The values for the geometric and construction complexities for each building main part or the entire building construction core elements are calculated respectively. The process for this stage is divided into two independent parts the first one is the geometric complexity, There the grouped elements in the grouping stage are used as input. The geometry complexity uses the metrics of the geometric entropy, variety and number of elements factors to assign a value to each building main part. The information required for the geometric complexity characterization is extracted directly from the 3D model geometry. A similar process occurs during the construction complexity characterization, here the entire elements in the BIM model obtain a value from an external database. The values obtained in this complexity are scores for the entire building.
Geometric Complexity: How hard is to describe the building main part geometry?
The factors selected to be responsible for this question measurement are the geometric entropy, variety and elements number. Below are the factors affecting this geometric complexity, their definitions and the metrics used for their calculation.
1 Geometric Entropy
The factor geometric entropy can involve many aspects in a 3D object. This research characterizes this factor regarding geometric entropy, which is a way to measure a 3D object shape. The method used to calculate the geometric entropy was the one proposed by Gero and Kazakov [23], where the vertex of a 3D solid is labeled depending on their adjacent face internal angles; then the 3D solid faces are labeled depending on their vertices, and finally the edges are labeled depending on the edge vertices adjacent edges vertex type. See Figure 9a.
To calculate the geometric entropy is used the number of the different vertex, edge and faces types; the total vertex, face and edge number in a planar solid. The ratio between 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑒𝑙𝑒𝑚𝑒𝑛𝑡 𝑇𝑦𝑝𝑒 𝑖 and 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐸𝑙𝑒𝑚𝑒𝑛𝑡 is represented by 𝑃𝑖. Those values are plotted in the entropy formula to calculate the geometric entropy obtained from that 3D solid. See Equation 1.
Figure 9a 3D Solid vertex, face and edge labeling.
The geometric entropy is calculated from a 3D solid of an instance. An architectural model may be composed by several instances that are represented by several 3D solids. Also, an architectural model may be entirely represented by one single 3D solid. The geometric complexity takes care of both cases, for this reason, this research applies the geometric entropy calculation to both. The general geometric entropy refers to the calculation of the geometric entropy to the entire building main part; this includes all the elements that form that building main part as one 3D solid by merging them. The individual geometric entropy refers to the calculation of the entropy to the individual instance that forms a building main part. See the Figure 9b and 9c.
Geometric Entropy = − ∑ 𝑝𝑖 𝑙𝑜𝑔2 (𝑝𝑖)
Figure 9b Building main part individual entropies 3D solid b
Figure 9c Building main part general entropy
Variety
The variety characterization for a geometric model refers to how different are the shapes of the elements in a building main part. This research uses the standard deviation to calculate the variety of the individual geometric entropy values of an entire building main part as calculation metric, where the higher standard deviation is equivalent on a higher range of individual shapes for that building main part. See equation 5.
The values used for this equation are calculated with the same formula used for the geometric entropy 𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝐺𝐸 is the value for a specific building main part element. 𝑀𝑒𝑎𝑛 𝑜𝑓 𝐴𝑙𝑙 𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝐺𝐸 is the average of all the individual geometric entropies in a building main part. 𝑁 is the total number of elements that are found in a building main part.
3 Number of Elements
The number of elements characterization refers to the number of elements that form a 3D solid in a building main part. The calculation of the number of elements in this research is the summation of all the 3D solid instances in a building main part. The way to calculate the building instance that composes a building main part is by filtering from the rest of the building instance and then do the summation. See equation 6.
Number of Elements = ∑ 𝐵𝑢𝑖𝑙𝑑𝑖𝑛𝑔 𝑚𝑎𝑖𝑛 𝑝𝑎𝑟𝑡 3𝐷 𝑠𝑜𝑙𝑖𝑑𝑠
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝑉𝑎𝑟𝑖𝑒𝑡𝑦) = √∑𝑁𝑖=1(𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝐺𝐸 − 𝑀𝑒𝑎𝑛 𝑜𝑓 𝐴𝑙𝑙 𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝐺𝐸 )2 𝑁 − 1
Eq.5
Eq.6
Construction Complexity: How hard is to create this building?
The factors selected to be responsible for this question are the buildability, multidisciplinarity, and size. This question refers to how hard is to create the real building instead of how hard is to create the building model. From those factors is expected to generate rational values that can allow the designer obtain a better understanding of the design from the construction perspective by knowing how hard will be to create.
1 Buildability
This research refers to buildability as ̏ the extent to which the design of a building facilitates ease of construction, subject to the overall requirements for the completed building being met ˝ [24]. Buildability is a factor that gives a score in percentage, for this research the main idea is to obtain how difficult make the design the construction of that specific building.
