Construction Research Congress 2012 © ASCE 2012
Formalizing the Four-Dimensional (4D) Topology as the Base for 4D analysis in
Construction Planning
Xing SU1, Lei ZHANG2, Abdul Rahman ANDOH3, and Hubo CAI4
1
Xing Su, Ph.D. Candidate, Division of Construction Engineering and Management,
School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West
Lafayette, IN 47906; PH (765)-418-4331; email: XSU@PURDUE.EDU
2
Zhang, L., Institute of Geological Surveying and Mapping of Anhui Province, 18
JiuHuaShan Road, Hefei, Anhui, PRC 230022.
3
Abdul Rahman Andoh, M.S., Division of Construction Engineering and Management,
School of Civil Engineering, Purdue University, 550 Stadium Mall Drive, West
Lafayette, IN 47906
4
Hubo Cai, Ph.D., P.E., GISP, Assistant Professor, Division of Construction
Engineering and Management, School of Civil Engineering, Purdue University, 550
Stadium Mall Drive, West Lafayette, IN 47906
ABSTRACT
Construction site is a dynamic environment in which workspaces of
construction activities continuously change in aspects of space and time throughout the
entire lifecycle of a project. Without a comprehensive plan that considers
spatial-temporal relationships between the site objects, conflicts or improper layout
may frequently occur on construction site and influence the success of the project. Four
dimensional (3D+time) modeling technique has been proven to be useful and
promising in construction planning. However, it still lacks the ability to capture the site
dynamic natures and analyze spatial-temporal relationships.
The overall goal of this study is to develop a 4D topology system based on GIS
concept for construction planning, which enables deriving 4D relationships between
site objects in real-time and provides a comprehensive 4D topological analysis function,
overcoming a major drawback in the current 4D practice. This paper presents the result
of the development of the 4D topology framework in construction. The semantics of 4D
topology are defined to describe corresponding dynamic construction site events. A 4D
topological framework is formalized to capture the site dynamics which forms the base
for 4D analysis. It could complement the CPM or 3D model in construction planning
under both spatial and temporal constraints. The direction of future research in 4D
topology-based analysis is also discussed.
INTRODUCTION
4D Techniques and Construction Planning
Construction site is a dynamic environment. Workspaces of construction
activities, layout of temporary facilities, and material deployment continuously change
on site in aspects of space and time throughout the entire lifecycle of a project. The
dynamic objects on site interact with each other in a complex spatial-temporal manner.
397
Construction Research Congress 2012 © ASCE 2012
Without a comprehensive plan that considers spatial-temporal relationships between
the site objects, conflicts and improper site layout may frequently occur on construction
site. It has been identified that time-space conflict is one of the major causes of
productivity loss in construction industry. The congested workspace and restricted
access can cause efficiency losses of up to 65% and 58%, respectively (Sanders et al.
1989). Developing a construction plan is a critical task in the management of a
construction project (Hendrickson, 2000).
Construction planning and control are not only temporal but also spatial (Winch,
2001). Recently, research efforts are emerging in the provision of project planners and
managers with computer-based advisory tools to visualize the construction plan in a 4D
(3D+time) environment. 4D models, such as 4D CAD, were seen as a natural
progression to 3D models, as it adds a further dimension (Phair, 2000). Positive
attitudes were received from many researchers and practitioners towards the
development and application of 4D technology in construction (Liston et al. 2001, and
Fischer and Kunz, 2004).
Knowledge Gaps in Current 4D Techniques
Despite the benefit and demonstrated potential, to date, 4D technology is not
accepted on a large scale in construction management (Webb et al. 2004). Some
limitations of the current 4D technology are discussed such as the lack of a concept to
prepare the 4D model within appropriate time and in parallel to the creation of the
construction schedule (Tulke and Hanff, 2007), the visualization is not easily
customizable (Issa and O’Brien, 2003), and that spatial relationships and topology are
not well supported by most of the 4D models (Bansal, 2011). Akinci et al. (2002)
indentified the dynamic process problem and considered most of the previous 4D
model to be not informative enough as the spaces required by construction activities are
not integrated. They developed a methodology to generate space-loaded 4D production
models to create workspaces for each construction activity and detect space-time
conflicts. This achievement makes 4D simulations more realistic and advances spatial
conflict analysis. However, it still does not fully capture the dynamic geometry change
of workspaces since every workspace in it is of the same prism shape through the
project duration. In addition, it focuses only on space-time conflicts, and does not
consider other relationships between site objects.
