator. The excess mortar was removed using a metallic rod, levelling off the mixture at the level of the upper board of the formwork, leaving a smooth, flat and even top surface ( Figure 6).   The six construction slab components remained in the laboratory for 28 days at a temperature of 20 °C and a relative humidity of 50%. The mortar was covered with plastic for the first seven days of curing, to minimize water evaporation. Over the first few days, water was softly pulverized over the surface to humidify it, thereby avoiding loss of mix water due to the increased hydration heat, in order to ensure proper setting and hardening of the mortar. After 7 days, the plastic was removed and the samples remained in the laboratory until the 28 days of curing was over.

Full-Scale Flexural Test of the Composite Slab
Following 28 days, the mortar had properly set and hardened and the flexural test could be performed using a hydraulic press in the laboratory with a load capacity of 100 t, connected to a The six construction slab components remained in the laboratory for 28 days at a temperature of 20 • C and a relative humidity of 50%. The mortar was covered with plastic for the first seven days of curing, to minimize water evaporation. Over the first few days, water was softly pulverized over the surface to humidify it, thereby avoiding loss of mix water due to the increased hydration heat, in order to ensure proper setting and hardening of the mortar. After 7 days, the plastic was removed and the samples remained in the laboratory until the 28 days of curing was over.

Full-Scale Flexural Test of the Composite Slab
Following 28 days, the mortar had properly set and hardened and the flexural test could be performed using a hydraulic press in the laboratory with a load capacity of 100 t, connected to a five-channel electronic measurement unit. The press is an MTS brand, model 201.70 HF, with the following characteristics: a tension force of 965 kN and a compression force of 1460 kN. Equipped with an MTS transducer model 661.31F-01, it had a capacity of 1000 kN (Figure 7). The process was managed with the MTS Flex Test GT digital controller [50], which displays information from the force transducer that controls the force applied through the hydraulic piston, and records both force and displacement. The flexural failure test was performed in accordance with the diagram that is shown in Figures 8 and 9:  It can apply continuous and variable loads, with the objective of achieving a uniform displacement of the transducer. The application of a variable downward load in the test was decided upon at a velocity of 0.01 mm/s.
The process was managed with the MTS Flex Test GT digital controller [50], which displays information from the force transducer that controls the force applied through the hydraulic piston, and records both force and displacement. The flexural failure test was performed in accordance with the diagram that is shown in Figures 8 and 9: The process was managed with the MTS Flex Test GT digital controller [50], which displays information from the force transducer that controls the force applied through the hydraulic piston, and records both force and displacement. The flexural failure test was performed in accordance with the diagram that is shown in Figures 8 and 9:  The process was managed with the MTS Flex Test GT digital controller [50], which displays information from the force transducer that controls the force applied through the hydraulic piston, and records both force and displacement. The flexural failure test was performed in accordance with the diagram that is shown in Figures 8 and 9:

Analytical Models
The analytical models that will be employed, in application of the current norms in the European Union (EuroCode 5) [51] and in Spain (Código Técnico de la Edificación Documento Básico SE-M Seguridad en Madera) [52], are explained in the following sections [53].
The specific loading hypotheses are, on the one hand, the dead loads corresponding to the weight of the materials, and on the other, the variable load applied by the hydraulic piston up until the failure limit, as described in Section 3. Subsequently, the ultimate limit state criteria that corresponded to the composite section will be applied, in so far as it refers to the fatigue failure of sections subjected to stress orientation, along the main directions. These verifications fundamentally correspond to shear forces between the section of the wooden joist and the mortar in the compression layer through the connection, so that the collaboration was effective as a mortar-wood joist to protect against fatigue (breakage), taking the section subjected to simple flexion.

Ultimate Fatigue Limit State of the Sections Subjected to Shear Forces-Justification of the Union of the Laminated Wood-Mortar Composite Section
The theoretical requirement for collaboration of the mortar layer in the laminated wood-ecological mortar construction unit design is that the screws or connectors will prevent the displacement of the head of the joist, for which reason it was necessary to arrange them at an angle, as shown in Figures 4  and 10.

