Author Contributions
Conceptualization, H.L. and X.L.; methodology, H.L.; software, J.L.; validation, H.L., X.L. and J.L.; formal analysis, H.L.; investigation, X.L.; resources, S.D.; data curation, S.D.; writing—original draft preparation, H.L.; writing—review and editing, X.L.; visualization, J.L.; supervision, X.L.; project administration, X.L.; funding acquisition, H.L. All authors have read and agreed to the published version of the manuscript.
Figure 1.
The impact of installation deviations in prefabricated components.
Figure 1.
The impact of installation deviations in prefabricated components.
Figure 2.
The process of obtaining dimensions of prefabricated components through 3D photogrammetry.
Figure 2.
The process of obtaining dimensions of prefabricated components through 3D photogrammetry.
Figure 3.
The horizontal deviation.
Figure 3.
The horizontal deviation.
Figure 4.
The vertical deviation.
Figure 4.
The vertical deviation.
Figure 5.
The three-dimensional photographic measuring instrument.
Figure 5.
The three-dimensional photographic measuring instrument.
Figure 6.
Fitted curve for the axis position deviations of wall panels.
Figure 6.
Fitted curve for the axis position deviations of wall panels.
Figure 7.
Logarithmic frequency distribution of axis deviations of wall panels.
Figure 7.
Logarithmic frequency distribution of axis deviations of wall panels.
Figure 8.
Fitted curve for the axis deviation of columns.
Figure 8.
Fitted curve for the axis deviation of columns.
Figure 9.
Logarithmic frequency distribution of axis deviation for columns.
Figure 9.
Logarithmic frequency distribution of axis deviation for columns.
Figure 10.
A Q–Q plot of the logarithm of the wall panels centerline deviation.
Figure 10.
A Q–Q plot of the logarithm of the wall panels centerline deviation.
Figure 11.
A Q–Q plot of logarithm of column centerline deviation.
Figure 11.
A Q–Q plot of logarithm of column centerline deviation.
Figure 12.
The fitted curve for qualification rate of axial position deviation—wall panels.
Figure 12.
The fitted curve for qualification rate of axial position deviation—wall panels.
Figure 13.
The fitted curve for qualification rate of axial position deviation—columns.
Figure 13.
The fitted curve for qualification rate of axial position deviation—columns.
Figure 14.
The manufacturing dimensions and designated dimensions of prefabricated components.
Figure 14.
The manufacturing dimensions and designated dimensions of prefabricated components.
Figure 15.
The assembly component installation dimensional chain system.
Figure 15.
The assembly component installation dimensional chain system.
Figure 16.
A Three-Story Prefabricated Kindergarten Teaching Building.
Figure 16.
A Three-Story Prefabricated Kindergarten Teaching Building.
Figure 18.
A schematic diagram of the dimensions of prefabricated beams and columns.
Figure 18.
A schematic diagram of the dimensions of prefabricated beams and columns.
Figure 19.
A Histogram of Cumulative Sizes of Component Assemblies at Minimum Joint Width.
Figure 19.
A Histogram of Cumulative Sizes of Component Assemblies at Minimum Joint Width.
Figure 20.
A Histogram of Cumulative Sizes of Component Assemblies at Maximum Joint Width.
Figure 20.
A Histogram of Cumulative Sizes of Component Assemblies at Maximum Joint Width.
Figure 21.
Size deviations for different reliability levels at the minimum joint width.
Figure 21.
Size deviations for different reliability levels at the minimum joint width.
Figure 22.
Size deviations for different reliability levels at the maximum joint width.
Figure 22.
Size deviations for different reliability levels at the maximum joint width.
Figure 23.
The installation reliability for different manufacturing dimensional deviations.
Figure 23.
The installation reliability for different manufacturing dimensional deviations.
Figure 24.
The vertical axis component installation dimensional schematic.
Figure 24.
The vertical axis component installation dimensional schematic.
Figure 25.
Size deviations for different reliability levels at the minimum joint width.
Figure 25.
Size deviations for different reliability levels at the minimum joint width.
Figure 26.
Size deviations for different reliability levels at the maximum joint width.
Figure 26.
Size deviations for different reliability levels at the maximum joint width.
Figure 27.
Size deviations for different reliability levels at the minimum joint width.
Figure 27.
Size deviations for different reliability levels at the minimum joint width.
Figure 28.
Size deviations for different reliability levels at the maximum joint width.
