2.1.4. Pathway Generation

Pathways are subsequently created were portfolios of abatement measures for the respective supply chain activities are constructed with selections of measures applied on a timeline up to year 2045. In the pathway analysis, the production levels of each material in each time step was estimated based on the remaining material demand after implementation of abatement options a ffecting demand of each material:

$$M\_{m,t} = \left(1 - A\_{\rm tr,m,t}\right) \* \left(1 - A\_{\rm ms,m,t}\right) \* \left(1 - A\_{\rm m,m,t}\right) \* M\_{\rm m,t} \tag{12}$$

where *Mm*,*<sup>t</sup>* is the material demand of material *m* in time step *t*; *A* is the total material demand reduction of material m in time step *t* associated with each of the following abatement measures: *re*- recycling, *ms*–material substitution, *me*–material e fficiency measures; and *Mm* is the original material demand of each specific material *m* in the base year of 2015. An illustration of how this generic calculation is performed for concrete demand (and resulting demand for cement and Supplementary Cementitious Material, SCM) is illustrated in Figure 2.

In the pathway analysis, the emissions and energy demand associated with material production, material transports and construction processes were adjusted based on the abatement options selected and applied in the assessment for each supply chain activity, as described in Section 2.3. The energy intensity factors, and energy mixes, were adjusted based on abatement measures, including energy efficiency and hybridization, biofuel substitution, and electrification. The energy demand for *Qcp*,*<sup>t</sup>* construction process *cp* in timestep *t* is consequently calculated as:

$$Q\_{\mathbb{CP},t} = \left(1 - A\_{\text{op},\text{cp},t}\right) \* \left(1 - A\_{\text{cc},\text{cp},t}\right) \* Q\_{\mathbb{CP},t} \tag{13}$$

where *A* is the total energy demand reduction for construction processes in time step *t* associated with each of the following abatement measures: *op*–optimization and *ee*–energy e fficiency (including from hybridization and electrification); *Qcp* is the energy demand for construction processes in the base year of 2015.

The energy demand *Qmt*,*<sup>t</sup>* for material transport *mt* in timestep *t* is, consequently, calculated as:

$$Q\_{mt,t} = \left(1 - A\_{\overline{m}c,mt,t}\right) \* \left(1 - A\_{\text{op},mt,t}\right) \* \left(1 - A\_{\text{er},mt,t}\right) \* Q\_{\text{Cp}}.\tag{14}$$

where *A* is the total energy demand reduction for construction processes in time step *t* associated with each of the following abatement measures: *me–*average of material efficiency measures for main materials (concrete, steel, asphalt), *op*–optimization and *ee*–energy efficiency (including from hybridization and electrification); *Qmt* is the energy demand for material transports in the base year of 2015.

The energy demand per energy source in each time steps is consequently calculated as:

$$Q\_{\rm tot,t,s} = \sum\_{m} \left( M\_{\rm m,t} \ast Qf\_{\rm m,t} \ast q\_{\rm m,t,s} \right) + \sum\_{\rm ttc} Q\_{\rm tc,t} \ast q\_{\rm tc,t,s} \tag{15}$$

where *Qtot*,*s*,*<sup>t</sup>* is the total energy use of energy source *s* in timestep *t*; *Mm*,*<sup>t</sup>* is the material demand of material *m* in timestep *t*; *Q fm*,*<sup>t</sup>* is the energy intensity factor for production of material *m* in timestep *t*; *qm*,*s*,*<sup>t</sup>* is the share of energy source *s* for the production of material *m* in timesteps *t*; *Qtc* is the energy demand for construction stage *tc*; *qtc*,*t*,*<sup>s</sup>* is the energy share for construction processes and material transports in timestep *t* for energy source *s*.

**Figure 2.** Schematic illustration of the calculation of concrete, cement, and Supplementary Cementitious Material (SCM) demand, along with associated energy demand and emissions for concrete manufacture and SCM. Boxes linked with an encircled x are multiplied, a box linked with an encircled x combined with 1-in brackets are reduced by the percentage figure in the box closest to the brackets, while a box linked via an encircled minus sign is subtracted. Boxes with thick outlines are metrics that are adaptable over time in the pathways depending on the abatement measures applied, while boxes with cursive texts are input data provided in Tables A1 and A2 in Appendix A. The initial material demand figure is only adaptable in the sensitivity analysis. Blue boxes are result figures. The cement demand figure is used as input for the cement production calculation, as displayed in Figure 3.

**Figure 3.** Schematic illustration of the calculation of emissions and energy demand per energy source for cement production. The cement production figure stems from the concrete calculation depicted in Figure 2. Boxes linked with an encircled x are multiplied, a box linked with an encircled x combined with 1-in brackets are reduced by the percentage figure in the box closest to the brackets, while a box linked via an encircled minus sign is subtracted, and boxes linked with an encircled plus sign are added up. Boxes with thick outlines are metrics that are adaptable over time in the pathways depending on the abatement measures applied, while boxes with cursive texts are input data provided in Table A1, Table A2, and Table A3 in Appendix A. Blue boxes are result figures.

For material production, emissions from direct energy use, together with process emissions, were also adjusted based on the level of carbon capture applied. The resulting emissions for each material *m* are calculated as:

$$E\_{m,t} = M\_{m,t} \* \left( \left( Ef\_{pr,m} + Qf\_{m,t} \* \sum\_{s} \left( q\_{m,s,t} \* Ef\_s \right) \right) \* \left( 1 - \mathbb{C} \mathbb{C}\_{m,t} \right) + Qf\_{m,t} \* q\_{m,t,t} \* Ef\_{d,t} \right), \tag{16}$$

where *Em*,*<sup>t</sup>* is the emissions resulting from the production of material *m* in timestep *t*; *Mm*,*<sup>t</sup>* is the material demand of material *m* in timestep *t*; *E fpr*,*<sup>m</sup>* is the process emissions intensity factor to produce material *m*; *Q fm*,*<sup>t</sup>* is the energy intensity factor for production of material *m* in timestep *t*; *qm*,*s*,*<sup>t</sup>* is the share of direct energy sources *s* for the production of material *m* in timesteps *t*; *E fs* is the emissions intensity factor of direct energy source *s*; *CCm*,*<sup>t</sup>* is the share of direct and process emissions captured via carbon capture technologies in the production of material *m* in timesteps *t*; *qm*,*el*,*<sup>t</sup>* is the share of energy use from electricity in the production of material *m* in timestep *t*; *E fel*,*<sup>t</sup>* is the emissions intensity factor of electricity in timestep *t*. Illustrations of how the generic calculation of materials emissions is performed for cement and primary steel production is displayed in Figures 3 and 4. The abatement options considered and applied are described in Sections 2.2.1 and 2.2.2, respectively. Below, an example calculation is made for construction steel in Pathway 1 for the year 2040, where 30% of the coal use is substituted for biofuel and 30% of the thermal emissions are captured:
