1. Introduction
Pipelines are widely used in infrastructures to transport water, wastewater, and energy products. The USA uses 2.2 million miles of underground pipes to deliver drinking water. However, the recently released report by ASCE [
1] classifies the USA drinking water infrastructure as a poor category “-C”, as the pipelines are aged. Financing shortages result in an estimated water leakage of 6 billion gallons per day of drinking water. The estimated deteriorated pipelines length was 12,000 miles in 2019 [
1]. Pipelines and culverts are considered the most economical options compared with highway bridges, where the utilities of water, wastewater, or energy products intersect with roadways and barriers of high soil depths. However, limited studies were conducted to investigate the performance of pipelines and culverts under deep soil burial since it is difficult to measure the response of such structures experimentally, and it costs a significant amount of money to conduct the experimental setup. On the other hand, the successful use of validated finite element analysis in recent years has significantly helped researchers and designers to measure the structural response of such infrastructural utilities.
The interaction between the pipeline structure and the compacted soil around them is critical in their structural performance. The interface layer between the pipeline structure and the surrounding soil requires a unique estimation. Analyzing such a soil−structure interaction is not easy to estimate, as no closed-form solution can predict this interaction accurately; however, this interaction can be effectively analyzed using the finite element analysis (FEA) [
2,
3,
4,
5,
6]. In addition, the soil−structure interaction usually is not considered in pipeline and box culverts designs, where the applied pressure above the pipeline and the box culvert is assumed to be equivalent to the geostatic load, which is the earth prism weight measured above the pipeline or the box culvert (Pimentel et al., 2009 [
7]). As the soil−structure interaction is challenging to experimentally estimate, several studies have efficiently exploited numerical tools such as finite element modeling and artificial intelligence to predict the effect of the soil−structure interaction for various structural types [
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19]. Therefore, the soil−structural interaction should be included in the pipeline and culvert design in order to estimate the structural response of such infrastructures accurately. Excluding this interaction may result in the erroneous structural design of these elements.
Various studies have investigated pipelines’ stress redistribution and performance under a deep soil fill depth. For example, Marston and Anderson (1913) [
20] were the pioneer researchers who studied loading distribution on buried pipes, whereas Marston (1930) [
21] found that installation conditions and pipe properties influence the loading distribution. Likewise, Spangler (1950 [
22], 1968 [
23]) revealed that vertical pressure on the steel buried pipes developed by the surrounding compacted soil layers is coupled to the relative settlement between the soil barrier and the original soil. Similarly, Abuhajar et al. (2015) [
24] indicated that soil arching is significantly affected by the soil fill depth, culvert thickness, elastic modulus of soil, and poison ratio.
Bashir (2000) [
25] investigated several steel pipelines with diameter-to-thickness ratios ranging from 50 to 150, subject to soil fill depths ranging from 0.6 m to 3.7 m. The study detected that regardless of the pipe diameter-to-thickness ratio, the live load of vehicles was insignificant for soil depths more than 2.5 m. Similarly, Orton et al. (2015) [
26] investigated 10 reinforced concrete box culverts, and the soil fill depth ranged from 0.76 to 4.1 m. The study found that the live load of vehicles was not significant when the soil fill depth increased. In addition, the experimental results indicate that the deflection of culverts subjected to soil fill of less than 2.4 m is overestimated by the American Association of State Highway and Transportation Officials (AASHTO) load resistance design factors (LRFD) bridge design specifications (AASHTO 2012 [
27]).
The experimental investigation of the structural performance of pipelines and culverts under a high soil fill depth is uneconomical and difficult to conduct. Finite element modeling is an effective alternative tool. For instance, Shatnawi et al. (2017) [
28] effectively used the finite element analysis (CANDE software) to explore the behavior of various box culvert geometries under a high soil fill depth. This paper used CANDE-2019 [
29] as the FEA tool to perform the parametric study.
