Multi-Objective Analysis for the Optimization of a High Performance Slab-on- Ground Floor in a Warm Climate

Abstract

The building sector is responsible for a large part of the overall energy demand in Europe. Energy consumption may be reduced at the design stage by selecting the proper building elements. This study develops a multi-objective analysis for a highly efficient slab-on-ground floor, whose design is optimized for a warm climate. Possible floor configurations have been obtained using the software tools modeFRONTIER, for the multi-objective analysis, and MATLAB, for the computational code. To proceed with the optimization of the different floor layers, a dataset has been developed for several materials in relation to a number of parameters: thermo-physical properties, eco-sustainability score according to the ITACA Protocol, costs, source, and structural features. Results highlight how a high surface mass is preferable when guaranteed by concrete in the innermost and outermost layers. Furthermore, insulating materials are better placed in the middle layers, with the insulating and synthetic materials adjacent to the ground and insulating and natural materials adjacent to the floor. Results emphasize the importance of thermal transmittance close to the Italian regulation limit (0.38 W/m² K) in the climatic zone C, to allow an adequate exchange with the ground in summer, avoiding overheating. The outcomes show that the obtained slab-on-ground floor configurations favor the use of local, recyclable, sustainable, and eco-friendly materials, which is in line with energy policies and sustainability protocols. The paper supports the decision making process that takes many variables into account at the building design stage.

1. Introduction

In Europe, the building sector accounts for approximately 40% of final energy consumption and 36% of CO₂ emissions [1]. The European Directive Energy Performance of Building (EPBD) recast [2] aims at decreasing energy consumption in buildings, establishing that all new buildings have to be Nearly Zero Energy Buildings (NZEBs) by 31 December 2020 [3]. Different studies highlighted that reaching the NZEBs target is achievable [4,5], but it is not always proven that the selected design choices are the most suitable from both an environmental and economic perspective [6,7].

All phases of the building life-cycle have an impact on the environment and on the human well-being, both directly (through material and energy consumption) and indirectly (due to inefficient infrastructure) [8]. Therefore, the selection of building materials has a key role in achieving ‘Green Buildings’ [9]. However, the choice of the technologies to be implemented in a building is not an easy task at the design stage.

In light of the European energy policy framework, a wide range of technologies used to increase energy savings have become available during the last decade [10,11,12]. In efficient buildings, there are many different energy saving tactics: summer heat gains and winter heat losses are minimized; passive heating and cooling techniques are available; a rational use of daylight reduces lighting; the envelope dynamically controls the exchange between indoors and outdoors; renewable energy production compensates energy consumptions; and systems are generally more efficient [13,14,15].

The impact assessment of building elements on energy performance is crucial and requires the development of specific analysis and simulation tools to select the most appropriate technologies. Despite several studies that deal with the characterization of different envelope components, such as walls [16] and windows [17], few studies focus on slab-on-ground floors.

The main objective of this paper is to design a slab-on-ground floor that is able to guarantee a proper thermal comfort inside a building. In particular, the paper is focused on this component in the reduction of overheating, a common issue in a warm climate.

A generic model of a slab-on-ground floor of five layers has been considered in this research. It searches for a range of configurations to reduce energy consumption and CO₂ emissions linked to heating and air conditioning. The study evaluates the sustainability of several materials, according to the environmental score obtained by the ITACA Protocol. The ITACA Protocol is a tool for assessing the level of energy and environmental sustainability of buildings, developed by the Institute for the Transparency of Contracts and Environmental Sustainability. The Protocol tests the performance of a building when considering the building’s consumption, energy efficiency, impact on the environment, and human health.

Another important goal of this study is to propose a method which permits to reduce the implementation costs.

The statistical method used to perform the simulations is the DOE (Design of Experiment), which satisfies the relations between inputs (objectives and constraints) and outputs. The set of initial configurations is processed according to Moga II (Multi Objectives Genetic Algorithm), which uses different methodologies for playback: classic crossing, directional crossover, mutation, and selection. The algorithm permits the individuals to evolve during the execution, making a selection of individuals of the current population for the generation of new elements, which are the new population for the following iteration.

The optimal slab-on-ground floor configurations are then identified within the set of optimal solutions of the Pareto front, whose solutions represent the best compromise between constraints and objectives, which means that there are no other solutions that are better at the same time for all the objectives considered in the optimization function. These configurations are finally analyzed and discussed.

1.1. Literature Overview

In recent years, there has been a great attention on environmental issues linked to buildings. Several researches investigate strategies to reduce of CO₂ emissions, while pursuing the indoor comfort. In particular, buildings located in a warm climate have been investigated for the identification of the best solutions in terms of energy and economic feasibility. Several parametric studies on envelope, fenestration, and technical systems have been carried out using building simulations [18,19]. Wright et al. [20] demonstrate that the building design can be considered as a multi-criteria problem. Castro-Lacouture et al. [21] state that the choice of building materials with low environmental impact results in an optimization model. The multi-criteria methodology is also suggested by Baglivo et al. [22,23], who show that the key parameter to monitor the envelope performance located in a warm climate is the internal heat capacity, useful to minimize overheating and discomfort inside the building.

In the literature, other studies deal with this topic, paying attention to the thermal behavior of construction materials. Rantala et al. [24] show that the difference in thermal conductivity between the subsoil and the drainage materials should be considered to identify the temperature distribution and the heat loss through the slab-on-ground floor. It is demonstrated that capillary rise decreases when a coarse gravel layer (drainage layer) is placed before the ground. Furthermore, the authors suggest the inclusion of a non-capillary insulating material (i.e., EPS) which reduces rising damp and heat dissipation. Choi et al. [25] study the heat transfer across the slab-on-ground floor.

Wang et al. [26] present evidence of the impact of climates on the requirement for heating and cooling residential buildings. Evola et al. [27] focus on the identification of optimal design solutions for NZEBs [27]. Suárez et al. [28] shows different passive solutions to avoid overheating problems in a Single-Family Home in Southern Spain. Rehman [29] focuses on an experimental assessment of insulating materials for passive buildings located in warm and humid climate. Environmental

Principi et al. [30] study the application of the ITACA Protocol, which will be presented in Section 1.4. Bribian et al. [31] show that the impact of the construction process may be reduced using the best available techniques of eco-innovation during the production processes.