Analytical Models
The analytical models that will be employed, in application of the current norms in the European Union (EuroCode 5) [51] and in Spain (Código Técnico de la Edificación Documento Básico SE-M Seguridad en Madera) [52], are explained in the following sections [53].
The specific loading hypotheses are, on the one hand, the dead loads corresponding to the weight of the materials, and on the other, the variable load applied by the hydraulic piston up until the failure limit, as described in Section 3. Subsequently, the ultimate limit state criteria that corresponded to the composite section will be applied, in so far as it refers to the fatigue failure of sections subjected to stress orientation, along the main directions. These verifications fundamentally correspond to shear forces between the section of the wooden joist and the mortar in the compression layer through the connection, so that the collaboration was effective as a mortar-wood joist to protect against fatigue (breakage), taking the section subjected to simple flexion.

Ultimate Fatigue Limit State of the Sections Subjected to Shear Forces-Justification of the Union of the Laminated Wood-Mortar Composite Section
The theoretical requirement for collaboration of the mortar layer in the laminated wood-ecological mortar construction unit design is that the screws or connectors will prevent the displacement of the head of the joist, for which reason it was necessary to arrange them at an angle, as shown in Figures 4 and 10. This arrangement guarantees that the collaboration between both materials laminated wood-ecological mortar is effective and the total height of the slab section will be the sum of the heights (height of the laminated wood and of the mortar). This design principle will ensure that the stress forces are jointly shared, so that the neutral fiber of the constructive unit that is designed will be optimized.
The mathematical model recommended by EuroCode 5 was applied for the study of the shear force generated at the laminated wood-mortar interface [51] < where, maximum shear force applied to the wood-mortar joint maximum shear strain that the vertical connection will withstand based on connectors in the composite section The following expression was adopted, in order to calculate = 0.78 where, calculated crushing strength of the wood (16 N/mm 2 ) elastic limit of steel connector reduced by a reduction coefficient of 1.05 number of connectors per section This arrangement guarantees that the collaboration between both materials laminated wood-ecological mortar is effective and the total height of the slab section will be the sum of the heights (height of the laminated wood and of the mortar). This design principle will ensure that the stress forces are jointly shared, so that the neutral fiber of the constructive unit that is designed will be optimized.
The mathematical model recommended by EuroCode 5 was applied for the study of the shear force generated at the laminated wood-mortar interface [51] where, R d -maximum shear force applied to the wood-mortar joint ϕ d -maximum shear strain that the vertical connection will withstand based on connectors in the composite section The following expression was adopted, in order to calculate ϕ d where, f hd -calculated crushing strength of the wood (16 N/mm 2 ) f yd -elastic limit of steel connector reduced by a reduction coefficient of 1.05 n-number of connectors per section d-diameter of the connectors (mm) s-interval between planes of connection (mm) The calculated value of the shear force, R d , on the wood-mortar slab was calculated with the expression where,

V pp -shear strength of composite slab V q -shear force loading H-section height
The result of the application of these formulas will determine the suitability of the collaboration between the composite wood-mortar sections.