Buildability calculation method adapt the same calculation as the one used in the Buildability Assessment Method (BAM) developed for Hong Kong [25]. See Figure 10.
Other studies about BAM implementation by other countries were applied by countries like Malaysia, where the metrics followed the same pattern but the indices and max scores changed due to the country standards [26].
Figure 10 Adapted buildability scoring method metrics for construction core systems. [25]
BAM has the purpose of scoring the building when the design of the same is almost completed and help the designer to revise the design to improve buildability [25].
The buildability score is subtracted from the total buildability so can be obtained the difficulty for construction of this design. See equation 7
𝐵𝑢𝑖𝑙𝑑𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑓𝑎𝑐𝑡𝑜𝑟 = 100 − 𝑏𝑢𝑖𝑙𝑑𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑠𝑐𝑜𝑟𝑒 𝑖𝑛 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒
In the BAM metrics, the 𝑆𝑦𝑠𝑡𝑒𝑚 𝑀𝑎𝑥 𝑆𝑐𝑜𝑟𝑒 and 𝐵𝑢𝑖𝑙𝑑𝑎𝑏𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥 are obtained from data collections and analytical hierarchy process (AHP) [25]. The data collection process will vary depending on the area where is made. This means that different countries may have different buildability indexes for different building elements and systems max score. The 𝐴𝑟𝑒𝑎 𝑜𝑟 𝑉𝑜𝑙𝑢𝑚𝑒 𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 represents the way the different systems are distributed in the entire building. 𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟 is obtained by dividing the 𝑆𝑦𝑠𝑡𝑒𝑚 max 𝑠𝑐𝑜𝑟𝑒 𝑎𝑛𝑑 𝑡ℎ𝑒 𝐵𝑢𝑖𝑙𝑑𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥(𝐵𝐼).
See equation 8.
The buildability score is a normalized factor. It does not take in count the building size, but it is directly affected by the way the construction methods or materials are distributed in the entire building. In this case, the core construction systems for a specific area may have predetermined their specific construction method that is linked to the material type used in construction.
The area or volume percentage of all the instances that are part of specific system type in one of the core construction systems are calculated to obtain the buildability. The summation of the percentage for each core construction system needs to be equal to one
Eq. 7
Eq. 8 Construction System Sub score =∑(𝐴𝑟𝑒𝑎 𝑜𝑟 𝑉𝑜𝑙𝑢𝑚𝑒 % ∗ 𝐵𝑢𝑖𝑙𝑑𝑎𝑏𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥 ∗ 𝑁𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑓𝑎𝑐𝑡𝑜𝑟)
hundred. Each percentage is multiplied by a buildability index, depending on its system type. Then its multiplied to a normalization factor that is obtained by dividing the construction core systems' max score to the highest buildability index. The summation of all the construction core systems' subscores, lead to the total buildability score for the core construction systems in a building.
In table 1 its presented the best and worst buildable possible cases according to the data obtained from the buildability assessment model done in Hong Kong [25]. This table has the parameters needed to calculate the buildability of a building core construction systems. Moreover, emphasizes the results for a hypothetical building that has the best buildable conditions and worst buildable conditions are presented to illustrate the meaning of this factor.
Table 1 Worst and best buildable hypothetical cases. [25]
Best and Worst Buildable Possible Cases [25]
Construction
23 Precast RC frame 0.239 0.962 100 23.000
23 Structural steel with fireproofing 0.21 0.962 100 20.209
23 In situ RC frame 0.194 0.962 100 18.669
23 In situ load bearing cross-wall 0.181 0.962 100 17.418
23 Steel encased in concrete 0.176 0.962 100 16.937
14 Precast slab with in situ topping 0.27 0.510 100 13.770
14 Steel deck with in situ concrete topping 0.253 0.510 100 12.903
14 In situ RC slab 0.2 0.510 100 10.200
14 Flat slab 0.176 0.510 100 8.976
14 Pre-stressed concrete slab with in situ topping 0.101 0.510 100 5.151
19 Precast concrete wall with pre-installed windows and finishes 0.257 0.739 100 19.000
19 Curtain wall 0.206 0.739 100 15.230
19 In situ concrete wall 0.179 0.739 100 13.234
19 Pre-finished precast concrete formwork with in situ filling 0.179 0.739 100 13.234
19 Concrete block/brick 0.178 0.739 100 13.160
10 Precast concrete roof 0.271 0.369 100 10.000
10 Steel decking with in situ concrete topping 0.271 0.369 100 10.000
10 Steel truss roof with composite decking 0.238 0.369 100 8.782
10 In situ concrete roof 0.22 0.369 100 8.118
3 Dry wall 0.434 0.069 100 2.999
3 Concrete block/brick 0.317 0.069 100 2.190
3 In situ RC wall 0.249 0.069 100 1.720
Best buildable conditions Best buildable conditions Total of 69 68.76
Worst buildable conditions Worst buildable conditions Total of 69 45.08
Roof Building Envelope Slab
Best and Worst Buildable Possible Cases [23]
Structural Frame
Internal Wall
2 Multidisciplinarity
This research refers to multidisciplinarity as the number of direct stakeholders in the design and construction. The stakeholders in concern are the ones involved in the project consultation and work as the project contractor or subcontractor. Form the consultant’s perspective the main roles according to generalized work breakdown structures can be the 3D modeler, cost modeler, sequencing modeler [27]. The subcontractors involved can be categorized from the generalized work break down structure proposed by Makarfi, Kaka, Aouad, and Kagioglou [28]; where its mentioned that ̏ the work sections reflect a type of construction activity requiring certain skills applied to a particular type of resource. It, therefore, relates to various trades and subcontractors who procure the work˝. These work sections includes main work, formwork, concrete production, stone/block/brick production, other element production, responsible for waterproofing and others.