Alkaff et al. [32] state that the ground can be considered as a heat tank and useful in microclimate control. Hait et al. [33] explain how heat can be stored and retrieved throughout the year, without energy from mechanical systems. The most important point is that heat can be naturally stored in the ground since it absorbs the radiation from the sun in summer, while the ground releases it during the cold seasons. This allows controlling the summer heat gain and the heat losses in winter.

1.2. Multi-Objective Analysis

Multi-objective analysis can help the decision-maker to deal with specific problems, as well as to compare and rank alternatives based on an evaluation of multiple criteria. Mathematical models are then used to weight criteria, score alternatives, and synthesize final results selecting the best alternatives [34,35]. These methods have rapidly grown in research in recent years [36].

However, due to a lack of confidence and established best practices, designers and building managers rarely perform this kind of analysis [37]. Moreover, in relation to buildings, the decision-making process often uses only an economic criterion which is mainly related to the cost-benefit ratio obtained with a financial analysis [38].

In the literature, multi-objective analysis has been applied to buildings with different purposes [39]. Among them: to assist with green technologies selection [40], to evaluate climate change mitigation policies [41], to assist with building certification [42,43], to optimise the NZEB design [44], to compare passive and active technology options [45], and to improve thermal and energy performance [46,47].

There is a growing need to investigate how this analysis can support the choice of energy-efficient technologies considering more criteria in the selection. This paper proposes the use of multi-objective analysis for the optimization of the slab-on-ground floor in a warm climate.

1.3. Thermal Behavior of Slab-on-Ground Floor

Insulation and thermal mass are key parameters for thermal comfort in buildings. Insulation reduces the heat transfer between the inside and outside, while thermal mass results in a delay of the heat transfer. Therefore, both help to keep the building cool in summer and warm in winter.

The building performance in semi-arid warm climate has previously been studied [48]. The authors carry out an investigation combining thermal insulation and inertia in a building. They state that it is convenient to place the thermal mass in correspondence of passive gains, where it can absorb more heat radiated from the sun during the day. The mass must be externally insulated to reduce the heat transfer from the inside to the outside.

Table 1. Dynamic thermal characteristics of building components.

Description	Equation
Periodic penetration depth of a heat wave in a material (m).	$\delta =\sqrt{\frac{\lambda T}{\pi \rho c}}$	(1)
Ratio of the thickness of the layer to the penetration depth.	$\xi =\frac{d}{\delta }$	(2)
Z11: temperature amplitude factor, i.e., the amplitude of the temperature variations on side 2 resulting from an amplitude of 1 K on side 1.	$Z_{11}=Z_{22}=\cosh \left(\xi \right)\cos \left(\xi \right)+j\sin h\left(\xi \right)\sin \left(\xi \right)$	(3)
Z12: amplitude of the temperature on side 2 when side 1 is subjected to a periodically varying density of heat flow rate with an amplitude of 1 W/m2.	$Z_{12}=-\frac{\delta }{2\lambda }\left\{\sin h\left(\xi \right)\cos \left(\xi \right)+\cos h\left(\xi \right)\sin \left(\xi \right)+j\left[\cos h\left(\xi \right)\sin \left(\xi \right)-\sin h\left(\xi \right)\cos \left(\xi \right)\right]\right\}$	(4)
Z21: amplitude of the density of heat flow rate through side 2 resulting from a periodic variation of temperature on side 1 with an amplitude of 1 K.	$Z_{21}=-\frac{\lambda }{\delta }\left\{\sin h\left(\xi \right)\cos \left(\xi \right)-\cos h\left(\xi \right)\sin \left(\xi \right)+j\left[\sin h\left(\xi \right)\cos \left(\xi \right)+\cos h\left(\xi \right)\sin \left(\xi \right)\right]\right\}$	(5)
Thermal admittance: complex quantity defined as the complex amplitude of the density of heat flow rate through the surface of the component adjacent to zone m divided by the complex amplitude of the temperature in the same zone when the temperature on the other side is held constant.	$Y_{11}=-{\left(\frac{\widehat{{\Phi }_i}}{\widehat{{\theta }_i}}\right)}_{{\widehat{\theta }}_e=0}=- \frac{Z_{11}}{Z_{12}}$	(6)
	$Y_{22}=-{\left(\frac{\widehat{{\Phi }_e}}{\widehat{{\theta }_e}}\right)}_{{\widehat{\theta }}_i=0}=- \frac{Z_{22}}{Z_{12}}$	(7)
Decrement factor: ratio of the modulus of the periodic thermal transmittance to the steady-state thermal transmittance U.	$f_d=\frac{U_{din}}{U}= \frac{\left|Y_{12}\right|}{U}$	(8)
Periodic thermal transmittance: complex quantity defined as the complex amplitude of the density of heat flow rate through the surface of the component adjacent to zone m divided by the complex amplitude of the temperature in zone n when the temperature in zone m is held constant.	$Y_{11}=-{\left(\frac{\widehat{{\Phi }_i}}{\widehat{{\theta }_e}}\right)}_{{\widehat{\theta }}_i=0}=- \frac{1}{Z_{12}}$	(9)
Areal heat capacity: heat capacity divided by area of element (1 internal 2 external).	$k_1= \frac{T}{2\pi }\left|\frac{Z_{11}-1}{Z_{12}}\right|$	(10)
	$k_2= \frac{T}{2\pi }\left|\frac{Z_{22}-1}{Z_{12}}\right|$	(11)
Time shift: time lead (if positive). or time lag (if negative). where the argument evaluated in the range 0 to 2π. The time shift is a period of time between the maximum amplitude of a cause and the maximum amplitude of its effect.	$\Delta t= \frac{T}{2\pi }\arg \left(Z_{12}\right)$	(12)
Heat transfer matrix: matrix relating the complex amplitudes of temperature and heat flow rate on one side of a component to the complex amplitudes of temperature and heat flow rate on the other side.	$Z=\left(\begin{array}{c}{\widehat{\theta }}_2\\ {\widehat{q}}_2\end{array}\right)= \left(\begin{array}{cc}{Z}_{11}& Z_{12}\\ Z_{21}& Z_{22}\end{array}\right)\cdot \left(\begin{array}{c}{\widehat{\theta }}_1\\ {\widehat{q}}_1\end{array}\right)$	(13)

reports the dynamic thermal characteristics of building elements as assessed by the EN ISO 13786. It provides the heat transfer matrix Z to correlate the complex amplitude of temperature and heat flow rates at the external side with the internal side. The periodic penetration depth δ (construction material properties) and ξ (ratio of the thickness of the layer to the penetration depth) are essential to compute the components of the heat transfer matrix Z.