Ultimate Fatigue Limit State of the Section Subjected to Oriented Stress along the Main Directions-Simple Flexion
It must be ensured that the calculated stress forces of the loading (σ md ) will be less than the ultimate failure limit strength of the wood material ( f md ), in order to guarantee the flexural strength of the laminated wood-mortar construction unit The calculation hypotheses of the Technical Building Code-CTE-SE M [52], similar to those used by the Eurocode 5 [51] were considered, in order to calculate the theoretical ultimate limit states and their corresponding stresses.
The calculated strength under flexion of the wood, f md , was calculated with the expression where: k mod -is the modification factor in accordance with the class of duration of the load combination (in our case instantaneous load), the type of wood (laminated Gulam joist) and the class of service (service 1: temperature 20 ± 2 • C and relative humidity at 65%), in this case 0.60 k h -coefficient that depends on the relative size of the section. According to the CTE-SE M, for rectangular sided GULAM joists under 600 mm, the following minimum values will be used where, h-height of the side under flexion (mm) f mk -characteristic strength of the wood for GL24c (24 MPa) γ m -partial safety limit coefficient for the laminated wood, extraordinary situation 1.0 Substituting the earlier values in Equation (7), the following value of f md was given as The following expression was applied, to determine the calculated stress limit under flexion (σ d ) at the ultimate flexural moment of the section where, M p -ultimate flexural moment of the composite section W d -strength modulus of the homogenized section (module W i Table 3) The ultimate tensile stress under uniaxial solicitation, (σ d ), is equaled by the maximum admissible stress of the material, ( f md ), in order to obtain the maximum load at the ultimate moment of failure. The tensile stress produced at the ultimate moment that is generated by the load is therefore equated with the maximum stress that the composite laminated wood-mortar section can withstand. In this way, it is possible to obtain the maximum ultimate load breaking the section Solving the above equation for M p yields The load, (P), at the ultimate moment, M p , of the section for a joist loaded mid-span and supported at both ends, was calculated with the expression where, P-load under flexion L-length between supports (see Figure 8) Equaling the ultimate moment of the composite section (11) with the load at the ultimate moment (12), yields Solving the above equation for P yields The maximum stresses generated at the upper and lower fibers, both for the joist itself and the composite laminated wood-mortar section, were determined in the following way: •

Isolated wooden Gulam joist
The stress on the lower fiber, σ i (shear), and upper fiber, σ s (compression), were calculated with the following expression and compared with the maximum admissible stress, f mk , of the wood where,

1.
M p -moment produced by the force P 2.
W-strength modulus of the wooden section referring to h/2 (see Table 3) A diagram is shown in Figure 11, of the stress state.
Solving the above equation for P yields The maximum stresses generated at the upper and lower fibers, both for the joist itself and the composite laminated wood-mortar section, were determined in the following way: •

Isolated wooden Gulam joist
The stress on the lower fiber, (shear), and upper fiber, (compression), were calculated with the following expression and compared with the maximum admissible stress, fmk, of the wood = = ≤ 24 (15) where, Mp moment produced by the force P strength modulus of the wooden section referring to h/2 (see Table 3) A diagram is shown in Figure 11, of the stress state. Figure 11. Stress state of an isolated joist. Figure 11. Stress state of an isolated joist.

•
Composite laminated wood-mortar section The stresses that are exerted on the lower fiber, σ i (shear), of the composite section were compared with the maximum admissible stress, f mk , through the expression where, σ i -stress at lower fiber compared with the ultimate stress of the wood, f mk M p -moment produced under solicitation (in this case strength P) W i -strength modulus of the wooden section referring to Y 1 (distance, Y G , to the lower fiber, see Table 4) The stresses that were produced on the upper fiber, σ s (compression), of the composite section were compared with the maximum admissible stress, f k , of the mortars forming the compression layer, in accordance with the expression where, σ s -upper fiber stress compared with the ultimate stress of the mortar under compression, f k , (MR/MLC/MLM) M p -moment generated under solicitation, in this case force P W s -strength modulus of the wooden section referring to Y 2 (distance, Y G , to the upper fiber, see Table 4) In Figure 12, a diagram is shown of the stress state of the laminated wood-mortar compression layer construction unit.
where, σs upper fiber stress compared with the ultimate stress of the mortar under compression, fk, (MR/MLC/MLM) Mp moment generated under solicitation, in this case force P Ws strength modulus of the wooden section referring to Y2 (distance, YG, to the upper fiber, see Table 4) In Figure 12, a diagram is shown of the stress state of the laminated wood-mortar compression layer construction unit.

