Estimation Modeling of Abutment Volume with Variations of Bridge Span, Abutment Height, and Seismic Zone

ABSTRACT The initial cost estimate for a bridge project using an estimation model can be done based on the dimensions, type, and material of the bridge. Research that has included bridge location as a determinant variable for initial bridge cost estimation has not been carried out much. The different locations of the bridge project will have different seismic accelerations and seismic load analysis. This study aims to create a model used to calculate the quantity needed for the construction of abutment in various locations with a PCI-Girder superstructure. The data used for the quantity estimation model was derived from the abutment design results. The data obtained from the calculation of concrete and reinforcing steel quantities from the abutment design with variations in bridge span i.e. 20 m; 25 m; 30 m; 35 m; and 40 m, abutment height i.e. 4 m; 6 m; and 8 m, and seismic zone 1, 2, 3, and 4. Volume estimation models are obtained by multiple linear regression analysis. The results show a very strong correlation between the span of the bridge and the height of abutment with the dependent variables. While the seismic zone has a strong correlation with the dependent variables. However, the seismic zone in this study did not meet the linear regression assumptions. This study developed 8 models to estimate abutment volumes. The R2 values of these models are 0.983 – 0.997. These showed that the models are properly made to be used to estimate abutment volumes with a PCIGirder superstructure.


BACKGROUND
The accuracy of initial cost estimation is necessary to reach success in project budgeting. This depends on the available information and data related to the project (Oh, et al., 2013). The initial cost estimation often not accurate because of the incompleteness of the information and data. The most frequent discrepancy occurs in works volume. Therefore, more accurate initial cost estimation can be done by increasing the accuracy in calculation of works volume needed for bridge construction. However, initial cost estimation usually is done based on data from previous projects. The initial cost estimation will become more accurate if it was adjusted to the new bridge characteristics and type. Without that, bridge estimation will become less accurate. Moreover, accurate initial cost estimation was difficult due to limited information on a new project (Fragkakis, et al., 2015). Variable that often used as determinant/independent variable for initial cost estimation are dimensions (such as span, width, and height), bridge type, and bridge materials (such as concrete, steel, timber, composite). Research that has included bridge location as a determinant variable for initial bridge cost estimation has not been carried out much.
SNI 2833:2016 is Indonesian's newest standard about Bridge Design Specification for Earthquake Load. In this standard, the seismic zone is divided into four categories consist of zone 1; zone 2; zone 3; and zone 4. The seismic zone is determined based on soil surface acceleration at 1 second period (SD1). The different locations will have different accelerations based on geological conditions and Indonesian seismic records. Hence, different locations will have a different seismic zone and will result in different seismic load analysis. This difference can lead to variation in the volume needed for bridge construction. Therefore, initial cost estimation using the seismic zone as a predictor variable becomes the main study in this research.
Several studies about cost estimation for construction have been carried out. Early cost estimating models for roads construction project was developed using multiple linear regression by Mahamid (2011). The initial cost model for socket foundation, bor pile foundation, and footplate foundation using linear regression have been conducted by Fragkakis, et al. (2011). A study about a model to an approximate cost estimate for a railway bridge project in the planning phase was done by Kim (2011) using CBR (Case Based Reasoning) method. A study about abutment, pier, and foundation cost estimation model was carried out by Oh, et al. (2013) based on standard quantity. The preliminary engineering cost estimation model for bridge projects was developed by Hollar, et al. (2013) based on preliminary cost estimation of completed projects using linear regression. A study to determine the best estimating techniques for building construction cost was conducted by Kim, et al. (2013). An estimation model for culverts material quantities has been carried out by Fragkakis, et al. (2015) using linear regression. A parametric approach for a better pavement cost estimate by enhancing the earlier cost estimation approaches was conducted by Swei, et al. (2017). An early bill-of-quantities (BoQ) estimation of concrete road bridges was developed by Dimitriou, et al. (2018) using feed-forward artificial neural networks (FFANNs). A study that used project location as a determinant factor for cost estimate was carried out by Kim (2011), however, through the calculation of attribute weight using Generic Algorithm, project location was not significant or had very little impact to the cost estimate in CBR method used thus it was removed. Some studies involved seismic zone as a cost estimate predictor, unfortunately, the data did not provide adequate data samples since most of the data had similar seismic zone thus it was excluded (Fragkakis, et al., 2011;Fragkakis, et al., 2015). All of those studies were done using data from the previous project. A similar study about the bridge cost estimation model based on engineering design results in the design stage has been conducted by Alhusni, et al. (2019).
In his study (Alhusni, et al., 2019) bridge cost estimation model was developed to calculate the abutment and well foundation volume needed for construction based on volume from engineering design. A regression analysis was used in his study. The predictor variables used are bridge span and abutment height for the model. However, his study was conducted based on an outdated standard (SNI 2833(SNI :2008 while the newest standard is SNI 2833:2016. Not only that, but the case study in his research is in one location only so the use of his estimation model is limited only to this location or other possible location with similar characteristics. Therefore, this study used the seismic zone as a predictor variable to represent the various locations of the bridge project. Moreover, this study was conducted based on SNI 2833:2016 regarding the newest standard. The bridge load analysis was calculated based on SNI 1725:2016 (Indonesian standard about bridge loading). The reinforced concrete structure analysis was conducted based on RSNI-T-2004 (Indonesian standard about concrete design for bridge construction). The resistance factor used in this study refers to AASHTO LRFD Bridge Design Specification 2012, which in accordance with SNI 1725:2016.
This study aims to create a model used to calculate the quantity needed for abutment construction in various locations. The model is not only limited to several case study locations but it can be used for various locations in Indonesia with similar characteristics as the case study and abutment design. The initial cost estimate for abutment can be done properly by applying a proper material unit price to the estimated volume. This can provide a quick and flexible cost estimate. The model was developed with variations of the bridge span, abutment height, and seismic zone as predictor variables. Multiple regression analysis was used for developing models. The models are simple and only require minimum information in the early stage of the bridge project thus in can be used in the early stage of the project.
Another contribution this study can offer is descriptions about the influence of these variations toward abutment volumes. At last, this study suggests a point of concern for others to develop a better estimation model for bridge construction in the early stage of a bridge project.

METHODS
This study consist of two steps. First (i), a database for statistic analysis was developed. The database consists of the total quantity of concrete and reinforcing steel needed for a complete bridge abutment construction (with a total of two abutments) from each design variation (bridge span, abutment height, and seismic zone). These quantities were calculated based on each design result. There are a total of 60 design. In this study, the database was displayed in graphics. Through these graphics, the direction and the correlation between variables can be known. The data plot was done with an independent variable as X (axis) and a dependent variable as Y (ordinate). Second (ii), statistic analysis was conducted to find out the correlation between variables, linear regression assumption, regression linear analysis, and goodness of fit. Statistic analysis in this study used SPSS software.

Study Case and Limitations
Several cases in this study were determined to fulfill the structure analysis requirement. Concrete (fc = 25 MPa) and reinforcing steel (fy = 390 MPa) was determined. Soil parameter was assumed to be non-cohesive (c = 0 kPa) with weight volume, λ = 18 kN/m 3 and internal friction angle, = 35°. The soil condition below the foundation was assumed to be hard soil. The seismic zone considered several locations in Indonesia. The location details can be seen in Table 1. The elastomer bearing pad was designed based on product specifications from PT. Basis Pancakarya (2019). These cases also specify the limitations of this study. The detailed limitations such as bridge type and dimensions are explained in sections 2.2 and 2.3.

Superstructure Dimensions
The superstructure design conducted in an earlier study is only to determine the bearing reaction and was not conducted specifically (Alhusni, et al., 2019). The same way was applied in this study. However, I-Girder used in this study was detailed regarding the bridge span. The superstructure was designed based on the product specification of precast post-tension concrete PCI-Girder that was produced by PT. Wijaya Karya (WIKA BETON) (2019) in Indonesia. The superstructure dimensions complied with the A-class bridge superstructure based on Direktorat Jendral Bina Marga (department of highway in Indonesia). The superstructure has a 7 m width roadway and 1 m width sidewalk at both sides, so the total width is 9 m. The typical superstructure cross-section in this study showed in Figure 1. Breastwall width was determined based on bearing placement minimum length. Bearing placement length is designed to be able to accommodate elastomer length and provide sufficient space for elastomer to develop their deformation. The breast wall eccentricity towards the center base of footing is allowed not more than 0.20 m.
The footing has 0.60 m height at the free end. At the fixed end, footing height was determined based on abutment height variation (4 m; 6 m; and 8 m) respectively i.e. 1.20 m; 1.60 m; and 2.00 m. The footing length was determined based on the pile reaction so that any negative reaction (upward) did not occur on the bored pile. The amount of pile used is determined based on the abutment height variation (4 m; 6 m; and 8 m) respectively i.e. 2 x 5 pile; 3 x 5 pile; and 4 x 5 pile. Bored pile analysis was conducted only to get the reaction on each pile.
Wingwalls height equal to the overall height of abutment. Wingwalls have 0.60 m width. The length of the wing walls taken the length of back footing with an additional 0.80 m length. Corbel dimensions were the same for all variation with 0.45 width; 0.50 m height at the free end; and 0.95 m height at the fixed end. The abutment analysis in this study was done by calculating the load working on the abutment based on the dimension determined before. The loads from the superstructure are calculated as static loads and transferred to abutment through bearing pads. The loads working directly on the substructure was considered as static loads. Then, the abutment cross-section capacity on each part was calculated based on the combined load according to SNI 1725:2016. Satisfied abutment design result reached when all parts of the abutment cross-section have enough capacity to support all of the combined load.
The single-mode static earthquake analysis was used in this study. It was chosen because the bridge only has one span and the superstructure is considered to be a simple beam while the substructure was considered as a cantilever wall with the support on the bottom of the footing. This modeling has the system of SDOF (single degree of freedom). The fundamental period of each superstructure and substructure is calculated and put into the design response spectrum to get the seismic acceleration coefficient (Csm). The seismic load is calculated by multiplying the structure self-weight with Csm. The seismic load is applied in the center of gravity on each superstructure and substructure separately as a static horizontal load.

Estimation Modeling
The estimation model was developed using multiple linear regression analysis. Therefore, dependent and independent variables are determined. Dependent variables are determined based on the variables that we seek the value, while independent variables are determined based on the variables that can predict the value of the dependent variables. The dependent variables consist of concrete volume (Vc) and reinforcing steel weight (Vs), while independent variables consist of bridge span (L), abutment height (H), and the seismic zone (Alhusni, et al., 2019). The illustration of the independent variable is shown in Figure 3. The seismic zone has ordinal/categorical data types. While bridge span and abutment height have ratio/numerics data types. Linear regression has underlying assumptions. Several linear regression assumptions were considered in this study i.e. linearity, normality, multicollinearity, and homoscedasticity. Any breach of these assumptions can lead the regression model to be inefficient. However, this does not mean the model can not be used at all, although it will reduce the accuracy of the model (Williams, et al., 2013). Several ways can be done to make the data met these assumptions i.e. data transformation, adding more data, separate the analysis, etc. The multiple linear regression equation is shown in Equation (1).
In Equation (1), Y, Xi, and βi respectively refer to the dependent variable, independent variable, and regression coefficient, while β0 is constant.

RESULTS
The correlation between bridge span (L) and concrete volume (Vc) for each seismic zone (1, 2, 3, and 4) is shown in Figure 4; Figure 5; Figure 6; and Figure 7, respectively. There were three curves in each graph. Each curve represents an abutment height (H). All these graphs showed a positive and linear correlation. This happens because the greater the bridge span then the I-Girder being used is higher, causing a higher bearing reaction at the support and higher dimension of the bearing pad, so the bearing also becomes wider. As a result, breast wall width and back wall height were increasing. All these graphs showed a positive and linear correlation between abutment height (H) and concrete volume (Vc) too. This can be seen from the difference of Vc values between each H. However, the volume difference does not indicate any extreme change.  The correlation between bridge span (L) and reinforcing steel weight (Vs) for each seismic zone (1, 2, 3, and 4) is shown in Figure 8; Figure 9; Figure 10; and Figure 11, respectively. All these graphs showed a positive and linear correlation. The higher the bridge span is led to an increasing abutment bearing load and also led to higher cross-section capacity needed on several abutment parts. As a result, the reinforcing steel volume is increasing. All these curves show a positive and non-linear correlation between abutment height (H) and reinforcing steel weight (Vs) too. They showed that the difference is displaying an extreme change. The change becomes higher as the seismic zone increase. The increase of H led to the rise of moments works on the footing. The footing length also increases to withstand abutment stability. The  The correlation between seismic zone and concrete volume (VC) is shown in Figure 12; Figure 13; and Figure 14, respectively. There were 5 curves in each graph. Each curve represents each bridge span (L). All these graphs showed a positive correlation and it tends to be linear. The increase of the seismic zone is followed by the increase of seismic acceleration, horizontal load, and bending moment in the bottom support, footing length, and concrete volume. The concrete volume change becomes higher as the abutment height increase. The correlation between seismic zone and reinforcing steel weight (VS) is shown in Figure 15; Figure 16; and Figure 17, respectively. All these curves showed a positive non-linear correlation. An increase of the seismic zone caused a higher seismic acceleration and led to higher seismic forces on the abutment. The non-linear correlation is caused by the non-linearity increase of the seismic acceleration, as shown in Table 1. The reinforcing steel weight change becomes higher as the abutment height increase.

DISCUSSION
At the discussion stage of this research, statistical analysis was conducted. The seismic zone, as a dependent variable, did not meet several linear regression assumptions. Therefore, statistic analysis was done separately for each seismic zone.

Linearity Test
The linearity test was done graphically based on the data from the design result. The correlation between L with VC, also L with VS showed a linear correlation. The correlation between H and VC showed a linear correlation too. While the correlation between H and VS is non-linear. Therefore, to get a better (and more linear) correlation, transformation data was conducted, so H data is transformed into H 2 .

Normality Test
The normality test was conducted toward residuals from multiple linear regression, although for multiple linear regression it was not required (Williams, et al., 2013). However, the small samples in this study become the main reason for this test to be carried out. The analysis used the Kolmogorov-Smirnov normality test, with the result is shown in Table 2. The result showed that all residuals are normally distributed with asymptotic significance values greater than 0.05. Therefore, the normality assumption for linear regression is accurate.

Multicollinearity Test
The multicollinearity test was aimed to check whether there is any correlation between independent variables. In a good regression model, there should not be found any correlation between independent variables, although for prediction purpose this problem is not a significant obstacle, however, a perfect correlation of two or more predictor variable can lead to the fail of linear regression analysis (Williams, et al., 2013). Since the predictor variable values in this study are determined, the obtained result of Tolerance and VIF (variance inflation factor) gives a value of 1.00. Therefore, it can be concluded that there is not any multicollinearity problem in the data.

Homoscedasticity Test
The homoscedasticity test was aimed to check whether there is any difference in variance between residuals and predictor variables. In a good regression model, there should not be found any violation of homoscedasticity which can be called heteroscedasticity (Williams, et al., 2013). The analysis was done using a heteroscedasticity test with the Glejser test. The analysis result was displayed in Table 3. The result showed that significance for each dependent variable is greater than 0.05. It can be concluded that there is not any heteroscedasticity problem.

Correlation Analysis
The multiple correlations were conducted to know how strong the correlation between the dependent variable and the independent variable. The result was displayed in Table 4 and Table 5. A Coefficient correlation between 0.600-0.799 belongs to a strong correlation while the coefficient correlation between 0.800-1.000 belongs to a very strong correlation (Sugiyono, 2019). Partial correlation analysis was conducted between the seismic zone and abutment volumes (VC and VS) with L and H as constant variables. The result was displayed in Table 6.  Multiple linear regression analysis resulted in several models. Concrete volume (VC) estimation models for each seismic zone (1, 2, 3, and 4) showed in Equation (2), Equation (3), Equation (4), Equation (5) Reinforcing steel weight (VS) estimation models for each seismic zone (1, 2, 3, and 4) showed in Equation (6), Equation (7), Equation (8) The goodness of fit test was conducted to find out how well the regression model performance was. Although, if all linear regression assumptions were fulfilled, then regression models should be good. The goodness of fit test was done by checking R 2 value. The test result was displayed in Table 7. The result showed that all models have R 2 greater than 0.98. This showed that the models were properly made to be used to estimate abutment volumes.

CONCLUSION
This study offers 4 concrete volume estimation models and 4 reinforcing steel weight estimation models. The statistic analysis results showed a very strong correlation between bridge span and abutment height toward abutment volume. The regression models are developed with all linear regression assumptions. The goodness of fit test for all models resulted in R 2 more than 0.98. This showed that the models are properly made to be used to estimate abutment volume. Using volumes estimated from these models, by applying material unit price that was determined by the user, the initial cost estimate can be provided quickly and flexible.