Two issues are identified here as the critical primary research themes for
advancing the development of 4D systems to automate construction project planning
and control tasks. The first issue is the analytical capability. Current 4D technique
focuses on visualizing 3Dgraphics over time and cannot support analytical programs
(Halpin 2006). For instance, topological queries such as identifying columns within the
200ft crane radius cannot be answered. This is the main reason that 4D models are
rarely used for construction phase decision making and administration (Martinez and
Halpin 1999). The second issue is the dynamic capability. Visualizing 3D objects at
discrete points throughout the duration of the associated task, i.e. displaying the entire
product for the whole task duration, is not representative of the construction process
398
Construction Research Congress 2012 © ASCE 2012
399
(North and Winch 2002,). The shape, location, and properties of a construction object
change throughout its life cycle.
RESEARCH OBJECTIVES
The overall goal of this research is to create a 4D system for construction
planning to enable 4D topological analyses to address the second issue. The system
contains a 4D topology framework that defines the semantics of the 4D topology in
construction and their mathematical formulization, and a 4D construction model that
integrates construction dynamics to be analyzed in the aspect of 4D topological
relationships. The system structure is illustrated in Figure 1.
4D Topology System
Method
Temporal
Interaction
Research
Entity
Construction
Construction Lifecycle
Object
Model
Life cycle
Geometry;
Temporal
area
Location;
Interaction
Pattern
Existing
Site Dynamics in:
Spatial
3D
Interaction
Topology
Evolution style;
4D
Topology
3D Model
1D Schedule
knowledge
9-IM
4D Visualization
Figure 1. 4D Topology System Architecture
This paper proposes a conceptual 4D topology framework for the left part. The
following sections introduce the existing 3D topology framework, identify the temporal
interaction patterns, and integrate both to form the 4D topology framework.
Specifically, the research objectives include:
1. Define the semantics of 4D topology in construction;
2. Identify site objects’ temporal interaction pattern;
3. Formalize the 4D topology in construction in a matrix format;
4D TOPOLOGY SEMANTICS IN CONSTRUCTION
4D Topology in construction describes relationships between site objects in
temporal and spatial aspects. The site objects here has a generalized meaning, including
building elements, temporal facilities, equipments and labors, their workspaces, and
paths. During construction planning, not only building products and schedule need to
Construction Research Congress 2012 © ASCE 2012
be considered, but also the work activities to create the building products as well as the
interaction between those activities spatially and temporally.
Some characteristics of 4D topology in construction are identified. First, the
space and time attributes of each site object all have explicit boundaries. The
information could be obtained from the 2D/3D drawing and the schedule. Second,
every site object has an evolutionary geometry along periods. Nothing could appear on
site without necessary activities which occupy certain spaces. A cast-in-place element
needs concreting work; a prefabricated element needs installation, temporary facilities
needs assembling and disassembling. Those activities for every object all need
workspaces with different geometries at different construction stages. At last, the
geometry evolution of each object all has predefined or expected evolutionary patterns.
The patterns are determined by construction methods. The characteristics enable
certain simplification of the 4D topology framework in construction, which is further
discussed in the following sections.
3D TOPOLOGY FRAMEWORK IN GIS
In most cases the architectural and/or structural function of a particular object or
component is associated with its shape, position, and relationship to other components
so that the geometric properties and 3D spatial relationships between building
components accordingly play an important role in solving most of the design and
engineering problems (Borrman and Rank, 2009). The first substantial progress
towards a formalization of topological relationships was the development of the
4-Intersection Model (4-IM) by Egenhofer and Herring (1990). It was extended to
9-Intersection Model (9-IM) by incorporating the exteriors to solve topological
relationships between elements including lines and regions. The 9-IM examines the
intersections of each of the interior and boundary and exterior of object A with each of
the interior and boundary and exterior of object B, resulting in the 3x3 matrix as
follows:
⎡ Ao ∩ B o
⎢
I = ⎢ ∂A ∩ B o
⎢ A− ∩ B o
⎣
Ao ∩ B − ⎤
⎥
∂A ∩ B − ⎥
A− ∩ B − ⎥⎦
A○ denotes the interior, ∂A denotes the boundary, A⎯ denotes the exterior of A,
and ∩ represents the intersection operator. Each element is the result from the
intersecting operation, which can be TRUR or FALSE. This framework is updated to
support 3D objects (Zlatanova, S., 2000). There are 8 basic possible relationships
between 3D and 3D objects, which are illustrated in Figure 2. In construction context,
most of the product and workspace could be presented by 3D geometries. The 4D
topology framework developed in this study adopts this 9-IM to represent the spatial
relationships.