Theoretical Model, CYPE Program
Cype software, with the Cypecad plugin v2019.e [54] was used for modelling the design of the construction units. This program performs a three-dimensional spatial calculation with matrix rigidity methods, in which the connections between nodes are the elements that define the structure: pillar, joist, and joist header. In addition, the program can establish the deformation compatibility at all nodes considering all six degrees of freedom.
A static calculation was performed, for the purposes of obtaining the solicitations and displacements, at all loading states, considering a linear behavior of the material, in other words, a numerical calculation of the first order, for computerized computation.
The program generates a mesh of bar-type elements sized 0.25 × 0.25 m (grid with node ports). A wooden joist was discretized and modelled for the design of the construction unit using the parameters listed in Table 1, and ecological mortar compression layers with compressive strengths, fck, of 35 MPa (MR) and 17 MPa (MLC and MLM). The discretization of the test model may be seen in Figure 13.

Theoretical Model, CYPE Program
Cype software, with the Cypecad plugin v2019.e [54] was used for modelling the design of the construction units. This program performs a three-dimensional spatial calculation with matrix rigidity methods, in which the connections between nodes are the elements that define the structure: pillar, joist, and joist header. In addition, the program can establish the deformation compatibility at all nodes considering all six degrees of freedom.
A static calculation was performed, for the purposes of obtaining the solicitations and displacements, at all loading states, considering a linear behavior of the material, in other words, a numerical calculation of the first order, for computerized computation.
The program generates a mesh of bar-type elements sized 0.25 × 0.25 m (grid with node ports). A wooden joist was discretized and modelled for the design of the construction unit using the parameters listed in Table 1, and ecological mortar compression layers with compressive strengths, f ck , of 35 MPa (MR) and 17 MPa (MLC and MLM). The discretization of the test model may be seen in Figure 13.

Full-Scale Flexural Test
Flexural failure tests were performed at the Large Infrastructures Laboratory of the Higher Polytechnic School of the University of Burgos, in order to test the behavior of the full-scale specimens.
Two specimens of the laminated wood-ecological mortar construction unit were tested for each slab that was constructed. The two joists of laminated wood and their performance were also separately analyzed, with the aim of establishing their influence on the strength capacity of the composite section.
The maximum load values under flexural failure load of the specimens, as well as their displacement may be seen in Table 6 and Figure 14. The values of the table are the result of the arithmetical average of the two test specimens of each constructive unit.
If the flexural behavior of the composite laminated wood-ecological mortar section is compared with the wooden joist, a higher maximum failure load can be observed for f the design model, with

Full-Scale Flexural Test
Flexural failure tests were performed at the Large Infrastructures Laboratory of the Higher Polytechnic School of the University of Burgos, in order to test the behavior of the full-scale specimens.
Two specimens of the laminated wood-ecological mortar construction unit were tested for each slab that was constructed. The two joists of laminated wood and their performance were also separately analyzed, with the aim of establishing their influence on the strength capacity of the composite section.
The maximum load values under flexural failure load of the specimens, as well as their displacement may be seen in Table 6 and Figure 14. The values of the table are the result of the arithmetical average of the two test specimens of each constructive unit.

Results Obtained by the Analytical Models
Applying the analytical model developed under Section 3.3, the maximum failure loads both of the laminated wood-ecological mortar section designs and of the wooden joist in isolation were obtained. In Table 7, the results are shown of the ultimate failure loads for the stress levels on both the lower fiber, σi (shear), and on the upper fiber, σs (compression). If the flexural behavior of the composite laminated wood-ecological mortar section is compared with the wooden joist, a higher maximum failure load can be observed for f the design model, with values that are 43.55% higher for the MLM mortar, and 71.45% higher for the MLC and MR mortars. This observation leads us to affirm that the mortar compression layer works through the connectors in unison with the wooden joist ( Figure 15).

Results Obtained by the Analytical Models
Applying the analytical model developed under Section 3.3, the maximum failure loads both of the laminated wood-ecological mortar section designs and of the wooden joist in isolation were obtained. In Table 7, the results are shown of the ultimate failure loads for the stress levels on both the lower fiber, σi (shear), and on the upper fiber, σs (compression). Likewise, if the deformations of the pieces are analyzed, a reduction of the displacement in the three composite laminated wood-mortar sections may be observed, with respect to the displacement of the wooden joist in isolation. The displacements, signs of impending breakage, for the three types of composite laminated wood-mortar section were very similar, at approximately 23-25 mm, while they reached 34 mm for the wooden joist in isolation. This behavior is explained by its lower inertia moment (I), and elasticity modulus (E).

Results Obtained by the Analytical Models
Applying the analytical model developed under Section 3.3, the maximum failure loads both of the laminated wood-ecological mortar section designs and of the wooden joist in isolation were obtained. In Table 7, the results are shown of the ultimate failure loads for the stress levels on both the lower fiber, σ i (shear), and on the upper fiber, σ s (compression). In the same way as in the full-scale test, it was confirmed that both materials (wood and mortar) were working together as the failure load of the wooden joist-calculated with the analytical method-was lower than the failure load of the composite wood-mortar sections.
In contrast, the analytically calculated stress state of the wooden joist in isolation implies shear and compression forces on the lower and upper fibers of 15.80 MPa, which are below the tensile stress limits that are characteristic of wood under both flexion and compression (f mgk < 24 MPa).
The analytically tested stress state of the composite laminated wood-mortar section provided shear strengths of 15-19 MPa in the lower fibers, close to those obtained by the isolated wooden joist, but below the characteristic flexural stress (f mgk < 24 MPa). Moreover, the tensile stress under compression forces produced on the upper fiber, σ s (5-8 Mpa), were very much lower than the compression strengths of the mortars themselves (35 and 17 Mpa).

Results Obtained with the CYPE Program
The application of Cypecad v2019.e software [53] yielded the results of the response of the designed model, under eventual center-span loading. The most representative isovalue lines of the forces that are produced are shown so as to visualize the results of the laminated wood-mortar model.
In Figure 16, the isovalues corresponding to the deformation resulting from the action of the maximum failure load (mauve color) are shown, observing values between the two supports and at approximately 25 mm mid-span (blue color). The theoretical values were somewhat lower than those from the full-scale laboratory tests.
In Figure 17, the values of the maximum moments obtained when applying the maximum failure load may be seen, expressed in isovalues (yellow-orange colors), which progressively diminished towards the supports (blue color). The values at those moments were similar to those obtained with analytical methods, such that the validity of the model may be affirmed. designed model, under eventual center-span loading. The most representative isovalue lines of the forces that are produced are shown so as to visualize the results of the laminated wood-mortar model.
In Figure 16, the isovalues corresponding to the deformation resulting from the action of the maximum failure load (mauve color) are shown, observing values between the two supports and at approximately 25 mm mid-span (blue color). The theoretical values were somewhat lower than those from the full-scale laboratory tests. In Figure 17, the values of the maximum moments obtained when applying the maximum failure load may be seen, expressed in isovalues (yellow-orange colors), which progressively diminished towards the supports (blue color). The values at those moments were similar to those obtained with analytical methods, such that the validity of the model may be affirmed.  approximately 25 mm mid-span (blue color). The theoretical values were somewhat lower than those from the full-scale laboratory tests. In Figure 17, the values of the maximum moments obtained when applying the maximum failure load may be seen, expressed in isovalues (yellow-orange colors), which progressively diminished towards the supports (blue color). The values at those moments were similar to those obtained with analytical methods, such that the validity of the model may be affirmed.

Results Analysis and Commentaries
The increase in resistance of the composite section of the mortar beam was significantly higher compared to the isolated beam. The increase of the failure load that was observed in the full-scale tests implied strength increases of 43% for the MLM mortar type, 75% for the MLC mortar type, and 71% for the mixed MR mortar type, following the addition of the compressive layer acting in unison.
In Figure 18, the flexural failure load values from the full-scale test and the results of the analytical models are shown. The space or gap between both values is the safety margin.

Results Analysis and Commentaries
The increase in resistance of the composite section of the mortar beam was significantly higher compared to the isolated beam. The increase of the failure load that was observed in the full-scale tests implied strength increases of 43% for the MLM mortar type, 75% for the MLC mortar type, and 71% for the mixed MR mortar type, following the addition of the compressive layer acting in unison.
In Figure 18, the flexural failure load values from the full-scale test and the results of the analytical models are shown. The space or gap between both values is the safety margin. As may be seen in Figure 18, the safety margin presents increases with respect to the analytical values, registering 10.71% in the case of reference mortar MR, 12.04% for mortar MLC, and 5.16% in the case of MLM. As may be seen in Figure 18, the safety margin presents increases with respect to the analytical values, registering 10.71% in the case of reference mortar MR, 12.04% for mortar MLC, and 5.16% in the case of MLM.
The failure load of the composite laminated wood-mortar section, according to the analytical model, was lower than the results of the experimental tests. These results validated the mathematical models that were employed, because they confirmed that the safety margin was sufficient in response to the loads that were transferred.
In the case of the wooden joist in isolation, the safety margin was much higher, as the differences between the values of the maximum failure load in the full-scale tests, and those obtained from the analytical models were twice as high. This behavior can be justified, because a larger number of variables intervene in the calculation of the mechanical behavior of the composite section, such as the use of materials with different elasticity moduli, and the compatibility of the laminated wood-mortar interface working in unison.

Conclusions
A theoretical and practical study of the mechanical behavior of a construction unit designed with laminated wood and an ecological mortar has been conducted, for the restoration of wooden slabs within historic buildings. The following conclusions can be drawn from the analyses that were performed.
It has been confirmed that the incorporation of the mortar compression layer increased the strength of the slab, as opposed to the wooden joist in isolation at an average percentage of over 40%. It implies a very significant strength gain, because it will compensate possible drawbacks with the materials in use and mistakes that can occur in the construction process. It will even permit an increase of the load with no problems relating to the collapse of the construction unit.
The results obtained from the real-scale tests were very similar, both for the reference mortar (MR) and for the mortars designed with recycled aggregate, MLC and MLM. Nevertheless, the objective of the investigation is to design a constructive unit formed of laminated wooden joists and a mortar dosed with construction waste, for which reason mortars MLC and MLM complied with the required mechanical strength conditions. In addition, both mortars presented a very low density, approximately half of the reference mortar dosed with natural aggregates. This contributes a competitive advantage over traditional mortar, as it adds less weight to the existing structure, which is an essential factor in the rehabilitation of old buildings.
On the other hand, using mortars manufactured with recycled aggregate, both mixed and from concrete, is respectful towards the environment, thereby contributing to the circular economy of construction materials.
Positive safety margins have in all cases been tested, as the values from the full-scale experimental test models surpassed those of the theoretical analytical models. It may be affirmed that the full-scale laboratory results validated the analytical methodology that was applied.
From the results obtained with the analytical model and from the full-scale laboratory experimental test results, and their comparison, it was confirmed that the safety margin was greater for the wooden joist in isolation.
The tensile stress state of the joist in isolation, obtained with the mathematical model, showed that the forces of both shear and compression were below the characteristic stress limits under flexion and compression of the strength class of the wood that was employed, taken from Standard CTE-SE M (f mgk < 24 Mpa).
In the same way, the stress state of the composite laminated wood-mortar section from the analytical test methods gave shear strain limits in the lower fibers close to those obtained in the wooden joist in isolation, but very much lower compression forces in the upper fiber due to the compression of the mortar. This latter point demonstrates and corroborates that the experimental failures, in all cases, collapsed due to excessive stress on the lower fibers.
It may be added that the results from the analytical models were similar to the simulation process with CYPE software.

Patents
The mortar used in this research is protected by the Invention Patent: ES 2 629 064 B2 Mortero estructural aligerado con arcilla expandida y agregados con áridos reciclados [Structural lightweight mortar with expanded clay and aggregates with recycled fines]. The patent holder is the University of Burgos-Spain, and the inventors are the authors of this paper.