Table A2 The relative equations and...

Table A2

The relative equations and descriptions for KPIs

Level	KPI	Formula			Data source	Assumption/Limitation	Reference
Material	E′ (CO₂ emissions)	$E^{'} = 1 - \frac{C}{C_{\max}}$ C’: the CO₂ of the case study C_max: maximum CO₂ possible within the material category			C: EPD C_max: EC3 tool	–	Mesa et al. (2020)
	EN (energy renewability)	$E N = \frac{R e n e w a b l e e n e r g y (w h o l e l i f e c y c l e)}{T o t a l e n e r g y c o n s u m p t i o n} \times 100 %$			EPD	–	WBCSD (2023)
	W (water circularity)	$W = \frac{% c i r c u l a r w a t e r i n f l o w + % c i r c u l a r w a t e r o u t f l o w}{2}$ Where $% c i r c u l a r w a t e r i n f l o w = \frac{Q t o t a l c i r c u l a r w a t e r w i t h d r a w a l}{Q t o t a l w a t e r w i t h d r a w a l} \times 100 %$ $% c i r c u l a r w a t e r o u t f l o w = \frac{Q t o t a l c i r c u l a r w a t e r d i s c h a r g e}{Q t o t a l w a t e r w i t h d r a w a l} \times 100 %$			EPD	–	WBCSD (2023)
	M_cl (additional material required during construction)	$M_{c l} = Ø_{l} \times m_{i}$ Ø_l: wastage percentage factor for material			One Click LCA	–	Khadim et al. (2023)
	W_O (Unrecoverable Waste)	$W_{O} = M (1 - C_{r} - C_{u} - C_{b} - C_{e})$ C_r: fractions of material collected for recycling C_u: fractions of material collected for reuse C_b: fractions of material collected for bio decomposition C_e: fractions of material collected for sustained production of biological material for energy recovery			EPD	Composting applies only to non-toxic biological materials that meet compostable standard	Ellen MacArthur and Granta (2019)
	W_C (recycling waste)	$W_{C} = M (1 - E_{C}) C_{r}$ E_C: efficiency of the recycling process			Literature (Krausmann et al., 2017)	–	Ellen MacArthur and Granta (2019)
	W_mn (manufacturing loss)	$W_{m n} = W_{f p} + W_{c p}$ Where $W_{f p} = \frac{(1 - F_{u}) M}{E_{f p} E_{c p}} (1 - E_{f p}) (1 - C_{f p})$ $W_{c p} = \frac{(1 - F_{u}) M}{E_{c p}} (1 - E_{c p}) (1 - C_{c p})$ C_fp and C_cp: fractions of material losses that are recovered as useful recycled material E_fp: efficiency of feedstock production E_cp: efficiency of component production			Literature (Bracquené et al., 2020)	–	Bracquené et al. (2020)
	W_ms (material separation loss)	$W_{m s} = M (1 - E_{m s}) C_{r}$ E_ms: efficiency of the material separation			Literature (Bracquené et al., 2020)	–	Bracquené et al. (2020)
Component	CD (Disassembly)	$\frac{\sum {D D F}_{j} \times m_{i}}{7 \times \sum m_{i}}$ (A full list of DDFs and their corresponding fuzzy values will be provided based on request.)			Fuzzy values input by user	–	Durmisevic (2005)
System	DE (Deconstruction)	$D E = \frac{\sum ({DEt}_{i} \times {D E m}_{i} {\times m}_{i})}{\sum m_{i}}$			Fuzzy values input by user	–	O’Grady et al. (2021)
		DEt Availability, dimensions, and types of tools required to deconstruct a building	No tool		1
			Hand tool		0.9
			Power tool		0.8
			Gas/pneumatic tool		0.5
			Hydraulic equipment		0.2
		DEm People or equipment required to move components following deconstruction	One person: <20 kg		1
			Two people: <42 kg		0.9
			Hand trolley: <50 kg		0.7
			Forklift: <2,000 kg		0.4
			Crane: >2,000 kg		0.1
	Re (Resilience)	$R = \frac{\sum ({R e}_{i} \times m_{i})}{\sum m_{i}}$ Re_i: resilience of component i m_i: component i weight	Reusable indefinitely		1	–	O’Grady et al. (2021)
			Reusable up to three times		0.9
			Reusable only once		0.7
			Recyclable		0.6
			Downcyclable		0.2
			Disposable		0
	T (Transportability)	$T = \frac{\sum (T_{i} \times m_{i})}{\sum m_{i}}$ m_i: component i weight	One-lane road and railway combined		1	–	Coenen et al. (2021)
			One-lane road only		0.8
			Railway only		0.4
			Barge along river		0.4
			No available infrastructure		0
	N (Standardization)	$N / C$ Proportion of standardized components, N, with respect to the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)
	C (Commonality)	$C O M / C$ The proportion of components that are common within the product family, COM, concerning the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)
	TB (Take-back systems)	There is a take-back system for …				–	Struck and Flamme (2023)
		… the entire component, which reuses the component (if necessary, after reprocessing)			1
		… the entire component, which reuses or recycles all parts of the component			0.8
		… parts of the component, which reuses these parts (if necessary, after reprocessing)			0.6
		… parts of the component, which (after reprocessing, if necessary) will be recycled			0.4
		… construction waste generated during the construction of the component (pre-consumer), which is sent for recycling (if necessary, after reprocessing)			0.2
		None of the above descriptions applies			0
	RP (Repairability)	$R P = \sum R o * R F I$ RFI: a subcomponent’s significance within a component assembly Ro: component's structure-five key parameters (P1 to P5) (A detailed explanation of each parameter will be provided based on request.)			Fuzzy values input by user	–	Ruiz-Pastor and Mesa (2023)
	D (Durability)	$D = \frac{1}{2} (D G \times D M)$ Geometric Durability (DG) Material Durability (DM) (Scores and details for these parameters will be provided based on request.)			Fuzzy values input by user CES Selector database of GrantaDesign	–	Akanbi et al. (2019a), Mesa and González-Quiroga (2023)
Building	LKI (Level of Importance)	Site			0.1	–	Khadim et al. (2023)
		Structure			0.2
		Skin			0.7
		Services			0.8
		Space Plan			0.9
	BFS (Adaptability/Flexibility)	Flexibility Class	FLEX 4.0 score	BCP score	BFS	–	Geraedts (2016)
		1: Not flexible at all	12–48	9–14	0.2
		2: Hardly flexible	49–85	15–20	0.7
		3: Limited flexible	86–122	21–26	0.8
		4: Very flexible	123–159	27–32	0.9
		5: Excellent flexible	160–192	33–36	1
		(Sub-indicators and details will be provided based on request.)
	RFU (Refuse unnecessary construction)	$R F U = \frac{R e u s e d p o r t i o n o f S y s t e m}{T o t a l S y s t e m V o l u m e, A r e a, M a s s}$ Reused Portion of System: amount (volume, area, mass) of the building system that is reused from the existing structure Total System Volume, Area, Mass: total size of the system being evaluated			Drawings	–	Arup and Ellen Macarthur (2022), Ellen MacArthur and Granta (2019)
	SQ (Site Quality)	$S Q = (\frac{B_{i}}{A} \times (- 1)) + (\frac{B_{i i}}{A} \times (0)) + (\frac{B_{i i i}}{A} \times (3)) + (\frac{B_{i v}}{A} \times (5))$ A is the total site area B_i is the area in its natural state B_ii is the area previously used as green or agricultural land B_iii is the area previously developed with structures or infrastructure B_iv is the area where remediation has been conducted or is planned			Drawings	–	Fagone et al. (2023)
	M (Modularity)	$M / C$ Proportion of components considered as a module, M, with respect to the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)
	S (Simplicity)	$(1 - N * C) / C$ Measurement of the product complexity based on the number of components (C) and number of pieces (N)			Input by user	–	Mesa and González-Quiroga (2023)
	FB (Prefabricated assemblies)	$N_{f b} / C$ Proportion of prefabricated assemblies, N_fb, with respect to the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)

Level	KPI	Formula			Data source	Assumption/Limitation	Reference
Material	E′ (CO₂ emissions)	$E^{'} = 1 - \frac{C}{C_{\max}}$ C’: the CO₂ of the case studyC_max: maximum CO₂ possible within the material category			C: EPDC_max: EC3 tool	–	Mesa et al. (2020)
	EN (energy renewability)	$E N = \frac{R e n e w a b l e e n e r g y (w h o l e l i f e c y c l e)}{T o t a l e n e r g y c o n s u m p t i o n} \times 100 %$			EPD	–	WBCSD (2023)
	W (water circularity)	$W = \frac{% c i r c u l a r w a t e r i n f l o w + % c i r c u l a r w a t e r o u t f l o w}{2}$ Where $% c i r c u l a r w a t e r i n f l o w = \frac{Q t o t a l c i r c u l a r w a t e r w i t h d r a w a l}{Q t o t a l w a t e r w i t h d r a w a l} \times 100 %$ $% c i r c u l a r w a t e r o u t f l o w = \frac{Q t o t a l c i r c u l a r w a t e r d i s c h a r g e}{Q t o t a l w a t e r w i t h d r a w a l} \times 100 %$			EPD	–	WBCSD (2023)
	M_cl (additional material required during construction)	$M_{c l} = Ø_{l} \times m_{i}$ Ø_l: wastage percentage factor for material			One Click LCA	–	Khadim et al. (2023)
	W_O (Unrecoverable Waste)	$W_{O} = M (1 - C_{r} - C_{u} - C_{b} - C_{e})$ C_r: fractions of material collected for recyclingC_u: fractions of material collected for reuseC_b: fractions of material collected for bio decompositionC_e: fractions of material collected for sustained production of biological material for energy recovery			EPD	Composting applies only to non-toxic biological materials that meet compostable standard	Ellen MacArthur and Granta (2019)
	W_C (recycling waste)	$W_{C} = M (1 - E_{C}) C_{r}$ E_C: efficiency of the recycling process			Literature (Krausmann et al., 2017)	–	Ellen MacArthur and Granta (2019)
	W_mn (manufacturing loss)	$W_{m n} = W_{f p} + W_{c p}$ Where $W_{f p} = \frac{(1 - F_{u}) M}{E_{f p} E_{c p}} (1 - E_{f p}) (1 - C_{f p})$ $W_{c p} = \frac{(1 - F_{u}) M}{E_{c p}} (1 - E_{c p}) (1 - C_{c p})$ C_fp and C_cp: fractions of material losses that are recovered as useful recycled materialE_fp: efficiency of feedstock productionE_cp: efficiency of component production			Literature (Bracquené et al., 2020)	–	Bracquené et al. (2020)
	W_ms (material separation loss)	$W_{m s} = M (1 - E_{m s}) C_{r}$ E_ms: efficiency of the material separation			Literature (Bracquené et al., 2020)	–	Bracquené et al. (2020)
Component	CD (Disassembly)	$\frac{\sum {D D F}_{j} \times m_{i}}{7 \times \sum m_{i}}$ (A full list of DDFs and their corresponding fuzzy values will be provided based on request.)			Fuzzy values input by user	–	Durmisevic (2005)
System	DE (Deconstruction)	$D E = \frac{\sum ({DEt}_{i} \times {D E m}_{i} {\times m}_{i})}{\sum m_{i}}$			Fuzzy values input by user	–	O’Grady et al. (2021)
		DEtAvailability, dimensions, and types of tools required to deconstruct a building	No tool		1
			Hand tool		0.9
			Power tool		0.8
			Gas/pneumatic tool		0.5
			Hydraulic equipment		0.2
		DEmPeople or equipment required to move components following deconstruction	One person: <20 kg		1
			Two people: <42 kg		0.9
			Hand trolley: <50 kg		0.7
			Forklift: <2,000 kg		0.4
			Crane: >2,000 kg		0.1
	Re (Resilience)	$R = \frac{\sum ({R e}_{i} \times m_{i})}{\sum m_{i}}$ Re_i: resilience of component i m_i: component i weight	Reusable indefinitely		1	–	O’Grady et al. (2021)
			Reusable up to three times		0.9
			Reusable only once		0.7
			Recyclable		0.6
			Downcyclable		0.2
			Disposable		0
	T (Transportability)	$T = \frac{\sum (T_{i} \times m_{i})}{\sum m_{i}}$ m_i: component i weight	One-lane road and railway combined		1	–	Coenen et al. (2021)
			One-lane road only		0.8
			Railway only		0.4
			Barge along river		0.4
			No available infrastructure		0
	N (Standardization)	$N / C$ Proportion of standardized components, N, with respect to the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)
	C (Commonality)	$C O M / C$ The proportion of components that are common within the product family, COM, concerning the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)
	TB (Take-back systems)	There is a take-back system for …				–	Struck and Flamme (2023)
		… the entire component, which reuses the component (if necessary, after reprocessing)			1
		… the entire component, which reuses or recycles all parts of the component			0.8
		… parts of the component, which reuses these parts (if necessary, after reprocessing)			0.6
		… parts of the component, which (after reprocessing, if necessary) will be recycled			0.4
		… construction waste generated during the construction of the component (pre-consumer), which is sent for recycling (if necessary, after reprocessing)			0.2
		None of the above descriptions applies			0
	RP (Repairability)	$R P = \sum R o * R F I$ RFI: a subcomponent’s significance within a component assemblyRo: component's structure-five key parameters (P1 to P5)(A detailed explanation of each parameter will be provided based on request.)			Fuzzy values input by user	–	Ruiz-Pastor and Mesa (2023)
	D (Durability)	$D = \frac{1}{2} (D G \times D M)$ Geometric Durability (DG)Material Durability (DM)(Scores and details for these parameters will be provided based on request.)			Fuzzy values input by userCES Selector database of GrantaDesign	–	Akanbi et al. (2019a), Mesa and González-Quiroga (2023)
Building	LKI (Level of Importance)	Site			0.1	–	Khadim et al. (2023)
		Structure			0.2
		Skin			0.7
		Services			0.8
		Space Plan			0.9
	BFS (Adaptability/Flexibility)	Flexibility Class	FLEX 4.0 score	BCP score	BFS	–	Geraedts (2016)
		1: Not flexible at all	12–48	9–14	0.2
		2: Hardly flexible	49–85	15–20	0.7
		3: Limited flexible	86–122	21–26	0.8
		4: Very flexible	123–159	27–32	0.9
		5: Excellent flexible	160–192	33–36	1
		(Sub-indicators and details will be provided based on request.)
	RFU (Refuse unnecessary construction)	$R F U = \frac{R e u s e d p o r t i o n o f S y s t e m}{T o t a l S y s t e m V o l u m e, A r e a, M a s s}$ Reused Portion of System: amount (volume, area, mass) of the building system that is reused from the existing structureTotal System Volume, Area, Mass: total size of the system being evaluated			Drawings	–	Arup and Ellen Macarthur (2022), Ellen MacArthur and Granta (2019)
	SQ (Site Quality)	$S Q = (\frac{B_{i}}{A} \times (- 1)) + (\frac{B_{i i}}{A} \times (0)) + (\frac{B_{i i i}}{A} \times (3)) + (\frac{B_{i v}}{A} \times (5))$ A is the total site area B_i is the area in its natural state B_ii is the area previously used as green or agricultural land B_iii is the area previously developed with structures or infrastructure B_iv is the area where remediation has been conducted or is planned			Drawings	–	Fagone et al. (2023)
	M (Modularity)	$M / C$ Proportion of components considered as a module, M, with respect to the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)
	S (Simplicity)	$(1 - N * C) / C$ Measurement of the product complexity based on the number of components (C) and number of pieces (N)			Input by user	–	Mesa and González-Quiroga (2023)
	FB (Prefabricated assemblies)	$N_{f b} / C$ Proportion of prefabricated assemblies, N_fb, with respect to the total number of components (C)			Input by user	–	Mesa and González-Quiroga (2023)

Source(s): Authors’ own work

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