Keywords

1 Introduction

Infrastructures such as buried pipeline systems have great importance in daily life. Sewer systems enable people to process the municipal waste, and oil pipelines contribute to transporting petroleum products.

One of the most common materials used for such systems is PVC pipes. The most important reasons are that they are cheaper and non-corrosive, and due to the that fact, they are less susceptible to microbiological growth. Furthermore, their durability is competitive with other materials such as steel.

The analysis and design of such systems require the consideration of soil-structure interaction [1]. When designing buried pipeline systems, estimating parameters such as displacements, internal stresses caused by transported materials, and external stresses caused by the surrounding soil are necessary.

In the literature, many researchers conducted experiments to evaluate the performance of buried pipes, focusing on the load–displacement behavior of pipes [2,3,4,5,6,7]. Additionally, there is limited research about pipe-soil interaction in terms of bearing capacity [6, 8, 9].

One of the most popular techniques for image analysis, called Particle Image Velocimetry (PIV), was used for the analyses of the images captured during the model tests conducted in this study. PIV is a non-invasive velocity measuring procedure that adapts to geotechnical applications [10]. In this study, MATLAB based GeoPIV_RG software [11] was used. The software operates by dividing a reference image into user-defined meshes and calculates displacements between consecutive images regarding the reference image. This way, displacement vector field can be determined. With the GeoPIV_RG algorithm, the formation of the failure surface in the soil can be observed with a map consisting of different colors indicating different displacement surfaces. The obtained results are presented and discussed.

2 Experimental Studies

2.1 Experimental Setup

Physical model tests were carried out in a rigid box that contains backfill of target density with a pipe buried. Pipe location was varied between experiments. In the tests, a model surficial continuous footing was loaded to observe backfill-pipe-foundation interaction.. The model tests were designed to examine the effect of pipe embedment depth. The tests were recorded by employing different types of data recorders which can measure both load acting on the foundation model and the resulting displacements. The steel frame in which the model tests are conducted allows the preparation of a model backfill with dimensions 100 cm × 50 cm × 60 cm. The front and back sides of the frame are made of plexiglass for capturing consecutive images of soil deformations. For this purpose a Nikon D90 camera was used and the images are later analyzed using GeoPIV-RG. In the model tests, a strip foundation model is placed with dimensions of 50 cm × 10 cm × 3 cm on the backfill and loaded using a loading piston. Foundation loads and the resulting displacements were measured using a load cell and LVDT transducers, respectively. Furthermore, pipe strains were measured using TML brand strain gauges. All measurements are and recorded via National Instruments (NI) modules equipped with NI developed LabView software. Three different load cells having different capacities of 500 kg, 1 tonne, and 2 tonnes were used throughout the experiments. LVDT stroke length is 150 mm, and the strain gauges are GFLA–6–50–4L type. Strain gauges were attached to the PVC pipe with a unique cyanoacrylate adhesive. Experimental setup is shown in Fig. 1.

Fig. 1
A photo of an experimental setup. The setup includes a pipe, loading system, strip footing, test box, camera, and loading frame.

Overview of the test setup

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The rate of the loading piston was kept constant at 10 mm/min. The images were captured with a rate of one photo for every 12 s. This corresponds to 2 mm of piston displacement per image making it easier to translate pixel-based displacements to actual displacements. After the completion of the tests, captured images were analyzed using GeoPIV_RG using the initial image as the reference which is meshed with 50px × 50px-sized patches (Fig. 2). The results were expressed in millimeters. As a result, the stress–displacement curves were presented are plotted with 2 mm intervals up to 10 mm displacement, which corresponds to the 10% of the foundation width, due to adopted failure criterion [12].

Fig. 2
A photo of the P I V analysis space of the experimental setup along with a mesh illustration illustrated from the test box.

PIV analysis area and mesh

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2.2 Soil Properties

For this research, sand obtained from Çerkezköy region of İstanbul was used. Index properties of Çerkezköy Sand are summarized in Table 1 and (Fig. 3).