Ao ∩ ∂B
∂A ∩ ∂B
A− ∩ ∂B
400
Construction Research Congress 2012 © ASCE 2012
401
Disjoints
Meets
Contains
Covers
Inside
Covered by
Equals
Overlaps
Figure 2. Configurations of topological relationships between 3D and 3D objects
IDENTIFY TEMPORAL INTERACTION PATTERNS
Site Object Life Cycle
There are many types of construction site objects such as building element,
temporary facility, equipment, and path. Those objects all interact with surrounding
objects and environment and have different patterns of dynamics. For example, the
concrete face of a rock-filling dam has its geometry changing through the concreting
period; and a crane usually involves geometry change (arm swing and extending) and
position change (translation and rotation). All the motions need time to perform and
time is closely related to the evolution progress of these spatial properties.
In traditional 1D scheduling method, every construction activity could be
represented by a line segment on the time axis from “Start Time” (ST) to “Finish Time”
(FT). It separates the time axis into three parts: 1, before ST, 2, from ST to FT, and 3,
after FT (Figure 3).
Activity
1
ST
2
FT
3
Time
Figure 3. Representing an activity on the time axis
From the geometry evolution perspective, every site object has different statues
of geometry or spatial information during the three stages. Taking a concrete wall for
example, it’s geometry does not exist at stage 1, which is represented by “empty” and
indexed by “Emp”; at stage 2, the geometry becomes the concreted part plus its
required activity workspace including formwork and labor working area, which can be
called “activity geometry” and indexed by “Act”; at stage3, the wall has been finished
and there is no activity workspace requirement, and its geometry is just the solid wall
itself, which is called “solid geometry” and indexed by “Sol”. Therefore, along the time
axis the concrete wall’s geometry has three distinguishable stages: empty, activity
geometry, and solid geometry. Table 1 lists the geometry evolution in different stages
Construction Research Congress 2012 © ASCE 2012
402
for six types of construction objects including building elements, excavated part,
temporary facilities, equipments, storage, and paths. Akinci et al. (2000) actually has
identified and classified space types into eight categories, which are product space and
workspace, process space, equipment space, equipment path, storage space, path space,
protected space, and support space. The space classification used in this study at this
moment is more generalized to illustrate the geometry evolution process along time.
Table 1. Site objects geometry evolution
Stage
Object
Building Element (Ele)
Excavated Part (Exc)
Temporary Facility Assemble (TempA)
Temporary Facility Dissemble (TempD)
Equipment (Equ)
Storage (Sto)
Path (Path)
1
2
Empty
Solid space
Empty
Solid space
Solid space
Solid space
Empty
Activity space
Activity space
Activity space
Activity space
Activity space
Activity space
Activity space
3
Solid space
Empty
Solid space
Empty
Solid space
Solid space
Empty
The temporary facility itself has three types of statues: assembling, assembled,
and disassembling. The table lists its assembling and dissembling statues as two
different objects. During the assembled statues, the temporary facility could be
considered as equipment. In practice, the objects should also be selectively considered
depending on the expected detail level of the construction planning work.
Temporal Relationships Configurations
Since the temporal stage determines an object’s geometry pattern, it is
necessary to examine the temporal attribute as a first step for 4D topology formalization.
When there are two objects, more stages could happen. Figure 4 illustrates an example
that two objects have five different interaction stages. Assume both objects are building
elements, according to Table 1, the geometries of the two objects in the five stages are:
P1: Emp(A) vs. Emp(B); P2: Act(A) vs. Emp(B); P3: Act(A) vs. Act(B); P4: Sol(A) vs.
Act(B); and P5: Sol(A) vs. Sol(B).
A
A2
A1
A3
B2
B1
B
P1
P2
P3
B3
P4
P5
Figure 4: Possible temporal relationships for building elements
A 3x3 Temporal Interaction matrix TIAB examining the intersection of stages
between A and B is utilized to identify the temporal relationships:
Construction Research Congress 2012 © ASCE 2012
403
A ∩B A ∩B A ∩B
TIAB = A ∩ B A ∩ B A ∩ B
A ∩B A ∩B A ∩B
The element of the matrix is either 0 (false) or 1 (true). There are 4 possible
configurations for interaction without temporal overlaps and 9 possible configurations
for interaction with temporal overlaps as shown in Table 2. Each configuration has a
unique TIAB matrix so that Table 2 also serves as a lookup table for determination of
temporal relationship configurations. The terminology describing the temporal
relationships is similar to those in the 9-Intersection framework. The difference is that
an “ahead” or an “after” is added as a prefix to describe the sequence of the two
activities.
Table 2 Two objects temporal relationship configurations
No temporal overlaps:
Config.4:
Config.3:
Config.2:
Config.1:
A after-Disjoint B
A ahead-disjoint B A after-meet B
A ahead-meets B
1 0 0
1 1 1
1 1 0
1 0 0
1 0 0
1 0 0
0 0 1
0 0 1
0 1 1
0 A0 1
0 0A 1
1 1 1
A
A
B
Temopral overlaps:
Config.1:
A ahead-overlaps B
1 1 0
0 1 1
0 0 1A
B
B
B
Config.2:
A ahead-coveredby B
1 0 0
0 1 1
0 0 1
A
B
Config.3:
A equals B
1 0 0
0 1 0
0 0 1
Config.4:
A ahead-covers B
1 0 0
0 1 0
0 1 A
1
Config.5:
A contains B
1 1 0
0 1 0
0 1 1 A
Config.6:
A after-covers B
1 1 0
0 1 0
0 0 1A
B
Config.7:
A after-overlaps B
1 0 0
1 1 0
0 1 1 A
B
Config.8:
A after-coveredby B
1 0 0
1 1 0
0 0 1 A
B
B
B
B
A
B
Config.9:
A inside B
1 0 0
1 1 1
0 0 1 A
B
Construction Research Congress 2012 © ASCE 2012
FORMULATE 4D TOPOLOGICAL MATRIX
A 4D ToPological (4DTP) matrix integrates 9-IM with the TI matrix. As for a
TI matrix of object A and B, each element represents a certain period of temporal
intersection or a simple result of “no intersection”. The geometries of A and B evolve
and interact in the intersected periods. Assume A and B have fixed (non-time
dependent) workspaces in A2 and B2 stages; each intersected period will have a unique
9-IM matrix representing the spatial interaction status of A and B. To simplify the
matrix, two transform vectors are suggested to index the 9-IM matrices:
100 10 1 …… (4.1)
1 2 4 ………… (4.2)
T1 and T2 are designed to convert a 3x3 matrix into an integer without
∙ , the Disjoints
information lost. By using dot product operation ∙ 9
9-IM matrix could be indexed by a single integer as follows:
0 0 1 1
Disjoints: 100 10 1 ∙ 0 0 1 ∙ 2
447;
1 1 1 4
Similarly, other 9-IM matrices could all be indexed: Contains – 744; Inside –
117; Equals – 124; Meets – 467; Covers – 764; Covered by – 137; Overlaps – 777. The
vector 4.2 contains the three smallest integers that the sum of any two of them is a
different number, which guarantees that every transformed matrix is uniquely
corresponding to the original one. Using the vector 4.1 and 4.2 together makes sure that
no information is lost during the transform and the result is easy to present. Thus, a
combination matrix could be formed containing all the spatial interaction information
in all possible temporal interacting periods:
9
9
9
9
9
9
9
9
9
Each element of the above matrix is the index of the 9-IM matrix of A and B at
the corresponding period. Considering the example shows in Figure 5, the
spatial-temporal matrix of building element Wall (A) and building element Column (B)
would be:
0
0
0
0 777 447
0 777 447
According to equations 4.3 and 4.10, “777” means “overlaps” and “447” means
“disjoints”. The matrix tells that A’s workspace and B’s workspace overlap, A’s solid
product and B’s workspace disjoint, A’s workspace and B’s solid product overlap, and
A’s solid product and B’s solid product disjoint.