In this study, FEA was used to investigate the structural performance of reinforced concrete pipelines under various soil fill depths (9.1, 12.2, 15.2, and 18.3 m) with different pipe diameters (610, 915, 1220, and 1524 mm). A soil depth of 18 m may be reached in deep embankment soil; an example of deep-buried culverts is the Peter Smith Brook Culvert with a 23.4 m deep embankment soil, which is a part of a highway upgrade near Longs Creek, New Brunswick, Canada [
30]. This study provides a guideline for engineers to estimate the most efficient pipeline geometry for various soil filling depths. In addition, this research also explored the optimum diameter-to-thickness ratio for various pipeline conditions. The shear reinforcement in this study was excluded, as Yee (2003) [
31] found that the provided shear reinforcement in reinforced concrete culverts did not improve the load capacity of the culverts, but the culvert section became over-reinforced. Shatnawi et al., 2017 [
28], previously published work related to the investigated topic, and thus this study aimed to compare the obtained results with the previously gained ones.
2. Methodology
Using finite element analysis (FEA), this study investigated reinforced concrete (RC) buried pipelines under various soil depths using finite element analysis (FEA). Culvert Analysis and Design (CANDE-2019 software [
29]) was used to conduct the nonlinear FEA. The description of CANDE-2019 [
29] is discussed in
Section 3.
The following points represent the most critical features of the executed FEA modeling. Various pipe diameters, as shown in
Table 1, were investigated, where Pipe 24, Pipe 36, Pipe 48, and Pipe 60 were 610, 915, 1220, and 1524 mm, respectively. The geometric properties of the RC pipelines are illustrated in
Figure 1.
Varying soil fill depths (h) were investigated: 9.1, 12.2, 15.2, and 18.3 m.
Flexural steel reinforcement (FSR) was provided in the RC pipelines. However, no shear reinforcement was provided.
Duncan et al. (1980 [
32]) and Selig (1988 [
33])’s hyperbolic stress−strain parameters were used for the nonlinear FEA soil properties.
The parametric FEA study investigated various variables (e.g., soil fill depth, pipeline diameter, and pipeline thickness).
Fifty-eight FEA runs were executed to calculate the FSR for each pipeline model, as indicated in
Table 2. In each FEA model run, the following process was carried out:
The soil fill depth was defined considering the values in
Table 2.
The diameter of the RC pipeline was selected from the dimensions specified in
Table 1.
The thickness of the RC pipeline was reduced in each FEA model until the ratio of applied-to-capacity shear stress (τa/τc) was equal to or less than the unity to exclude the shear reinforcement and reduce the cost of constructing the pipelines. In addition, the thickness reduction process was stopped once the maximum crack width (wmax) reached 0.25 mm, which allowed the pipeline to have small crack width at the ultimate loading state.
The FEA results were summarized and analyzed to investigate the effect of soil depth on the diameter and thickness of the reinforced concrete pipeline.
The total required FSR and the maximum deflection (∆max) of each pipe were recorded.
As discussed in Step 3 in the procedure mentioned above, the shear reinforcement was omitted. Furthermore, it was excluded because the ratio of applied-to-capacity shear stress was equal to or less than unity. The flowchart summary of the methodology in this study is shown in
Figure 2.
3. FEA Model and Construction Stages
Figure 3 represents the FEA model’s geometry, boundary conditions, and mesh. The soil layers are the in situ soil, bedding, and fill soil. As the pipeline is symmetric about the pipe centerline, one-half of the pipe and soil layers were modeled. The pipeline was simulated using 10 equal-length beam elements connected between 11 nodes. The 2D quadrilateral elements of the modeled soil layers were defined below and above the pipeline up to three times the pipeline radius. The load factor of 1.42 was defined according to AASHTO 2020 [
34]. Therefore, the load pressure equals the factor 1.42 multiplied by the soil fill unit weight and soil fill depth. The live load was excluded from the FEA as all of the investigated cases in this study were subjected to a soil depth more than the 2.44 m-threshold proposed by AASHTO 2020 [
34], as the effect of live load on culverts diminishes for soil depths of more than 2.44 m. The bottom layer of the in situ soil was restrained in the horizontal and vertical directions.
In contrast, the left and right sides of the model were restrained in the horizontal direction only because the model was symmetric at the pipeline’s centerline. The FEA model considered the soil−structure interaction, as shown in
Figure 3. It is worth mentioning that an extensive investigation of the literature was conducted. However, the literature lacked experimental results related to this study. On the other hand, the used model was reliable and was validated using the project developed under the National Cooperative Highway Research Project NCHRP 15–28 [
35]. In this study, the Level 2 option (automatic FEA) automatically created the nodes and the optimum mesh size of the FEA model using simple input parameters; this option made the modeling process easy to implement and reduced the required time to generate debug for the mesh of the FEA models. The automatic mesh selected coarse mesh size in the soil layers and fine mesh size in the pipeline geometry, as we were more concerned about the response of the pipeline.