1.4. Assessment of the Environmental Score According to the ITACA Protocol

The aim of the internationally established sustainability rating systems is to encourage the adoption of measures with a low impact on human health and the environment. Although the availability of information on sustainable materials is rising, researchers have not agreed on a clear definition of sustainable materials and usage [49]. In general terms, the materials:

• have a high recyclable content [50,51];
• are characterized by rapid renewal periods [19];
• have a high reusable content [50,51];
• present low emission of contaminants [49,50];
• are characterized by low energy consumption [49,50,52];
• show low cost maintenance [53];
• are safe to use [51,52,53].

The ITACA Protocol is an energy-environmental labelling system for buildings certification to evaluate the sustainability and quality of the building and building components. The basic principle is to share a common standard at international level, as indicated in the sustainable construction method (SB method). The SB method has been developed by the international research project “Green Building Challenge”, run by iiSBE (International Initiative for Sustainable Built Environment) since 2002. The Italian Association of the Regions has decided to adopt the SB method as the basis for the creation of a tool for the sustainability assessment, the ITACA Protocol, which suggests the properties of “eco-friendly” materials. In particular, the ITACA Protocol promotes recycled and local materials. The supply of building material from local producers allows to decrease the distance that a given component must cover to reach the construction site, reducing the emissions during its transport. Local materials originate within 300 km from the construction site. Furthermore, the “sustainable materials” measure the percentage of an eco-sustainable material, which includes building materials certified as eco-friendly [54].

2. Methodological Approach

The methodological approach of this paper aims at the characterization of a high efficient slab-on-ground floor for a building located in a warm climate. It is designed to optimize the thermal behavior of the building allowing an interaction with the subsoil able to guarantee the proper heat exchange depending on the season.

The Italian climatic zone C has been considered in the analysis, based on the national classification linked to the number of the heating degree-days, which is equal to 1153 in Lecce (South Italy), the city under investigation. This is characterized by non-extreme winters and high aridity in summer (average temperature 30.3 °C) [55,56]. Rainfall is concentrated in autumn (240 mm seasonal average value) and winter (190 mm seasonal average value), while spring and summer have lower levels (average seasonal rainfall of 105 mm and 60 mm respectively). The building design temperature is equal to 20 °C in winter and 26 °C in summer.

2.1. The Multi-Objective Optimization

The model of the slab-on-ground floor used in the simulations is characterized by five layers; this is typical in common practice. The optimization has been carried out using the modeFRONTIER tool. The software modeFRONTIER (modeFRONTIER rel.4.3.0, ESTECO SpA, Area Science Park in Trieste, Italy) is a Multidisciplinary Design Optimization tool where multi-objective optimization algorithms are employed to optimize the technical design process, as well as reduce time and costs to achieve better results.

The following parameters have been analyzed: static transmittance, periodic thermal transmittance, decrement factor, time shift, heat areal capacity, thermal admittance, surface mass, and thickness. The outputs of the model have been conceived according to the research aims and the climate under investigation, setting specific constraints and objectives. The modeFRONTIER flow diagram is shown in Figure 1.

The first step of the simulation is the DOE (Design of Experiments) sequence, which consists of 10,000 individual combinations. These combinations have been elaborated by the MOGA II (Multi Objective Genetic Algorithm), setting up 10 generations, for an amount of 100,000 iterations. The MOGA II starts from a series of possible solutions (DOE), representing the “initial population”, which evolves during the simulation. At each iteration, new elements are generated from the current population, and the new element replaces an equal number of individuals already present, thus creating a population for the next iteration. This succession of generations evolves towards a local optimum or global solution assigned to the problem. The outcome of each simulation is a set of possible solutions which represent the Pareto front. These combinations are the best compromise between the objectives and the constraints imposed in the model.

They are represented in a correlation matrix, a statistical method used to express a linear correlation between the two variables. It appears as a symmetric square matrix (M × M), where the r_ji element is the correlation coefficient between the i-th and j-th variable. The correlation coefficients are values ranging from −1 to + 1, but the main diagonal coefficients are equal to 1. The correlation shows the dependence between the two variables. In particular, the variables have a linear correlation when the correlation coefficient is between 0 and 1, while they have an inverse correlation when the correlation coefficient ranges between −1 and 0. The value 0 implies that there is no correlation between the two variables.

2.1.1. The Input Values

The simulation requires the definition of the input values. These are composed of five materials, which correspond to the five layers of the slab-on-ground floor under investigation. Each layer assumes a random value between 1 and 380. Each input value corresponds to a specific material, with defined properties:

• physical characteristics (

  Table 2. Thermo-physical properties of the studied building materials.