404
Construction Research Congress 2012 © ASCE 2012
405
Wall (A)
A
Column
B
Column
Wall (A)
Figure 5: An example of using 4D topology in construction planning
The 4D topology matrix is finally generated by the following operation:
1000
Since all the elements in the Spatial-Temporal matrix are three-digit integers,
the factor 1000
put the temporal interaction information on the thousandth
digit. Referring to the example in Figure 5:
1 1 0
0
0
0
1000 1000 0000
4
1000
0 1 1
0 777 447
0000 1777 1447
0 0 1
0 777 447
0000 0777 1447
The matrix contains all the 4D topological information regarding to the
interaction between Wall (A) and Column (B) based on the assumption that A and B all
have fixed (non-time dependent) geometries during construction. In real construction
projects, there are some types of construction activities actually have their geometry
varies along time, such as trenching (geometry grows) and backfilling (geometry
shrinks). In this case some elements in the 4DTP matrix may have two or more values.
Multiple values are used in one matrix location to solve this problem by listing all the
interacting situations in time sequence.
4
CONCLUSION AND DISCUSSION
As part of an overall research, this paper presents the theoretical foundation of a
4D topology system for construction planning. A set of 4D topological matrices is
developed to describe the interacting manner of site objects in 4D context. The
geometry evolution of the site objects is considered and formatted by the matrices. The
resulting framework of the 4D topology forms the base for 4D analyses and
complements the CPM or 3D model in construction planning under both spatial and
temporal constraints.
The main work of the remaining part of this research is the development of the
4D dynamic model. Currently, this part of is in progress. The model is designed to serve
as an entity to conduct 4D topological analyses. It could be generated from CAD
models by incorporating the site dynamic information such as construction methods
and the schedule. A construction method library will be developed based on field
observation to store default parameters of different construction methods for site space
requirements. A topology operation libraries based on GIS concept will be integrated as
the technical tools to enable 4D topological analysis. The resulting system of the 4D
Construction Research Congress 2012 © ASCE 2012
topology will enable 4D analysis and visualization considering workspaces. It could
also serve as an effective explanative communication tool in construction project
management.
REFERENCE
Akinci, B., Fischer, M., Levitt, R. and Carlson, R. (2002). “Automated generation of
work spaces required by construction activities,” Journal of Construction
Engineering and Management, 128(4), ASCE, 306-315.
Bansal V. K. (2011) “Use of GIS and Topology in the Identification and Resolution of
Space Conflicts.” J. Comput. Civ. Eng., 22(4), 233-242.
Borrmann, A. and Rank, E. (2009). “Topological Analysis of 3D Building Models
Using a Spatial Query Language,” Advanced Engineering Informatics, 23,
Elsevier Ltd. 370-385.
Egenhofer, M., and Herring, J. (1990) “A mathematical framework for the definition of
topological relationships”, Proc. of the 4th Int. Symp. on Spatial Data
Handling.
Halpin, D. W. (2006). Construction Management, Chapter 7, Project Scheduling, John
Wiley & Sons, Inc. 101-125.
Hendrickson, C. (2000) “Project Management for Construction – Fundamental
Concepts for Owners.” Engineers, Architects and Builders, 2nd edition.
Issa, R. R. A., Flood, I., and O’Brien, W. J., eds. (2003). “Closure.” 4D CAD and
visualization in construction: Developments and applications, A.A. Balkema,
Tokyo, 281–284.
Martinez, L. H., and Halpin, D. W. (1999). “Real world applications of construction
process simulation,” Proc., 1999 Winter Simulation Conf., P. A. Farrington, H.
B. Nembhard, D. T. Sturrock, and G. W. Evans, eds., WSC Foundation,
Phoenix, 956–962.
North, S. and Winch, G.M. (2002). “VIRCON: a proposal for critical space analysis in
construction planning,” ECPPM, Slovenia, 9–11 September, Balkema,
Rotterdam.
Phair, M. (2000). “Software model builders add an extra dimension to 3D CAD.” ENR,
6 March.
Sanders, S.R., Thomas, H.R. and Smith, G.R. (1989). “An Analysis of Factors
Affecting Labor Productivity in Masonry Construction.” PTI # 9003,
Pennsylvania State University, University Park, PA.
Tulke J., Hanff J. (2007) “4D construction sequence Planning -- new process and data
model.” CIB 24th W78 Conference. Maribor, Slovenia, 79-84.
Webb, R. M., Smartwood, J., and Haupt, T. C. (2004). “The potential of 4D CAD as a
tool for construction management.” J. Constr. Res., 5(1), 43-60.
Winch, G.M. (2002). “Managing construction projects: an information processing
approach.” Blackwell Sicence, Oxford.
Zlatanova, S. (2000) “3D GIS for Urban Development”, ITC Dissertation Series No.69.
406