The multidisciplinarity factor score is obtained by the summation of needed to be involved disciplines in design and construction for a specific building design. See equation 9. Table 2 shows a compilation of the possible stakeholders needed for a simple construction case.
𝑀𝑢𝑙𝑡𝑖𝑑𝑖𝑠𝑐𝑖𝑝𝑙𝑖𝑛𝑎𝑟𝑖𝑡𝑦 = ∑ 𝐷𝑖𝑠𝑐𝑖𝑝𝑙𝑖𝑛𝑒𝑠 𝑖𝑛𝑣𝑜𝑙𝑣𝑒𝑑 𝑖𝑛 𝑑𝑒𝑠𝑖𝑔𝑛 𝑎𝑛𝑑 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛
Eq. 9
Table 2 Multidisciplinarity compilation [27, 28]
Elements Types Work Sections (Subcontractors) [26] Design Sections (Consultants) [25]
Substructure Concrete or precast
Groundwork, Main Work , Formwork , Concrete Production , Substructure Concrete or precast others
Structure,Architecture, Schedule, Cost, Substructure Design Others
Substructure Masonry Groundwork, Stone/block/brick Production
,Substructure Masonry others Substructure Waterproofing Groundwork, Substructure Waterproofing
others
Structure, Architecture,Schedule, Cost, Substructure Design Others
Frame Concrete or precast Main work,Formwork,Concrete Production, Frame concrete or precast others Slabs Concrete or precast Main work, Formwork, Concrete Production,
Slab concre or precast others Roof Concrete or Precast Main work,Fromwork,Concrete Production,
Roof concrete or precast others Roof Cladding/Covering Roof Cladding/Covering others
Structure,Architecture, Schedule, External Walls Concrete or precast Main work,Formwork,Concrete Production,
External Walls concrete or precast others
Architecture,Schedule, Cost, External Wall Design Other
External Walls Masonry Main work,stone production, External Walls Masonry others
Partitions Masonry Main work,stone production, Internal Walls Masonry others
Load Bearing Walls Concrete or precast Main work,Formwork,Concrete Production, Bearing Walls concrete or precast others
Structure,Architecture, Schedule, Cost, Load Bearing Wall Design Others
Load Bearing Walls Masonry Main work,stone production, Bearing Walls Masonry others
Structure,Architecture, Schedule, Cost, Load Bearing Wall Design Others Multidisciplinarity Table (Subcontractors and Consultants)
Elements Types Work Sections (Subcontractors) [28] Design Sections (Consultants) [27]
Multidisciplinarity Table (Subcontractors and Consultants)
3 Size
This research refers to the size of the area of all the floors that form a building, as it is presented by other studies [29, 30]. The calculation of this value only includes the total area of the construction core systems that make a floor at each level as input. See equation 10. The area will be expressed in square meters, and it allows a non-normalized comparable value between different building designs.
𝑆𝑖𝑧𝑒 = ∑ 𝐵𝑢𝑖𝑙𝑑𝑖𝑛𝑔 𝐿𝑒𝑣𝑒𝑙 𝐹𝑙𝑜𝑜𝑟 𝐴𝑟𝑒𝑎
The size of the building is obtained from the summation of all the building floor area that is composed of the pointing upward surfaces of the structural frames and slabs instance. See figure 11.
Eq. 10
Figure 11 Elements involved in the floor area calculation.
Based on all the information of the factors presented previously, a compilation has been made and can be referenced to table 3 as below: