Material Diets for Climate-Neutral Construction

The climate crisis is urging us to act fast. Buildings are a key leverage point in reducing greenhouse gas (GHG) emissions, but the embodied emissions related to their construction often remain the hidden challenge of any ambitious policy. Therefore, in this paper, we explored material GHG neutralization where herbaceous biobased insulation materials with negative net-global warming potentials (GWPs) were used to compensate for building elements that necessarily release GHGs. Different material diets, as well as different building typologies, were modeled to assess the consequences in terms of biobased insulation requirements to reach climate neutrality. Our results show that climate-neutral construction can be built with sufficient energy performance to fulfill current standards and with building component thicknesses within a range of 1.05–0.58 m when timber- and bamboo-based construction is chosen. Concrete-based ones require insulation sizes that are too large and heavy to be supported by the dimensioned structures or accepted by urban regulations. Moreover, a time horizon of 20 years is more appropriate for assessing the contribution of material shifts to biobased materials in the transition period before 2050. This paper demonstrates that this is technically feasible and that climate neutrality in the construction sector just depends on the future that we choose.


1.1.Geometric parameters for the Building Typologies
The TABULA/Episcope database 1 contains the main information about the composition of the reference residential buildings which are representative of the stocks across 21 European Countries, where more than 2700 buildings are analyzed and collected. From the excel file "tabula calculator.xlsx, the data that have been considered are: -A_C_Storey = single conditioned storey surface [m 2 ], -N_Storey_effective_envelope = number of conditioned storeys [-], -A_Esto, _W all_ExtAir = exterior wall surface [m 2 ], -A_Estim_Window = window surface [m 2 ].
Further simplifications were made in the definition of the geometric configurations. More precisely, the single area for every floor was kept the same for each storey. All the data of the different BT collected from TABULA/Episcope database were normalized according to the Reference Energy Surface (RES). RES is the total surface of the conditioned building, which in this case was the single conditioned storey surface multiplied by the number of conditioned storeys. Usually, the material used for the windows have high environmental impacts. For this reason, we calculated the emissions resulting for finishing and waterproofing membrane (see paragraph 2.1 in main paper) and the structures (see in paragraph 2.2 in main paper) for the three diets and assigned the higher window surfaces to the most polluting geometric configurations for each building typology (see final parameters in Table S1).

.1. Definition of the gravity frame systems
To define the carbon footprint of the different structural systems, a parametric model was set up to quantify the material incidence per gross floor area of a given structure over the total number of stories of the building. Four different structural configurations were defined, two foresee buildings with up to 20 stories, while the other two are designed for a maximum building height of 10 storeys. The first step of the structural design is the relevance of the technological options for each diet. Reinforced concrete as well as timber and engineered laminated bamboo were chosen for the above ground structures, while the foundation was done with reinforced concrete, and eventually deep foundation out of steel when needed. Reference numbers of conditioned storeys were the one collected and elaborated in the geometric parameter phase (see Table S1) and applied to the four structural schemes. The structural systems were designed considering the building height as main driving parameter. It was assumed that for buildings up to 14 storeys (as in AB case) lateral stiffness is not a conditioning factor, as the design is mostly controlled by vertical strength 2 . Nonetheless, a requirement for global stability, as well as provision for adequate strength against horizontal actions, may remain relevant even for low/mid-rise buildings. Consequently, simple pinned gravity frames were assumed for designing the four alternative structural systems, as shown in Figure   The first scheme consists of a reinforced concrete gravity frame with shear walls (RC), and it was designed for the cement-based diet. The second scheme, designed for timber-based diet, consists of a platform timber frame (PTF) where wooden post and beams are used for walls, floors and roof with a distance of 60 cm, and completed by OSBs on both sides. The third scheme, designed for bamboo-based diet, is based on a platform frame concept as well where both walls and slabs are made out of cross-laminated bamboo panels (CLB). Last scheme, specifically designed for both timber and bamboo-based buildings with a number of storeys n floor >10, consists of a gluelaminated timber frame stiffened by glulam bracing which supports either CLT or CLB panels. For option 1 (RC) the basement system is based on simple squared spread footing underneath each pillar while a wall footing supports concrete shear walls and CLB/timber frames. Additional friction piles are supposed to be anchored on concrete pad foundations for option 4 (PB). For each scheme, the vertical and horizontal loads are resisted by two separate sub-systems: pillars/panels and beams are designed to react to vertical loads while the shearing walls or the bracing system to react to horizontal loads and are assumed to give the lateral stiffness to the whole structure.
We have focused the structural analysis on the gravity frame sub-system of post, beams and columns (RC, PTF and PB) as well as cross-laminated panel (timber or bamboo), calculated as vertical load resisting system. Contrarily, no structural model was implemented for lateral load resisting sub-systems and their mass contribution was simply assumed to have a compatible dimension with the vertical load resisting sub-system (e.g., same thickness as the rest of the structure at the same floor).

Parametric model
The parametric model was coded in MATLAB 3 (see Annex A for the script) and defined the minimal load-bearing areas of columns, beams, walls and slabs, to support the structural, windows, finishing and insulation loads under two combinations: service state limits and ultimate state limits. The model was based on simplified modular geometries, with a mesh 10x10m and a floor height fixed of 3.2m and variable number of storeys in a range between 1 and 20 ( Figure S3). The parametric model is based on simple geometry which is assumed to be a representative portion of a whole modular structure. A small set of input parameters were used, described as follows according to Figure S 3: -geometric parameters: L x and L y indicate respectively the primary and secondary bay spans, while H floor is the inter-storey height. -topological parameters: n floor is the total number of floors.
-loading parameters (characteristic values): q k,floor and g k,floor are respectively the imposed variable floor load and the permanent floor load due to floor finishes, ceiling, services and partitions, whereas g env is the line-load (i.e., in kN/m) due to the building's cladding and envelope walls. In order to automate the task of calculating the structural masses for the entire population of reference buildings, a set of computer algorithms were specifically developed in MATLAB programming language. Given the geometric and topological input parameter values, for each structural option the sizing of each structural member was calculated assuming n floor as variable between 1 and 14 (max number of storeys assumed). The structural analyses are iteratively performed as part of an optimization phase, employed to minimize the cross-section of structural members against a set of constraints. All constraints are introduced to account for a series of SIAbased design requirements at both Serviceability Limit State and Ultimate Limit State to verify the resistance and stability as well as limiting the deflection. For each combination of input parameters, the stress tension matrix was calculated, and a reverse verification model applied in order to optimize the minimal cross-sections for all members and a minimum reinforcement content for concrete elements. Specifically, the optimization method enables to find the minimum crosssectional area of beams such that design requirements for bending resistance, shear and deflection are all satisfied, as well as to find the minimum cross-sectional area of columns against the requirements for compressive resistance and axial buckling. For concrete vertical members a minimum thickness of 200 mm was assumed both for columns and walls. For RC, the sequential search is performed on a range of square sections at size increments of 10 mm for columns, while beams are assumed to be rectangular with a fixed height of 250 mm and a variable width. For PTF, all vertical wooden posts are assumed to have a width equal to 60 mm, a structural pitch of 600 mm and a net span of 3.2 m. Similar assumptions were made for beams, with a simply supported configuration and a span of 5 m. For CLB, a minimum thickness of 120 mm for engineered bamboo panels was assumed were used for walls, while 160 mm is the minimal thickness assumed for floors and roof. Overall masses of steel reinforcement are estimated ex post, as a percentage of the concrete mass, specifically: 12.5‰ for columns, 10.5‰ for beams and 8.5‰ for floor slabs. The percentage values are based on practitioners' estimates. To take into account the influence of design rationalization on structural masses, the optimized cross-sections are rounded-off into groups: a uniform cross-sectional area is assumed for all columns that are vertically aligned, taken as the biggest area section within that line of columns. Similarly, two cross-section designations are considered within each floor, one for primary beams and one for secondary beams. Foundation sizing was calculated according to SIA262, assuming a sand ordinary ground with a compressive strength σ b,d =700 kN/m 2 and a maximum acceptable compression of the ground c c =30%. A continuous 100 mm concrete was assumed to level the ground and a minimum 25 cm of concrete used for footing, with an incremental thickness of 10 mm and a minimum reinforcement content equal to 3.0‰. In case of PB, a group of four steel friction piles are used under each pad foundation to reduce the stress on concrete, with a minimum size of 2x2m. The length of the pales was assumed to be equal to half of building height, the nominal diameter d p = 100 mm and the thickness of the section t p = 10 mm 1.2.3. Output of the structural parametric models The output of the static parametrization was the amount of materials used for each material diet structure expressed in m 3 normalized according to the gross area by varying the number of storeys ( Figure S 4-8). Since for the rest of the materials we normalized for the RES resulting from the geometric configurations, we assumed that the structural normalization is equal to the normalization to the RES. Therefore, to have integrity and correspondence with the unit of measurement, we also expressed the structural incidence per m 2 RES . For each geometric configuration, we extracted the value corresponding the number of storeys for each material diet to be used as the structural volumetric incidence. To obtain the mass incidence, we divided these values for the related material density. The share of steel compared to the total volume is almost insignificant, what has not to be misinterpreted with an insignificant contribution to climate change. In fact, carbon footprint of steel is almost ten times more than concrete per volume. Figure S 4.b displays the volumes of the materials normalized over the RES. The constant behavior of the slabs can be seen, where vertical elements increase almost linearly. These become rapidly dominant over the entire building materials, while the concrete foundation is absorbed with the increasing story height. The cumulative line, which is the sum of all concrete contributions, displays a constant evolution of the total concrete used in the entire building. From this last line, it can be concluded that low/mid-rise RC structures need roughly the same amount of volume per RES, no matter how tall the building is, which range a value around 0.33÷0.36 m 3 /m 2 . Contrarily, the timber-based diet for building with n floor ≤10, Figures S 5, shows a non-linear evolution of total volume of solid wood, which corresponds to a linear increase of wood volume per RES, while for concrete in foundation an evolution similar to cement-based diet was achieved. In case of PTF, low-rise buildings account for a lower wood incidence per RES than mid-rise buildings. When the structural configuration changes to PB, see Figure S 6, a similar evolution was registered for glulam which composes the vertical and horizontal linear membranes (columns and beams), with a lower sensitivity to building height compared to PTF case, ranging a mean value around 0.15 m 3 /m 2 . For bamboo-based diet, see Figure S 7, in case of CLB most of the structural mass of the laminated bamboo panels is allocated to the floors, which resulted in a nearly constant incidence per RES. Finally, in case of PB, a resulting similar volume incidence to the case of timber-based diet was achieved, with a mean value of bamboo glulam of around 0.148 m 3 /m 2 and a similar volume incidence of cross-laminated panels for floors (0.16 m 3 /m 2 ).

Insulation line-load
Since the thickness of the insulation material, and therefore its line-load, is and output of this research, during the structural preliminary dimensioning in the envelope walls parameter, we defined as permanent load of the insulation a value corresponding to the straw, which is the median herbaceous biomass here chosen. According to the literature, the range of the wall thickness obtained when building with biobased insulation material, such as straw, varies between 40-80 cm 4-6 . To give some margin, we extended the wall thickness to 1 m. Considering a density of straw equal to 95 kg/m 3 7 , the insulation permanent line-load (g env,ins ) on the structure is equal to as 0,93 KN/m, as shown in Equation (1): where: -D = Material Thickness (m), and in this case 1 m for the straw buildings; -= density of the biobased insulation material (kg/m 3 ) (in this case straw is equal to 95 kg/m 3 ); -= gravity on Earth; -is the conversion factor from N to kN. 10 -3

1.3.Construction materials and Net-GWP computation
Non-biobased, or "Mineral", are materials not composed by biogenic mass. In this investigation we assumed:  glass for the windows;  PVC, wood-aluminum and wood window frames;  polyethylene water proofing membrane;  steel for the reinforced concrete structure;  gypsum plasterboard, mineral plaster, ceramic tiles and clay plaster as internal ceiling and wall finishing. The biobased ones were divided in slow-growing, or "Timber-based", and fast-growing, or "Herbaceous", which is related to the time the plant needs to completely regrow before being clearcut and harvested again. Plants, whose time needed to regrowth is larger than 10 years, contributed to provide slow-growing biobased materials, e.g. timber, wood fibers, cellulose flakes, etc. In this project, five types of forest products were adopted for different applications:  solid wood used for structural and finishing applications. It is subdivided in softwood and hardwood;  glued laminated timber (GLT), is well suited for structural applications;  oriented strand board (OSB) is used for structural applications;  cross laminated timber (CLT) is used for structural applications. All these types differ in the fabrication process, nevertheless, are available worldwide. In this project, the regeneration period of coniferous forests for softwood supply, used in load-bearing elements and finishing, is assumed to be 90 years 8 . Plants with regrowth period lower than 10 years are categorized as fast-growing biobased materials, namely:  bamboo for structural or finishing applications with a regeneration period of 5 years; straw, hemp fibers and reed mats as insulation materials with a regeneration period of 1 year.
We extracted all the materials' properties either from KBOB 9 or from the scientific literature, whereas the GWP 100 were processed by using SimaPro 8, accessing the Ecoinvent v.3 database 10 + method 2013, at 100 years (see Table S 2). In particular we took the following processes from Ecoinvent 10 as shown in Table S 2. As the dynamic LCA requires single GHG inputs, missing processes from existing LCA databases cannot be substituted with data from available EPDs. For this reason, the only main assumption we made is for modelling hemp processes, whereas for reed and straw secondary data from ecoinvent database were used. Recent papers dealing with carbon footprint evaluation of agricultural practices for crops 11,12 demonstrated that the fertilization, in particular the level of nitrogen per hectare, contributes to the largest share of emissions. This is mostly dependent to the quality of the soil rather than type of crop. Thus, we decided to consider ecoinvent processes for maize seed production as representative for every missing germination processes, as for hemp species.

1.4.Replacement and service life of construction materials
To address the replacement of building assemblies and components, we defined the service lives for the identified building elements. The building service life is assumed to be 60 years 13 . The following table (Table S 3

1.5.GWP net calculation considering 100 years' time horizon
To quantify all CO 2eq emissions, we performed a dynamic LCA for all construction materials. As illustrated in Figure S 9, different GWP calculation logics were used for the biogenic and fossil emissions. The strategies were defined according to the type of material (biobased or not) and if the element is to be replaced after 30 years. As a matter of fact, the temporal dynamics of emissions and the spatial dynamics of the building elements' replacement must be considered from the year 31 to the end of life of the building. During the building life of 60 years, GHGs are released and generate an impact on the climate. By choosing a time horizon of 100 years, one might think that this LCA study focuses on the global warming impacts over 100 years. However, the emissions occurring after 30 years, e.g., for the replacement of building elements, are considered from year 31 to year 130. Therefore, to be coherent with the 100-year time analysis, there is the need to use a dynamic approach able to assess the impacts on the same temporal frames, as explained from Levasseur and coauthors 17 . When the materials are produced at year 1 , the dynamic method can be simplified with tabulated values, such as the GWP as defined by IPCC 2013 method (GWP 100 ), and the CO 2 uptake from biogenic regeneration in the land (GWP bio index ) with the Guest et coauthors simplified tabulated dynamic index (also considered as semi-static) 18 . Whereas when the building elements are replaced after 30 years, both the fossil emissions (GWP 100,dyn ) and the CO 2 uptake (GWP bio index, dyn 31-60 ) are calculated with the "DynCO2" calculation tool 19 .  GWP 100 is the either GWP 100, IPCC and/or GWP 100, dyn according to the material production time (see scheme in Figure S 9);  GWP bio see next subparagraph 1.5.1.
The Net-GWP for every single material used in this study, which is the most important output of this materials section, has been illustrated in Table S   Non-biobased materials do not contribute to carbon storage or uptake, therefore their Net-GWP values are always positive, as equivalent to GWP 100 (IPCC or Dynamic) value. Contrary, every biobased material used in construction can account for a removal potential and, depending on their carbon fossil emissions and their storage and rotation period, their Net-GWP values can be either negative or positive.

GWP bio calculation considering 100 years' time horizon
In the literature there is no consensus on how to model biogenic carbon released and reabsorbed during biobased materials' life cycle 26 . The established approaches can be summarized as the 0/0, +1/-1, the dynamic (with carbon uptake before or after construction). Assuming a sustainable supply of biomass, in traditional Life-Cycle-Assessment 27 (LCA), the biogenic cycle is usually considered neutral as the carbon used in construction is sequestered in new plants in the natural system (0/0). In fact, if timing is excluded from the analysis, the carbon-neutrality of biobased product correspond to their climate-neutrality. This widely used assumption has been progressively criticized by some researchers showed that the carbon cycle is in fact not neutral 17,28 . The +1/-1 approaches, such as the British Publicly Available Specification -PAS 2050 29 and the European Commission's ILCD Handbook 30 , tried to address this issue by tracking the biogenic carbon flows over the building life-cycle. However, these "static" models are still not able to consider the impact of timing of the carbon emissions and its influence of the rotation period related to the biomass growth. Therefore, the dynamic approach (DLCA) was developed 17,28 with two uptake scenarios (before or after the construction) leading to radically different results 31 . The latter has the advantage to have the same time frame as fossil emissions as the identical time 0 is assumed (time of production/construction). The dynamic methods are particularly relevant for biobased products that can store carbon and delay emissions. Specifically, wooden products have a longer rotation period related to the slow growth of forests; therefore, they cannot be considered climateneutral when a short time horizon is chosen. Contrariwise, fast-growing biobased materials, as straw or bamboo, are able to fully regrow in a shorter rotation period, providing an effective mitigation effect on GHG emissions 32 . Cherubini and coauthors 33 pushed this concept by determining a specific time-depending characterization factors for biogenic carbon dioxide, with the inclusion of the rotation period of plants. As a continuation, Guest and coauthors 34 further expanded this method by proposing an index, the biogenic global warming potential index (GWP bio index ), which is able to directly compute the carbon dioxide regeneration with the biogenic CO 2 pulse emissions, both acting as a perturbation to the atmospheric CO 2 decay according to the Bern CO 2 declining curve. Indeed, this index is capable to consider the storage period of harvested biomass with different rotation periods in the anthroposphere as a negative value to be considered at the beginning of a standard LCA, both for a100 or 500-year time horizon, in a semi-static way. Biobased materials can thus help decreasing the GWP by uptaking the CO 2 and keep it stored in a construction product for a long period. More precisely, the biomass is stored in the anthroposphere as a harvested product, e.g. solid wood, while the carbon uptake happens in the biomass that is regrowing through the photosynthesis, reducing the atmospheric carbon dioxide concentration. To account for this biogenic CO 2 storage in the anthroposphere, in two cases we used the semi-static tabulated values proposed by Guest and coauthors 18 and depicted in Figure S10. They defined a GWP bio index for considering the consequential GWP of storing 1 kg of biogenic CO 2 for a given storage period in a 100 years' time horizon. Thus, the method combines through a Dynamic LCA (DLCA) the annual CO 2 uptake in the land via biomass growth and the delayed biogenic CO 2 emissions through biomass incineration at end of life of a building, here assumed equal to 60 years 13 . The GWP bio index can assume a positive value if the storage period is short and rotation long, while can reach negative values, up to -1 kgCO 2eq , for long storage and very short rotation periods. Hence, to remove from the atmosphere the equal amount of carbon that is stored in biobased products, fast-growing spices need a shorter time than slow-growing ones, resulting in a more advantageous effect in lowering the radiative force remaining in the atmosphere in a short period. In this work, the storage period in the anthroposphere was assumed to be 60 years for structural elements, waterproof membrane in polyethylene and biobased insulation materials. For the finishing, windows and window frames, the storage period is of 30 years (Table S 3). For the replacing elements inserted on the building after 30 years, a particular index is computed with the use of the dynamic LCA (GWP bio index, dyn 31-60y ), as the possibility to address the timing of emissions and sequestration related to these boundaries with a Dynamic LCA is the most robust and transparent solution 35,36 . This dynamic GWP bio index dyn 31-60y has been calculated with the "DynCO2" calculation tool 19 . For the element inserted at year 1, by using Figure S 10, we extract the GWP bio for every biobased material by entering in the graph at 60 and 30 years and extracting the relative GWP bio index,60y and GWP bio index,30y indexes for the different biomass according to their rotation period.
In particular:  Solid wood with a rotation period of 90 years,  Bamboo with a 5-year rotation,  straw, reed and hemp biomass have a fast rotation period of 1 year. The GWP bio index,30y and the dynamic ones have not been considered because no fast-growing elements is replaced after 30 years.
The  To calculate the carbon sequestration of biobased materials, the following Equation (3) is considered, which calculate the mass of CO 2 that can be stored in the final product: (3) Where:  ρ 0 is the dry density of the material, in kg/m 3 ;  CC is the carbon content of the biogenic material;  BC the biomass content of the finished product;  3.67 is the molar weight ratio between CO 2 and C 37 .
Since the exact moisture content of biogenic materials is often unknown, we supposed a 20% moisture content for structural materials, 15% for finishing and membrane, and 10% for isolations. Therefore, we calculated the dry volumetric mass according to the CEN/TC 124 38 , as reported in the following Equation (4): where: -is the wood density at moisture content lower than 25%, in kg/m 3 ;

< 25
is the moisture content, in %.
Consequently, as reported in Equation (5), the contribution on GWP from carbon uptake can be calculated by multiplying the CO 2 storage with the GWP bio index expressed in [kg CO 2eq /kgCO 2 ] , which is a portion of the total carbon storage a material could reabsorb in the land during the storage period in 100 years of time horizon: Where:  GWP bio index is the either GWP bio index, 60y , GWP bio index, 30y or GWP bio index, dyn 31-60y , according to the situation (see scheme in Figure S 9 )

1.6.U-value Calculation
The general formula for calculating the U-Value is (Equation (6)): Where: U = Thermal Transmittance R t = Total Thermal Resistance of the element composed of layers, obtained according to Equation (7): Where: R si = Interior Surface Thermal Resistance, here assumed as 8 W/(m 2 K) R se = Exterior Surface Thermal Resistance, here assumed as 25 W/(m 2 K) R 1 , R 2 , R 3 , R n = Thermal Resistance of each layer, which is obtained according to Equation (8):

Insulation line-load calculation
Once computed the different wall biobased insulation thicknesses and their related thermal performance, it is possible to calculate the corresponding line-load on the structure to control that it does not exceed the one considered during the structural dimensioning for different material diets (i.e., 2,98 kN/m, in paragraph SI 1.2.4). According to Equation (9), we checked the load limits for each insulation and material diet as follow: is the conversion factor from N to kN. 10 -3 When the resulting insulation load, corresponding to a certain thickness, surpasses the one considered during the predimensioning, this solution is not acceptable. At this point, either the practitioner restarts the process by increasing the insulation dead loads (with the consequent increasement of structural material quantities and emissions for the diets) or simply chose among the acceptable solutions determined for other diets or with a different insulation material that suit its architectural needs.

Further analysis: Contribution to global warming with a time horizon of 20 years (GWP20)
The contribution to global warming with a time horizon of 20 years (GWP 20 ) can be calculated by keeping the same formulation explained in paragraph 1.5, with a replacement of the GWP 100 index for each BT and material diets with the GWP 20 one, still based on IPCC 2013 assessment method. In this case the building element replacement happens beyond the 20 years' time horizon chose, therefore was not considered. The indexes were assessed via SimaPro 8 by using processes from Ecoinvent 3 10 . The same processes from Ecoinvent shown in Table S2 were assumed for the calculation with time horizon of 20 years. Moreover, the GWP bio index,dyn 0-20y index were computed accordingly within the same time frames through a Dynamic Life cycle assessment with the "DynCO2" calculation tool 19 , to provide new indexes for three different rotation growth: 90 years, 5 years, and 1 year. The achieved values are respectively: -0.12, -0.92, and -1.00. Therefore, the higher -in absolute value -the index is and the more effective the CO 2 stored in the vegetal mass is in CO 2 removal. Consequently, if on one side the fossil based GWP 20,IPCC values per functional unit (FU) are larger than the ones calculated at 100 years, on the other side the carbon removal potential for shorter time horizon results in larger absolute values as well, due to the longer integration period over which the remaining fossil CO 2 in the atmosphere is responsible for a greater influence on radiative forcing. As a matter of fact, from Figure 4 in the main paper, it is possible to appreciate that we are already climate-negative by just using fast-growing biomass as structural materials. In Table S