Figure 28.
Size deviations for different reliability levels at the maximum joint width.
Figure 29.
The installation reliability for different manufacturing dimensional deviations.
Figure 29.
The installation reliability for different manufacturing dimensional deviations.
Table 1.
Specification of permissible tolerances (unit: mm) for installation dimensions of prefabricated components.
Table 1.
Specification of permissible tolerances (unit: mm) for installation dimensions of prefabricated components.
Canonical Name | Items | Permissible Tolerance |
---|
Staircase | External Wall Panel | Structural Wall Panel | Column | Slab | Beam |
---|
Tolerance manual for precast and prestressed concrete construction (MNL-135-00) | Axis position | ±13 | ±13 | ±13 | ±13 | ±25 | ±25 |
elevation | ±9 | ±6 | ±13 | ±13 | ±19 | 13 |
verticality | - | 6 | 6 | 6 | - | 3 |
Connection width | ±19 | ±6 | ±9 | - | ±13 (component length 0~12 m) | ±6 |
±19 (component length 12~18 m) |
±25 (component length > 18 m) |
Shelving length | - | ±19 | ±19 | - | ±19 | ±19 |
Specification for tolerances and material specifications for concrete construction (ACI 117-2010) | Axis position | - | ±13 | ±13 | ±25 | ±25 |
elevation | - | −8~6 | −8~6 | - | −13~6 |
verticality | - | ±13 | ±25 | - | ±25 |
Joint width | - | ±3 | - | ±3 | ±3 |
Shelving length | - | ±13 | - | ±13 | ±9 |
Table 2.
Allowable Installation Tolerances in DIN18202-1997 (unit: mm).
Table 2.
Allowable Installation Tolerances in DIN18202-1997 (unit: mm).
Application Scope | Allowable Position Tolerance |
---|
Dimensions < 0.4 m | 0.4~1 m | 1~1.5 m | 1.5~3 m | 3~6 m | Dimensions > 6 m |
---|
Incomplete wall panels and floor slabs | 8 | 8 | 8 | 8 | 10 | 12 |
Completed wall panels and floor slabs | 5 | 5 | 5 | 6 | 8 | 10 |
Linear components (such as beams and columns) | 4 | 6 | 8 | - | - | - |
Table 3.
Allowable Installation Tolerances for Prefabricated Components in Chinese Standards and Specifications (unit: mm).
Table 3.
Allowable Installation Tolerances for Prefabricated Components in Chinese Standards and Specifications (unit: mm).
Canonical Name | Items | Permissible Tolerance |
---|
Code for Acceptance of Construction Quality of Concrete Structures (GB/T 50204-2015) | Axis Position | Vertical components (columns, wall panels and trusses) | 8 |
Horizontal components (beams and floor slabs) | 5 |
Elevation | Column, wall panel, beam, floor slab bottom, or top surface | ±5 |
Verticality | Height of installed columns and wall panels | 5 (component length ≤ 6 m) |
10 (component length ≥ 6 m) |
Shelf length | Beam and slab | ±10 |
Joint width | Wall panel joint width | ±5 |
Technical Standards for Prefabricated Concrete Buildings (GB/T 51231-2016) | Axis position | Vertical components (columns, wall panels, and trusses) | 8 |
Horizontal components (beams and floor slabs) | 5 |
Elevation | Column, wall panel, beam, floor slab bottom, or top surface | ±5 |
Verticality | Height of installed columns and wall panels | 5 (component length ≤ 6 m) |
10 (component length ≥ 6 m) |
Inclination | Beam and truss | 5 |
Shelf length | Column, wall, slab, beam, and truss | ±10 |
Joint width | Wall panel joint width | ±5 |
Technical Code for Prefabricated Concrete Structures (JGJ 1-2014) | Axis position | Vertical components (columns, wall panels, and trusses) | 10 |
Horizontal components (beams and floor slabs) | 5 |
Elevation | Column, wall panel, beam, floor slab bottom, or top surface | ±5 |
Verticality | Column and wall panel | 5 (component length ≤ 6 m) |
10 (component length 5~10 m) |
10 (component length ≥ 10 m) |
Inclination | Beam and truss | 5 |
Shelf length | Column, wall, slab, beam, and truss | ±10 |
Joint width | Wall panel joint width | ±5 |
Table 4.
The Log-normal Model Test for the Distribution of Installation Deviation.
Table 4.
The Log-normal Model Test for the Distribution of Installation Deviation.
Items | Wall Panel Installation Axis | Column Installation Axis |
---|
Sum of Squares | Degrees of Freedom | Mean Square Sum | F Value | Sum of Squares | Degrees of Freedom | Mean Square Sum | F Value |
---|
Regression | 0.133 | 20 | 0.013 | 92.331 | 0.103 | 18 | 0.0011 | 80.122 |
Residual | 0.0188 | 146 | 0.001 | | 0.0155 | 187 | 0.000 | - |
Total sum of squares | 0.152 | 166 | - | - | 0.0118 | - | - | - |
Goodness of fit R2 | 0.968 | - | - | - | 0.891 | - | - | - |
Table 5.
Parameter Estimation and Validation of Log-normal Model for Installation Deviation Distribution.
Table 5.
Parameter Estimation and Validation of Log-normal Model for Installation Deviation Distribution.
Parameter | Wall Panel Installation Axis | Column Installation Axis |
---|
Estimated Value | Standard Error | 95% Confidence Interval | Estimated Value | Standard Error | 95% Confidence Interval |
---|
Lower Limit | Upper Limit | Lower Limit | Upper Limit |
---|
| 0.81 | 0.043 | 0.764 | 0.852 | 0.640 | 0.092 | 0.548 | 0.732 |
| 3.06 | 0.159 | 2.900 | 3.219 | 4.647 | 0.430 | 4.217 | 5.076 |
| 0.64 | 0.042 | 0.598 | 0.682 | 0.526 | 0.089 | 0.548 | 0.732 |
Table 6.
Installation position deviation statistics.
Table 6.
Installation position deviation statistics.
Component Type | Number of Measurement Points | Mean Value/mm | Standard Deviation/mm | Allowable Deviation/mm | Qualification Rate |
---|
Prefabricated wall panel | 166 | 4.09 | 3.51 | 8 | 88.6% |
Prefabricated column | 205 | 4.77 | 2.19 | 8 | 92.2% |
Table 7.
Qualification rates of axial position deviation for prefabricated wall panels and columns under different allowable deviations.
Table 7.
Qualification rates of axial position deviation for prefabricated wall panels and columns under different allowable deviations.
Allowable Deviation/mm | 4 | 5 | 6 | 7 | 8 | 9 |
---|
Qualification rate | Prefabricated wall panels | 62.0% | 75.9% | 80.7% | 85.5% | 88.6% | 90.4% |
Prefabricated columns | 40.0% | 61.0% | 72.7% | 84.9% | 92.2% | 95.1% |
Table 8.
The Recommended Joint Width and Thickness according to the Fib 74 Standard.
Table 8.
The Recommended Joint Width and Thickness according to the Fib 74 Standard.
Component Width/m | Minimum Joint Width/mm | Minimum Joint Thickness/mm |
---|
1.8 | 12 | 8 |
2.4 | 12 | 8 |
3.6 | 14 | 8 |
4.8 | 15 | 10 |
6.0 | 16 | 10 |
Table 9.
The construction dimensions and probability distributions of each component ring (unit: mm).
Table 9.
The construction dimensions and probability distributions of each component ring (unit: mm).
Items | Prefabricated Column Width | Prefabricated Beam Length | Joint Width | Axis Dimension |
---|
C1 | C2 | C3 | B1 | B2 | B3 | W | La |
---|
Distribution types | Normal distribution | Normal distribution | Uniform distribution | Logarithmic distribution |
Component design dimensions | 360 | 360 | 360 | 3600 | 3900 | 2400 | 10/20 | 11,050 |
Mean of dimensional deviations | 1.336 | −3.002 | - | 3.06 |
Standard deviation of dimensional deviations | 1.010 | 1.382 | - | 0.64 |
Table 10.
The construction dimensions and probability distributions of each component ring (unit: mm).
Table 10.
The construction dimensions and probability distributions of each component ring (unit: mm).
Items | Prefabricated Column Length | Prefabricated Beam Height | Joint Width | Axis Dimension |
---|
C | B | W | La |
---|
Distribution types | Normal distribution | Normal distribution | Uniform distribution | Logarithmic distribution |
Component design dimensions | 2170 | 800 | 10/20 | 3060 |
Mean of dimensional deviations | 1.883 | 2.449 | - | 3.06 |
Standard deviation of dimensional deviations | 4.344 | 3.272 | - | 0.64 |