It is imperative to simulate the construction stages of the reinforced concrete pipelines in order to model the structural responses of the pipelines accurately. Therefore, the pipeline, bedding, and in situ soil layer were modeled in the first stage, while the soil fill was added gradually in the second, third, fourth, and fourth stages, respectively. On the other hand, to increase the analysis accuracy and avoid solution divergence, the loading pressure was divided into several equal increments applied to the model in stages 6 to 20, as shown in
Figure 4.
3.1. FEA Soil Properties
We utilized three types of soil layers in the FEA model. The Duncan/Selig parameters were proposed by Duncan et al. (1980) [
32] and were modified by Selig (1988) [
33], where SW95 and SW90 gravely sand with 95% compaction was used to define the FEA modeling. The SW95 and SW90 soil were used in the fill soil and bedding. The library of CANDE-2019 contains the hyperbolic stress−strain parameters of SW95 and SW90, as summarized in
Table 3 [
36]. The in situ soil was considered isotropic, where the soil’s young’s modulus was 34.5 MPa, Poisson’s ratio was 0.4, and soil density was 18.9 kg/m
3. CANDE-2019 offers various culvert installations, including barrier and trench installations. In general, the installation type refers to the location of the culvert relative to the ground level. In the embankment installation, the bottom face of the culvert coincides with the original ground level, where soil excavation is not needed. While trench installation refers to the case when the bottom face of the culvert is below the original soil level, in this case, soil excavation is needed. In this study, embankment installation was considered in the FEA modeling.
3.2. FEA Steel and Concrete Properties
Normal strength concrete with a compressive stress of 34.5 MPa and unit weight of 23.6 kg/m
3 was utilized, the 448 MPa tensile strength steel reinforcement with a concrete cover of 32 mm was used, and more details of the concrete and steel properties are summarized in
Table 4.
5. Summary and Conclusions
The current practice does not include guidelines for using the most efficient reinforced concrete pipeline geometry under deep soil embankments. To fill this gap and propose a guideline for designing reinforced concrete pipelines, this study investigated the performance of reinforced concrete pipelines of various diameters buried under soil fill depths of 9.1 to 18.3 m. High costs accompany testing or inspecting pipelines. Thus, a tool such as finite element analysis is critical for reducing such costs; CANDE 2019 software was used here as the FEA tool to conduct the parametric study. As a result, 58 FEA runs were executed, whereas the flexural steel reinforcement (FSR) and the maximum pipeline deflection in each FEA run were reported. In addition, the optimum pipeline diameter-to-thickness (D/T) ratio that had the least required FSR and crack width did not exceed 0.25 mm, which was specified for various pipeline diameters and soil fill depths. The Duncan/Selig soil parameters SW90 and SW95 were used to define the soil properties for the in situ bedding and fill layers. The analysis results revealed that the optimum reinforced concrete pipeline diameter-to-thickness (D/T) ratio was 6.0, 4.6, 4.2, and 3.8 for soil fill depths of 9.1, 12.2, 15.2, and 18.3 m, respectively. In addition, the deflection range of the investigated reinforced concrete pipelines was between 0.5 to 13 mm, which indicates that the finite element analysis carefully selected the pipeline thickness, required FSR, and concrete crack width. In contrast, the pipeline did not undergo excessive deformation.
A detailed example was presented to help designers and practitioners select the optimum thickness for various soil depths (2.4 to 20 m) and different pipeline diameters (500, 750, 1000, 1250, and 1500 mm), which ensures the generalization of the proposed equation for a variety of pipeline conditions. The study proposed an equation to select the optimum diameter-to-thickness ratio for various soil fill depths, which will help practitioners select cost-effective pipeline geometry and steel reinforcement at a specific soil fill depth. The optimum pipeline thickness was significantly sensitive to the soil fill depth. In contrast, the optimum reinforced concrete pipeline thickness was substantially increased (almost doubled) when the soil fill depth increased from 2.4 to 20 m. Field data collection of pipelines is required for further research to reach a solid stage in order for more analytical investigations. It is thus recommended to use deep and machine learning algorithms to improve the analysis accuracy and pave the road for researchers to deeply validate the proposed model performance.