  Construction Materials	Commercial Thicknesses mm	λ W/mK	C J/kgK	ρ kg/m3
  Bio-brick	100; 140; 290	0.187	1112	1171
  Calcium silicate panels	80; 100; 120; 160; 180; 200; 240; 260; 300	0.045	1000	107.5
  Cellular glass	40; 60; 80; 100; 120; 140	0..55	850	120
  Cement mortar	30	1.4	836	2000
  Coconut fiber	20; 30; 40	0.043	1450	85
  Concrete	30; 40; 50; 60; 70; 80; 90; 100	1.67	880	2200
  Concrete closed structure. expanded clay	50	0.325	920	1000
  Cork panels expanded	10; 20; 30; 40; 50; 60; 80; 100; 120; 140; 160	0.039	1900	120
  EPS 1 (Expanded polystyrene)	20; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200	0.032	1350	28
  EPS 2	20; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200	0.033	1350	24
  EPS 3	30; 40; 50; 60; 80; 100; 120; 140; 160	0.034	1350	20
  EPS+graphite (Synthesized polystyrene foam with graphite)	20; 30; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200	0.003	1350	28
  Expanded clay	50	0.09	1000	300
  Exfoliated vermiculite	2	0.057	787	85
  Fiberglass	40; 50; 60; 85; 100	0.032	1030	32
  Flax fiber	40; 60; 80; 100	0.038	1410	30
  Granulated cellular glass	15; 20; 25; 30; 40; 50	0.078	850	160
  Granules of expanded perlite	5; 7; 10; 15; 20	0.045	837	92.5
  Gravel	50; 75; 100; 150	1.2	1000	1700
  Hemp fibers	30; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200; 220; 240	0.03	2200	38
  Hydraulic lime plaster	15	0.054	836	1150
  Hollow bricks 120/150*250*380	120; 150	0.08	850	1280
  Hollow bricks 160/200/250/300*250*380	160;200;250;300	0.08	1500	1280
  Kenaf fiber	20; 30; 40; 50; 60	0.039	2050	80
  Lime and gypsum plaster	15	0.007	837	1400
  Lightweight concrete	400	0.444	920	1300
  Plaster mixed ready	30	0.14	836	1000
  Pure gypsum plaster	12.5	0.035	837	1200
  Rigid polyurethane foam panels 1	20; 30; 40; 50; 60; 70; 80; 90; 100; 120	0.023	1500	40
  Rigid polyurethane foam panels 2	30; 40; 50; 60	0.028	1500	40
  Rigid polyurethane foam panels 3	80; 100	0.026	1500	40
  Rigid polyurethane foam panels 4	30; 40; 50; 60; 70	0.028	1500	40
  Rigid polyurethane foam panels 5	20; 30; 40; 50; 60; 80; 100; 120; 140; 160	0.023	1500	40
  Rigid polyurethane foam panels 6	20; 30; 40; 50; 60; 70	0.028	1500	40
  Rigid polyurethane foam panels 7	80; 90; 100	0.026	1500	40
  Rigid polyurethane foam panels 8	120; 140; 160	0.025	1500	40
  Rigid polyurethane foam panels 9	20; 30; 40; 50; 60; 70; 80; 90; 100; 120; 140; 160	0.023	1500	40
  Rock wool 1	50; 60; 80; 100	0.035	1030	70
  Rock wool 2	60; 80; 100	0.035	1030	100
  Rock wool 3	30; 40; 50; 60; 80; 100	0.037	1030	140
  Rock wool 4	20	0.036	1030	100
  Sheep wool	100; 150	0.037	1720	17.9
  Soft cellulose fibers panels	30; 40; 50; 60; 80; 100; 120; 140; 160	0.039	2000	70
  Tuff	110; 150; 180; 200; 250	0.336	1300	1215
  Wood fiber panels flexible	40; 50; 60; 80; 100; 120; 140; 160; 180; 200; 220; 240	0.038	2100	50
  Wood fiber hardboard	40; 60; 80; 100; 120; 140; 160; 180; 200	0.039	2100	160
  Wood wool	25; 35; 50	0.08	1800	385
  XPS 1 (Extruded polystyrene foam)	30; 40; 50; 60; 140; 160; 180; 200	0.034	1100	30
  XPS 2	80; 90; 100; 220; 240; 260; 280; 300	0.035	1100	30
  XPS 3	120; 220; 240; 260; 280; 300	0.036	1100	30
  XPS 4	200; 220	0.035	1100	30
  XPS 5	80; 100; 120; 240; 260; 280; 300	0.036	1100	30
  XPS 6	50; 60; 140; 150; 160; 180	0.034	1100	30
  XPS 7	200; 220	0.035	1100	30
  XPS 8	80; 100; 120; 240; 260; 280; 300	0.036	1100	30
  XPS 9	20; 30	0.032	1100	30
  XPS 10	25; 30	0.032	1100	30

  );
• eco-sustainability score according to the ITACA Protocol (

  Table 3. Evaluation of the eco-sustainability of the materials according to the ITACA Protocol.

  Material	Eco-Sustainable	Reused/Recycled	From Renewable Sources	Local Production (Heavy Materials)	Local Production (Materials for Finishing)
  Calcium silicate panels	x	x	x	-	-
  Bio-brick	x	x	x	-	-
  Cellular glass	x	-	-	-	-
  Cement mortar	-	-	-	-	x
  Coconut fiber	x	x	x	x	-
  Concrete	-	-	-	x	-
  Cork panels expanded	x	x	x	x	-
  EPS	-	-	-	x	-
  Exfoliated vermiculite	x	x	x	-	-
  Expanded clay	-	-	-	x	-
  Fiberglass	x	x	-	-	-
  Flax fiber	x	x	x	x	-
  Granulated cellular glass	x	x	x	-	-
  Granules of expanded perlite	x	x	x	-	-
  Gravel	-	-	-	x	-
  Hemp fibers	x	x	x	x	-
  Hollow bricks	-	-	-	x	-
  Hydraulic lime plaster	-	-	-	-	x
  Kenaf fiber	x	x	x	x	-
  Lime and gypsum plaster	-	-	-	-	x
  Plaster mixed ready	-	-	-	-	x
  Pure gypsum plaster	-	-	-	-	x
  Rigid polyurethane foam panels	x	x	x	x	-
  Rock wool	X	-	x	-	-
  Sheep wool	x	x	x	x	-
  Soft cellulose fibers panels	x	x	x	x	-
  Tuff	-	-	-	x	-
  Wood fiber panels	x	x	x	x	-
  Wood wool	x	x	x	x	-
  XPS	-	-	-	x	-

  );
• source and structural characterization of insulating materials (

  Table 4. Source and structural classification of insulating materials.

  Insulating Building Materials	Structure of the Materials			Source of the Materials
  	Fibrous	Cellular Mineral	Cellular Alveolar	Natural Vegetal	Natural Animal	Natural Mineral	Synthetic
  Bio-brick	x	-	-	x	-	-	-
  Cellular glass	-	x	-	-	-	x	-
  Coconut fiber	x	-	-	x	-	-	-
  Cork panels expanded	x	-	-	x	-	-	-
  EPS	-	-	x	-	-	-	x
  Exfoliated vermiculite	-	-	x	-	-	x	-
  Fiberglass	x	-	-	-	-	x	-
  Flax fiber	x	-	-	x	-	-	-
  Granulated cellular glass	-	x	-	-	-	x	-
  Granules of expanded perlite	-	x	-	-	-	x	-
  Hemp fibers	x	-	-	x	-	-	-
  Kenaf fiber	x	-	-	x	-	-	-
  Rigid polyurethane foam panels	-	-	x	-	-	-	x
  Rock wool	x	-	-	-	-	x	-
  Sheep wool	-	-	-	x	x	-	-
  Soft cellulose fibers panels	x	-	-	x	-	-	-
  Wood fiber hardboard	x	-	-	x	-	-	-
  Wood fiber panels flexible	x	-	-	x	-	-	-
  Wood wool	x	-	-	x	-	-	-
  XPS	-	-	x	-	-	-	x

  );
• cost from the regional price list (

  Table 5. Costs of the building materials.

  Construction Materials	Commercial Thicknesses (mm)	Cost (€/m2)	Cost (€/m3)
  Bio-brick	100; 140; 290	24.4; 32.94; 64.66	-
  Calcium silicate panels	80; 100; 120; 160; 180; 200; 240; 260; 300	58.23; 62.14; 65.68; 73.55; 77.36; 81.16; 101.45; 111.59; 131.63	-
  Cellular glass	40; 60; 80; 100; 120; 140	33.13 48.71 69.01 182.81 103.52	-
  Cement mortar	30		75.38
  Coconut fiber	20; 30; 40	18.20; 21.00; 26.50	-
  Concrete	30; 40; 50; 60; 70; 80; 90; 100	-	120
  Concrete closed structure. expanded clay	50	-	189
  Cork panels expanded	10; 20; 30; 40; 50; 60; 80; 100; 120; 140; 160	10.3; 13.3; 17.7; 23.60; 29.5; 35.4; 47.2; 59; 70.8; 82.6; 94.4	-
  EPS 1	20; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200	-	155
  EPS 2	20; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200	-	175
  EPS 3	30; 40; 50; 60; 80; 100; 120; 140; 160	-	120
  EPS+graphite	20; 30; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200	-	170
  Expanded clay	50	-	148
  Exfoliated vermiculite	2	-	165.29
  Fiberglass	40; 50; 60; 85; 100	4.95; 6.24; 7.51; 10.59; 12.48	-
  Flax fiber	40; 60; 80; 100	-	162.5
  Granulated cellular glass	15; 20; 25; 30; 40; 50	-	202
  Granules of expanded perlite	5; 7; 10; 15; 20	-	171
  Gravel	50; 75; 100; 150	-	26.1
  Hemp fibers	30; 40; 50; 60; 80; 100; 120; 140; 160; 180; 200; 220; 240	4.5; 5.75; 7.15; 8.55; 9.9; 11.75; 13.25; 15.35; 17.65; 19.8; 22; 24.2; 26.25	-
  Hydraulic lime plaster	15	-	112.4
  Hollow bricks 120/150/160 × 250 × 380	120; 150; 160	5.27	-
  Hollow bricks 200 × 250 × 380	200	5.45
  Hollow bricks 250 × 250 × 380	250	6.64	-
  Hollow bricks 300 × 250 × 380	300	11.52	-
  Kenaf fiber	20; 30; 40; 50; 60	5.10; 7.65; 10.20; 12.70; 15.30	-
  Lime and gypsum plaster	15	19.72	-
  Lightweight concrete	400	-	182
  Plaster mixed ready	30	-	182
  Pure gypsum plaster	12.5	18.48
  Rigid polyurethane foam panels 1	20; 30; 40; 50; 60; 70; 80; 90; 100; 120	7.2; 9.2; 11.3; 13.2; 15.15; 17.9; 19.7; 22; 24.1; 29.35	-
  Rigid polyurethane foam panels 2	30; 40; 50; 60	9.1; 11.3; 13.4; 15.55	-
  Rigid polyurethane foam panels 3	80; 100	20.15; 24.6	-
  Rigid polyurethane foam panels 4	30; 40; 50; 60; 70	10.1; 12.3; 14.3; 16.3; 19.4	-
  Rigid polyurethane foam panels 5	20; 30; 40; 50; 60; 80; 100; 120; 140; 160	9.5; 11.7; 14.1; 16.55; 18.6; 22.40; 26.9; 31.35; 36.2; 41.70	-
  Rigid polyurethane foam panels 6	20; 30; 40; 50; 60; 70	7.3; 9.15; 11.3; 13.25; 15.4; 18.3	-
  Rigid polyurethane foam panels 7	80; 90; 100	28.95; 31; 33.40	-
  Rigid polyurethane foam panels 8	120; 140; 160	38.15; 42.7; 47.65	-
  Rigid polyurethane foam panels 9	20; 30; 40; 50; 60; 70; 80; 90; 100; 120; 140; 160	7.4; 9.4; 11.5; 13.7; 15.5; 18.5; 20.2; 22.5; 2.8; 29.5; 34.5; 40	-
  Rock wool 1	50; 60; 80; 100	9.2; 10.59; 14.14; 17.65	-
  Rock wool 2	60; 80; 100	40.87; 48.43; 56.95	-
  Rock wool 3	30; 40; 50; 60; 80; 100	7.23; 9.63; 12.05; 14.46; 19.27; 24.10	-
  Rock wool 4	20	4.01	-
  Sheep wool	100; 150	4.95; 6.24; 7.51; 10.59; 12.48	-
  Soft cellulose fibers panels	30; 40; 50; 60; 80; 100; 120; 140; 160	7.5; 9.7; 12.15; 14.55; 18.45; 21.05; 25.2; 29.45; 33.7	-
  Tuff	110; 150; 180; 200; 250	15.94; 16.9; 31.5; 18.58; 19.63	-
  Wood fiber panels flexible	40; 50; 60; 80; 100; 120; 140; 160; 180; 200; 220; 240	4.17; 5.24; 6.26; 8.35; 10.43; 12.52; 14.69; 16.69; 18.95; 20.87; 23.12; 25.04	-
  Wood fiber hardboard	40; 60; 80; 100; 120; 140; 160; 180; 200	5.20; 7.79; 10.39; 12.99; 15.59; 18.18; 20.78; 23.38; 25.98	-
  Wood wool	25; 35; 50	18.6; 23.1; 31.9	-
  XPS 1	30; 40; 50; 60; 140; 160; 180; 200	-	90
  XPS 2	80; 90; 100; 220; 240; 260; 280; 300	-	90
  XPS 3	120; 220; 240; 260; 280; 300	-	90
  XPS 4	200; 220	-	150
  XPS 5	80; 100; 120; 240; 260; 280; 300	-	150
  XPS 6	50; 60; 140; 150; 160; 180	-	150
  XPS 7	200; 220	-	150
  XPS 8	80; 100; 120; 240; 260; 280; 300	-	150
  XPS 9	20; 30	-	93
  XPS 10	25; 30	-	98

  ).

In order to create a database with these values, a survey of various building materials available in the market has been conducted.

In relation to the physical characteristics of the analyzed materials (thermal conductivity, density, specific heat, and thickness), the evaluation of the dynamic thermal performance has been carried out through the calculation procedure defined by the EN ISO 13786:2008, described in Section 1.3 [57]. Temperature and heat flow rate are considered as a sinusoidal function of the time. A period equal to 86,400 s (corresponding to one day) has been evaluated, imposing a conductive thermal exchange condition.

Table 2 shows the thermo-physical properties of the building materials considered in this paper in terms of thermal conductivity (W/mK), specific heat (J/kgK), density (kg/m³), and thickness (mm). The calculation procedure has been developed using the software MATLAB (Matlab rel.7.0 MathWorks Inc, Natick, MA, USA). The numerical dataset of this study is detailed and reported in [58].

Table 3 shows the assessment of the materials as derived according to the section B of the ITACA Protocol, which is described in Section 1.4.

In the view of the design requirements, which prefers the use of sustainable resources, Table 4 shows a classification of the insulating materials with their structure and source. The classification shows 4 groups of insulating materials: vegetable, animal, mineral, and synthetic.

The costs of the analyses materials as derived from the Apulia regional price datasets are shown in Table 5.

2.1.2. The Output Values

In

Table 6. Objectives and constraints of the multi-objective optimization analysis.

Output	Objectives	Constraints
fd	Minimized	-
Δt	Maximized	<20 h
Y12	Minimized	<0.18 W/m2 K
κ1	Maximized	-
U	-	<0.38 W/m2 K
d	-	<0.70 m
Y11	Maximized	-
Y22	Maximized	-
% ITACA	Maximized	-
Cost	Minimized	-

, the constraints and objectives, in terms of cost, sustainability score, and thermal properties, are shown according to the passive building requirements placed in a warm climate. The optimal solutions are considered the best compromise between objectives and constraints.

In particular, the following constrains have been set to identify the best design of a high efficient slab-on-ground floor for a warm climate:

• the thermal transmittance (U) has been fixed minor than 0.38 W/${\mathrm{m}}^2$K, the legal limit (DM. 26/06/2015), considering the national climatic zone C;
• the maximum thickness of the floor has been set at 70 cm;
• the maximum achievable phase shift is 20 h, while the periodic thermal transmittance (Y₁₂) is minor than 0.18 W/m² K.

The remaining parameters are maximized or minimized without numerical constraints.

The sustainability score is given by an index (indicated as % ITACA) equal to the sum of the scores of the subsections of the ITACA Protocol. The ITACA score ranges from 0 to 88.8%, because the weight criteria of 11.1%, is not considered. This criterion is related to the use of building elements which permits a selective dismantling of the components that may be reused or recycled. Another objective is the minimization of the final cost with the goal of obtaining high efficient cost-effective solutions.

The different configurations of slab-on-ground floor obtained by the multi criteria analysis have been differentiated in accordance with the project goals. In the first preliminary step of the simulation, each layer can assume an arbitrary material and thickness, as a preparatory step for the following analysis (results in Section 3.1). Then, different configurations of slab-on-ground floor, in accordance with traditional construction methods, have been evaluated (results in Section 3.2). Three different types of slab-on-ground floors have been analyzed by imposing the constraint to place a specific material within a specific layer of the stratigraphy.

3. Results and Discussion

3.1. General Configurations

The first simulation, called “general configuration”, does not foresee any restriction on the material position in the layers and relative thicknesses, as shown in Figure 2. The constraints and objectives of Table 6 have been used.

A discriminant in the choice of the optimal configurations is to favor the thermal exchange with the ground, considered as a heat sink, useful in a warm climate. The histograms in Figure 3 show a statistical analysis obtained considering the characteristics of the materials reported in Table 4.

Moreover, Figure 4 highlights the presence of a specific material in a given layer. It can be noted that concrete is prevalent in the first layer, which is in contact with the ground, and in the fifth layer, facing the internal side. In particular, Figure 3 shows that there is a high probability of finding fibrous insulating materials in the first layer. In Figure 4, it is shown that the most frequent natural fibrous material in the first layer is wood fiber, characterized by a high specific heat. This result appears to disagree with the traditional methods and favors rising damp due to the porous structure.

In general, the optimal configurations are characterized by the presence of concrete in both the first and fifth layers. This result agrees with a feasible configuration, which provides:

• a layer of concrete in contact with the ground. This ensures a leveling and a support for a possible crawl space or insulating material placement;
• a layer of concrete in the fifth layer which allows the control of internal gains because of its high thermal capacity with high internal areal heat capacity and low decrement factor.

Furthermore, the presence of EPS in the second layer is an agreement with [12], which suggests to insert a thin EPS layer (not fibrous) to stop rising damp. This result is confirmed by the histograms shown in Figure 3 and Figure 4.

Table 7. Correlation matrix of the Pareto analysis for the variables of a generic simulation.

Variables	L1	L2	L3	L4	L5	k2	k1	d	U	Y12	Y22	Y11	fd	Ms	% ITACA	Cost €/m2	∆t
L1	1.000	−0.07	−0.041	−0.013	−0.113	−0.204	0.734	−0.023	0.080	0.128	−0.204	0.734	0.119	0.152	−0.222	0.167	−0.0097
L2		1.000	−0.078	−0.024	0.005	0.018	−0.034	0.005	0.074	−0.048	0.018	−0.039	−0.061	0.115	−0.134	0.052	0.012
L3			1.000	−0.081	−0.020	−0.021	−0.050	−0.008	0.081	−0.193	−0.021	−0.051	−0.200	0.189	−0.120	0.038	−0.054
L4				1.000	−0.070	−0.058	0.011	0.000	0.088	−0.096	−0.058	0.011	−0.097	0.166	−0.128	0.027	−0.007
L5					1.000	0.668	−0.183	0.092	0.048	0.023	0.668	−0.183	0.042	0.274	−0.311	0.123	−0.128
k2						1.000	−0.300	0.063	0.151	0.092	1.000	−0.300	0.064	0.316	−0.115	0.020	−0.157
k1							1.000	−0.067	0.124	0.162	−0.300	1.000	0.116	0.184	−0.158	0.123	−0.096
d								1.000	−0.519	−0.377	0.063	−0.066	−0.118	0.215	−0.072	0.0357	−0.107
U									1.000	0.068	0.151	0.124	−0.257	0.439	0.007	−0.326	−0.096
Y12										1.000	0.092	0.161	0.901	−0.478	−0.023	0.077	0.170
Y22											1.000	−0.300	0.064	0.316	−0.115	0.020	−0.157
Y11												1.000	0.116	0.184	−0.158	0.123	−0.095
fd													1.000	−0.561	−0.078	0.222	0.153
Ms														1.000	−0.203	−0.116	−0.367
% ITACA															1.000	−0.115	0.079
Cost €/m2																1.000	0.116
∆t																	1.000

shows the correlation matrix related to 17 variables of the problem:

• five variables relate to the input data of the five layers of the stratigraphy;
• 11 variables concern the thermal characteristics;
• one variable is linked to the sustainability based on the ITACA Protocol.

The values of the correlation matrix (Table 7) are highlighted with different colors: yellow for values ranging from 0.5 to 0.75, green for values ranging from −0.75 to −0.5, and blue from 0.75 to 1. From the correlation matrix, like predictable, it can be seen that there is a positive correlation between k₁–Y₁₁, k₂–Y₂₂, Y₁₂–fd, U–M_s, L₁–Y₁₁, and L₂–Y₂₂. Negative correlations are found between U and S_tot, fd and M_s.

Table 8. Example of high performance slab-on-ground floor with no constraints imposed in the stratigraphy.

Layer	Materials	U W/m2 K	Y12 W/m2 K	Y22 W/m2 K	Y11 W/m2 K	fd	Ms kg/m2	∆t h	κ1 kJ/m2 K	κ2 kJ/m2 K	d m	% ITACA	Cost €/m2
5	Concrete (80 mm)	0.081	0.01	13.44	4.81	0.148	408.88	15 h20’	66.17	184.70	0.51	77.7	84.3
4	Hemp fibers (160 mm)
3	Rigid polyurethane foam panels 8 (140 mm)
2	Rigid polyurethane foam panels 6 (30 mm)
M	Water protection membrane
1	Concrete (100 mm)
5	Concrete (90 mm)	0.122	0.01	11.08	4.85	0.081	394.88	15 h19’	66.71	152.31	0.41	77.7	41.7
4	EPS1 (60 mm)
3	Wood fiber hardboard (100 mm)
2	Rigid polyurethane foam panels 9 (80 mm)
M	Water protection membrane
1	Concrete (80 mm)
5	Concrete (90 mm)	0.229	0.03	9.82	4.86	0.139	502.4	11 h28’	67.28	135.25	0.44	55.5	87.4
4	Rigid polyurethane foam panels 7 (100 mm)
3	Concrete (70 mm)
2	Cellular glass (120 mm)
M	Water protection membrane
1	Concrete (60 mm)
5	Concrete (80 mm)	0.082	0.001	4.42	4.77	0.048	276	18 h44’	65.54	60.66	0.55	77.7	46.4
4	Wood fiber hardboard (160 mm)
3	XPS 2 (80 mm)
2	XPS 5 (200 mm)
M	Water protection membrane
1	Concrete (30 mm)

shows the optimal solutions as obtained by the simulations.

All the solutions in the Pareto front represent the best balance between constraints and objectives and can be identified as optimal solutions. The configurations show concrete in the first and fifth layers, while there are insulating materials within the intermediate layers. The concrete guarantees a high thermal inertia. In several stratigraphy configurations, it is interesting to note the presence of non-porous and non-fibrous insulating materials in the second layer (closed to the ground), which do not favor the absorption of water. Among the best solutions with similar thermal behavior (Table 8), the best ones are those with the minimum cost and the highest ITACA score.

3.2. Optimization of Typical Configurations

This section reports the results of various configurations considered technically feasible. These have been grouped into three categories of slab-on-ground floor (Section 3.2.1, Section 3.2.2 and Section 3.2.3). The principle is to bound determined layers with specific materials. The variables of the problem are the thicknesses and the choice of materials on which no constraints have been imposed.

3.2.1. Slab-on-Ground Floor with Concrete

Figure 5 shows the model of the analyzed stratigraphy characterized by concrete in the first and fifth layer. The concrete in the first layer, with additives against humidity, acts as a barrier between the ground and the insulating material in the other layers, preventing rising damp.

Furthermore, this gives the possibility to create a uniform surface from which the other layers can be adjoined.

Table 9. Example of high performance slab-on-ground floor with concrete.

Layer	Materials	U W/m2 K	Y12 W/m2 K	Y22 W/m2 K	Y11 W/m2 K	fd	Ms kg/m2	∆t h	κ1 kJ/m2 K	κ2 kJ/m2 K	d m	% ITACA	Cost €/m2
5	Concrete (70 mm)	0.380	0.17	8.48	4.73	0.439	302.33	6 h37’	66.37	118.85	0.235	77.7	46.81
4	Wood wool (25 mm)
3	Granulated cellular glass (30 mm)
2	Hemp fibers (50 mm)
M	Water protection membrane
1	Concrete (60 mm)
5	Concrete (100 mm)	0.380	0.11	16.45	4.87	0.276	538.4	10 h13’	68.37	227.46	0.33	77.7	38.8
4	Kenaf fiber (50 mm)
3	Wood fiber hardboard (40 mm)
M	Water protection membrane
2	Concrete (80 mm)
1	Concrete (60 mm)
5	Concrete (80 mm)	0.380	0.16	12.41	4.78	0.424	382.9	7 h05’	67.19	172.94	0.27	77.7	34.4
4	XPS 10 (30 mm)
3	Kenaf fiber (40 mm)
2	Granulated cellular glass (30 mm)
M	Water protection membrane
1	Concrete (90 mm)

highlights some optimal solutions, selected within the Pareto Front (Table 7), maximizing k1 and k2, in order to obtain a thermal balance between the ground, both floor and slab, in the indoor environment. The presence of concrete in the opposite sides permits to reach high values of k1 and k2, a beneficial choice in a warm climate.

Among the optimal solutions, there are slab-on-ground floor configurations with less number of layers, such as four. Indeed, the presence of the same adjacent materials implies the replacement of two layers with a single layer, reducing the overall number of layers, installation and implementation costs, as well as installation time. Specifically, the material that is more frequently repeated is concrete in layer four and five.

In Table 9, the optimal position of water protection membrane has been shown for each slab-on-ground floor. Furthermore, at the end of the optimization analysis, the user is free to choose the finishes that best suit the analyzed project. For this reason, the optimal configurations, from a thermal, environmental, and economic point of view, require further measures including the final flooring and the selection of specific water protection membranes.

This result is in agreement with [20], since it allows to have a high mass and therefore a high thermal inertia internally, as well as the presence of insulation close to the ground.

Moreover, it has to be highlighted that the insulating material in the second layer is a synthetic material, while a natural insulating material is detected in the fourth layer, which is not in direct contact with the ground.

3.2.2. Slab-on-Ground Floor with Gravel

Figure 6 shows the configuration of the slab-on-ground floor with gravel in the first layer in direct contact with the ground. In addition, the second and fifth layers have been bound with concrete. The presence of gravel between the concrete layer and the ground allows a water natural drainage hampering capillary rising.

As shown by the analysis of the operative temperature [59], it is not strictly necessary to obtain low transmittance values in warm climates. Therefore, the U value is preferable to be as high as possible and close to the law limit.

Table 10. Example of high performance slab-on-ground with concrete gravel.

Layer	Materials	U W/m2 K	Y12 W/m2 K	Y22 W/m2 K	Y11 W/m2 K	fd	Ms kg/m2	∆t h	κ1 kJ/m2 K	κ2 kJ/m2 K	d m	% ITACA	Cost €/m2
5	Concrete (80 mm)	0.380	0.15	13.53	4.78	0.384	419.30	7 h38’	67.29	188.03	0.27	55.5	37.3
4	Rock wool 1 (50 mm)
3	Rigid polyurethane foam panels 5 (20 mm)
M	Water protection membrane
2	Concrete (70 mm)
1	Gravel (50 mm)
5	Concrete (100 mm)	0.380	0.08	13.55	4.86	0.205	532.60	11 h51’	67.92	187.08	0.37	68.82	39.36
4	Wood fiber hardboard (40 mm)
3	Rigid polyurethane foam panels 2 (30 mm)
M	Water protection membrane
2	Concrete closed structure, expanded clay (50 mm)
1	Gravel (150 mm)
5	Concrete (80 mm)	0.380	0.16	10.19	4.78	0.425	333.00	6 h59’	67.16	142.43	0.23	77.7	31.5
4	Rigid polyurethane foam panels 1 (30 mm)
3	Cork panels expanded (40 mm)
M	Water protection membrane
2	Concrete (30 mm)
1	Gravel (50 mm)

points out the optimal solutions selected from among the 22,744 Pareto solutions.

The total surface mass values are very different both among these combinations and those presented in Table 9. This means that it is possible to obtain very similar transmittance and heat areal capacity with different total surface mass values. The configuration 6 of Table 10 demonstrates that it possible to have a high performance also with the lowest total surface mass among the analyzed combinations.

3.2.3. Slab-on-Ground Floor with Crawl Space

The crawl space is used to avoid rising dump and to physically split the floor from the ground. The presence of the crawl space increases comfort in the indoors, thanks to the creation of a ventilation space under the walking surface.

The air recirculation, which is formed inside the crawl space, mitigates the internal humidity by conveying it with possible harmful gases such as radon, outside the buildings.

Figure 7 shows the model used in the simulation with a ventilated crawl space. In

Table 11. Example of high performance slab-on-ground with crawl space.

Layer	Materials	U W/m2 K	Y12 W/m2 K	Y22 W/m2 K	Y11 W/m2 K	fd	Ms kg/m2	∆t h	κ1 kJ/m2 K	κ2 kJ/m2 K	d m	% ITACA	Cost €/m2
5	Concrete (50 mm)	0.375	0.10	8.05	4.25	0.272	332.40	8 h36’	59.75	112.06	0.68	77.70	36.99
4	Flax fiber (80 mm)
M	Water protection membrane
3	Concrete (50 mm)
2	Air-crawl space (450 mm)
1	Concrete (50 mm)
5	Concrete (30 mm)	0.369	0.16	6.67	3.47	0.424	216.80	8 h59’	49.88	95.02	0.46	77.70	28.85
4	Wood fiber hardboard (80 mm)
M	Water protection membrane
3	Concrete closed structure. expanded clay (50 mm)
2	Air—crawl space (260 mm)
1	Concrete (40 mm)
5	Concrete (40 mm)	0.373	0.18	9.31	3.88	0.473	272.28	7 h31’	55.56	130.38	0.47	77.70	36.00
4	Hemp fibers (60 mm)
M	Water protection membrane
3	Concrete closed structure. expanded clay (50 mm)
2	Air—crawl space (260 mm)
1	Concrete (60 mm)
5	Concrete (90 mm)	0.363	0.09	12.64	4.84	0.234	464.40	9 h55’	67.68	174.78	0.36	11.10	40.20
4	Rigid polyurethane foam panels 2 (60 mm)
M	Water protection membrane
3	Concrete (30 mm)
2	Air—crawl space (90 mm)
1	Concrete (90 mm)

, a set of solutions between 13489 Pareto solutions is selected.

4. Conclusions

This work optimizes the design of a slab-on-ground floor in a warm climate building. The obtained optimal combinations are the result of a multi-objective analysis, carried out using the modeFRONTIER tool, which aims to find the best configurations at lowest cost and in compliance with the ITACA Protocol. Several commercial and eco-friendly materials available in the market are included in the analysis.

Different layers have been considered in accordance with local traditional methods. Results show that the best solutions, among all the solutions extracted from the Pareto front, are obtained with a high surface mass, guaranteed by the presence of concrete in the innermost and outermost layers. Furthermore, the research highlights that insulating materials are better placed in the middle layers, with the insulating and synthetic materials adjacent to the ground and insulating and natural materials adjacent to the floor.

This study emphasizes the importance of the thermal transmittance, showing that is crucial to select solutions with U values close to the Italian regulation limit (i.e., 0.38 W/m² K). This permits an adequate exchange with the ground in summer, which is fundamental for buildings located in a warm climate where overheating must be avoided. In addition, it points out that it is possible to reach a high performance both with low and high total surface mass.

The developed multi-objective analysis allows the designer to achieve a wide range of optimal solutions. In addition, the methodology can be used for several purposes, different design requirements, and boundary conditions. Further studies are needed to investigate the applicability of the model in other climates, as well as introducing the ground properties as a variable parameter in the analysis. An evolution of the research may be an analysis of the floor when considering the ground temperature. This analysis provides the use of the simplified method as required by the UNI 12831, which considers the ground thermal conductivity of 2.0 W/mK. The effects of perimeter isolation are not considered. The heat loss through the floors directly or indirectly in contact with the ground depends on several factors, which include the exposed and perimeter of the slab on the ground floor (depending on the construction of the floor), the burial depth and the thermal properties of the ground. The thermal dispersion towards the ground can be calculated according to EN ISO 13370 in a detailed or in a simplified way.

In addition, the assessment could be broadened to include roof slab in order to have a whole set of solutions for the entire building.