Table 1 Index properties of Çerkezköy sand
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Fig. 3
A line graph of percent finer in percentage versus sieve opening size in millimeters. The line approximately decreases from (7, 100) to (0.1, 0).

Grain size distribution of Çerkezköy sand

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2.3 Experimental Method

In the scope of this experimental study, 6 model tests were conducted, in which them of them were with the pipe being buried at an embedment ratio of H/D = 1 and the other three were without the buried pipe. Each case was examined for different relative densities (Dr) of 35, 50 and 65%. The configuration of the tests are illustrated in Fig. 4 where H is the vertical distance between the bottom of the foundation and the crest of the pipe and D is the pipe diameter which is constant as 75 mm. The required relative density of the sand soil was established by calculating the total soil mass necessary for the whole volume of the frame, then placing and compacting it in ten layers, each layer corresponding to 1/10 of the volume of the frame hence 1/10 of the required soil mass. Details of the model tests conducted are given in Table 2.

Fig. 4
An illustration depicts the embedment of the pipe in the experimental setup. Q, H, B, and D are labeled.

Pipe embedment

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Table 2 Test program
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3 Results and Discussion

This study aims to examine the effect of the buried pipe and different sand relative densities on the bearing capacity of neighboring surficial strip foundations. Figure 5 shows the experimental distribution of vectorial displacements and resultant displacement contours obtained from GeoPIV_RG analyses for 10 mm foundation settlement, which corresponds to 10% of the foundation width that is considered to correspond to failure in this study. It is clear from the analysis results that pipe affects the wedge size and stress distribution due to creating a non-continuous soil zone. Also, resultant contours indicate that displacement zones created just below the pipes and the lowest relative density Cerkezkoy sand have the largest displacement zone just below the pipe, as expected.

Fig. 5
6 figures depict the stress-displacement behavior. All 6 include a vectorial displacement and a resultant contour. A, C, and E depict without pipe. B, D, and F depict with the pipe.

Vectorial displacements and resultant displacement contours from GeoPIV_RG. a Dr: 35% without pipe, b Dr: 35% H/D: 1, c Dr: 50% without pipe, d Dr: 50% H/D: 1, e Dr: 65% without pipe, f Dr: 65% H/D: 1

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Figure shows the stress-displacement behavior at 10 mm displacement, which corresponds to 10% of the foundation width of the Çerkezköy Sand with and without the presence of the pipe. As expected, for the case without pipe, the highest load is carried when the relative density is the highest. For the case with pipe, the loading capacity of the soil at 35 and 65% relative densities drops around 70%, whereas 50% relative density drops around 90% of the case without pipe load values (Fig. 6).

Fig. 6
2 line graphs. A, depicts ultimate base pressure when without pipe. 3 lines follow increasing trends starting from the origin. B, depicts base pressure for H over D = 1. 3 lines follow increasing trends starting from the origin.

Stress- displacement behavior of Çerkezköy sand with and without pipe

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4 Conclusions

In this study, six physical model tests and GeoPIV_RG analyses were conducted to observe the effects of the presence of the pipe and relative density on the deformation of the soil-pipe-foundation system under loading. Pressures and displacement acting on the model foundation were measured, and deformation of the soil strata was visualized by using GeoPIV_RG analyses. GeoPIV_RG analysis accurately envisioned the deformation zones of different sand relative densities. It is understood from the correct separation of the sizes and geometries of the displacement fields obtained from three different analysis results from each other. Furthermore, PIV_analyses were also accurate in visualizing the deformation zones with pipe since it can be seen that from the results, pipe leads to separate deformation fields in sands of different relative densities as expected.

Further studies could be carried out to investigate the effect of geosynthetic on deformation fields and bearing capacity of soil-pipe-foundation system under loading by using GeoPIV_RG analyses. Moreover, further research could examine different soil types using strain contours which can be provided by GeoPIV_RG analyses.