Experimental and analytical investigation on friction resistance force between buried coated pressurized steel pipes and soil

Abstract

This paper presents an analytical approach for estimating frictional resistance to pipe movement at soil and external pipe surface of buried coated pressurized steel pipes relative to the internal thrust force. The proposed analytical method was developed based on 36 experiments, which involved three coating types (cement mortar (CM), polyurethane type-I (PT-I), prefabricated plastic tape (PPT)) on pipes’ surfaces, three different soils (pea-gravel (PG), sand (S), silty-clay (SC)), and four simulated over burden depths above the pipe’s crown. Investigation showed frictional resistance decreased with increasing over burden depth above the pipe’s crown. The degree of frictional resistance at the pipe-soil interface was found to be in the order of PG > SC > S for all coating variations and overburden depths. CM coated pipe buried in all three types of soil produced significantly higher frictional resistance as compared to other coating types. Based on experimental data, the developed analytical introduced a dimensionless factor “Z”, which included effects of types of coatings, soil, and overburden depths for simplified rapid calculation. Analysis showed that the method provided a better prediction of frictional resistance forces, in comparison to previous analytical methods, which were barely close in predicting friction resistance for different coating variations, soil types, and overburden depths. Friction resistance force values reported herein could be considered conservative.

Graphical abstract

Keywords

friction resistance force / thrust force / coated pressurized steel pipe / soil type / overburden depth

1 Introduction

Changes in flow direction, pipe diameter, inline valves, pipeline terminations, thermal expansion/contraction, or short and long-term Poisson’s ratio of the pipe material often result in unbalanced thrust forces at the location of the bends, elbows, and branch connections in a pressurized pipeline network [1]. Such thrust forces can reduce the stability of the pipe network. A commonly used approach to restrain such thrust is installation of concrete reaction blocks, named thrust blocks or collars [1,2], which, through the support from the native soil, counteract the movement of pipes [3]. Frequent occurrence of unbalanced thrust force can destabilize the pipeline support system, resulting in shifting of the pipelines or fittings, and eventually resulting in leaks at those junctions. To prevent leaks in the pipe joint locations, restricting such movement is desirable as gradual leaking of water alters the phase relationship of the soil base, which supports the thrust block and the pipe network. Altered phase relation in the supporting soil not only eliminates its strength to support the thrust block, but also the soil takes over the role of thrust block. This reversal of role makes the thrust block an extra unplanned weight on the pipeline, not included in the standard design procedure, and can cause sudden failure of the pipe, which can potentially lead to a network-wide collapse.

Moreover, additional excavation and materials needed for installation of thrust blocks require time, resources, and caution. Also, the required thrust block can become excessive in dimensions. The poured concrete must not fill the hydrants’ weep holes, fitting joints, or valves. Placement of thrust blocks is also becoming increasingly difficult in case of complex situations like dead ends, possible future excavation, etc. [1]. Hence, extra attention is always required in successful casting of concrete thrust blocks. Moreover, increasing congestion in utility rights-of-way and the desire to minimize excavations has increased the deployment of restrained joint pipes and fittings.

To address such difficulties, thrust restraint system of buried pipes based on skin friction is becoming popular as a way to replace the role provided by the thrust block [4]. Thrust restraint pipeline networks are capable of providing resistance against thrust force by securing contribution from a large soil and pipe interface area. Placement of thrust restraint pipe networks also opens up the possibility of future installation near the existing pipeline, since the support system of existing pipeline will not be using a thrust block concentrating force transfer in a smaller area. Construction of parallel pipelines can also benefit from installation of thrust resistant pipe networks.

Thrust forces inside the restraint pipeline system are resisted by the pipe-surface interaction with the surrounding soil in both linear and transverse directions [5]. Therefore, design of a restrained joint pipe system requires considering pipe coatings, soil types (both surrounding and backfill soil characteristics), and overburden depth, along with pipe diameter and operating pressure. The trench backfill should be of proper material and compacted to the specified standard [6,7]. Inside a soil envelope, buried pipes are subjected to stress originating from different sources, such as geostatic conditions, surface live loads, internal fluid loads, hydrostatic pressure, and loads from ground movements. Surrounding soil characteristics govern proportion of loads acting on a buried pipe and are important design parameters for calculating the friction force developed between the soil and pipe-surface interface.

A series of tests to study the interface friction between soil and construction materials was performed by Potyondy [8]. That work calculated the skin friction coefficients between various types of soils and three common construction materials based on modified constant values of cohesion and internal friction. A study conducted by Webb et al. [9] showed that placement and compaction of the backfill soils had paramount effect on polymer pipes. Investigation on the lateral response of pipelines performed by researchers [10] showed that lateral forces due to ground movements can cause structural distress in sand (S) and clay. Full scale studies performed on steel pipes buried in S conducted by other researchers [11,12], showed that axial movement of the pipe changes stresses in surrounding soil and better interactive friction force between pipe surface and soil can contribute to counteracting the thrust forces originating inside the pipe. Studies by Rowe and Davis [13,14] confirmed that the anchor force coefficient for S and clay provided reasonable estimates of lateral force per unit length for the soil types. Pipe performance in soil is largely influenced by the properties of the backfill material and surrounding soil. Guidelines given by Selig [15] are found to be a useful starting point for estimating backfill soil cohesion, friction angle, modulus, and Poisson’s ratio.

Different American Water Works Association design manuals provide guidelines for designing different types of restraint pipe joint systems suitable for steel pipes [16], polyvinyl chloride (PVC) pipes [17], ductile iron (DI) pipes [18], and concrete pipes [19]. However, there are no common design practices that take into account the soil and materials of the pipe surfaces in counteracting the thrust force. This lack of common procedure leads the design practice of thrust restraint pipeline systems to vary significantly for the same soil conditions but different pipe materials [6,20]. Such unavailability of common design practice is mainly due to difficulties and substantial investment associated with conducting full-scale material focused soil-pipe interaction investigation programs. Such investigation could establish these relations (friction between soil and pipe materials’ surface) and develop design approaches suitable for restraint pipeline system.

In this study, a full-scale experimental investigation to estimating friction resistance forces was performed for steel pipes with three different external coating systems, i.e., cement mortar (CM) [21], polyurethane type-I (PT-I) [22], and prefabricated plastic tape (PPT) [23] under controlled laboratory conditions for three different soil types and four different overburden depths. The initial phase of the study involved evaluation of the behavior of the pipes under different conditions in terms of friction resistance force, rigid body displacement (RBD), and pressure in surrounding soil measured through earth pressure cells (EPCs) using full-scale experimental setups. Based on the experimental results, an analytical approach to predict the friction resistance force acting on steel pipes under different soil conditions and overburden depths was proposed.

The proposed analytical approach introduced a dimensionless factor “Z”, termed as pipe resistance coefficient in this study. The expression for Z was developed in terms of soil and coating type based on the experimental results. Hence, the parameter Z included the effect of pipe coating, soil characteristics and arching effect on pipe-soil interaction. Consequently, it provided the basis for a rapid calculation method for estimating friction resistance force. In addition, the resistance forces were also predicted using Coulomb’s equation, with modifiers for the cohesion and soil friction angle coefficients proposed by Potyondy [24], and a semi-empirical expression for the internal friction angle of the soil to account for stiffness of the pipe, overburden pressure, and nature of the bedding and backfill material, developed by a previous study [25]. Finally, the friction resistance forces predicted by the three approaches were compared with the experimental outcomes. It was found that the analytical approach based on pipe resistance coefficient Z exhibited excellent agreement with the experimental data as compared to the other two methods used. However, the application of this method is limited since it requires a known expression of Z with respect to soil type, coating variations, and overburden depth. Nevertheless, expressions for Z for different pipe materials under different soil conditions can be evaluated through comprehensive experimental procedures as described in Subsection 2.6, for wide applicability of this approach.

2 Materials and methodology

2.1 Materials and apparatus

In this study, pressurized coated steel pipes buried in different soils under different overburden depths were pulled along the axial direction as a part of a series of controlled laboratory experiments to evaluate the state of interaction between soil and pipe surface coatings. The resulting resistance force could be determined from this interaction. The study included three types of soil, four different overburden depths, and three external surface coating systems (CM, PT-I, and PPT). The soil types included in this test program were silty-clay (SC), S, and pea-gravel (PG), which are classified as low plasticity clay (CL), well graded sand (SW), and well graded gravel (GW), respectively following the Unified Soil Classification System [26]. S and PGs are usually used as backfill materials, while SC may present as native soil during trenchless installation and thus unavoidable. S and PG were obtained from a local vendor, while the SC was dug out from the back field located behind the trenchless technology center (TTC) at Louisiana Tech University. To obtain soil cohesion and friction angle, a direct shear testing machine Model G-128-26-2114/02 manufactured by ELE International LLC, and an unconfined compression strength measurement machine, Model ELE 25-3525/02, were used. Sieve analysis was conducted for development of the gradation curve by using a Tyler RX-29 model sieve shaker, which can accommodate 200 mm diameter full size sieves. AC Delco–Automotive Axle Grease for lubrication of various surfaces, as needed, was obtained from a local store. Polyethylene sheets of 0.80 mm (20 gauge) thickness were used to cover the inside surface of the soil box. Geokon Model 4800 EPCs connected to two SCXI-1308 boards installed on the NI PXI-1052 data acquisition system were used to collect the soil pressure data. Omega PX419-050GV pressure transducer was attached to record the overburden pressure applied on the soil surface inside the soil box, for achieving the required overburden depth. A soil compactor, Model JPC-80WT, was used for compacting the soil inside the soil box. The LabVIEW program data acquisition system recorded the force and displacement data produced by the MTS, Model 661.23E-01, 120kip capacity actuator system. The change in pressure inside soil stratum was obtained by the EPCs, and the overburden pressure was measured by the pressure transducer under the same time stamp.

2.2 Evaluation of soil properties

As the friction force developed on the pipe surface is a function of surrounding soil/backfill material, obtaining the different physical properties of soil such as cohesion, friction angle, bulk and apparent specific gravity, absorption, and grain size distribution is important for identification of the soil characteristics. Bulk and apparent specific gravity and moisture content of S and PG were measured following ASTM C127 [27] and SC were determined as per the ASTM C128 standard [28], and are provided in Tab.1. Grain size distribution of S and PG were determined as per ASTM C136 [29]. It was found that for S, 70% of the particles were retained in the range between 1.18 mm (No. 16) and 600 μm (No. 30) sieves, while for PG the sieve size ranged from 4.76 to 19 mm (No. 67). For SC, particle distribution revealed that 95% of the material was clay and 5% was medium-to-fine silt as per the ASTM D422 [30] standard. Fig.1 shows the particle size distribution of S and SC soil samples.

Direct shear test under consolidated drained condition was performed on remolded S and SC samples to obtain cohesion and friction angle values (also provided in Tab.1) following ASTM D3080 [31] and ASTM D2166 [32] standards. To obtain the dry density and optimum moisture content, a standard Proctor test was conducted on the soil samples (S and SC) following the protocol mentioned in ASTM D698 [33].

2.3 Steel pipe specimens

The external protective lining and coating types included in this test series were CM, PT-I, and PPT. Pipe specimens with these three types of external coating are shown in Fig.2. Each pipe specimen had caps welded on both ends. One end had a shackle system (pull head) made of two identical steel plates welded on the cap, while the other cap end had two valves installed for applying and releasing water pressure during and after the test.

2.4 Soil chamber

The TTC at Louisiana Tech University is the house of a 1.8 m × 3.6 m × 1.5 m (6 ft × 12 ft × 5 ft) steel made soil chamber, which was used for conducting this test series. The soil chamber is comprised of three principal components, actual soil box (ASB), air chamber unit (ACU), and lid, each stacked on top of the other and bolted during the testing. On the opposite short walls of the ASB, there were two 400 mm (16 in) diameter co-linear circular openings lying on the same plane through which pipe samples were inserted and pulled (Fig.3).

The main three components of the soil chamber were bolted using 570 mm long, 19 mm diameter (1.25 thread per mm) bolts, after two special sealing mechanism was placed in between them. Each sealing mechanism had a 2.1 m × 4.2 m (7 ft × 14 ft) and 3 mm (1/8 in) thick rubber sheet with 12 mm (1/2 in) rubber strip glued on the surface of the rubber-metal contact region. Thus, once the sealing mechanism was in place and no leak was found along the edges of the ACU the soil chamber was prepared for testing (Fig.4).

2.5 Range of air pressure on pipes to simulate overburden depths

Four targeted overburden soil depths were simulated by applying air pressures (OBPs) in the ACU (Tab.2) on the surface of soil inside the ASB and above the buried pipe. First, the total volume of soil required to achieve the target depth of cover was calculated based on the geometry, soil density, and embedded length of the pipe buried in the ASB. Next, the volume of soil from the height of the soil prism above the pipe inside the ASB was calculated and deducted from the required total volume. Eventually, the necessary air pressure was calculated to be applied in the ACU on the soil inside the ASB for simulating the corresponding overburden depth.

2.6 Experimental setup

The preparation of the experimental setup started by covering the bottom and the peripheral walls of the ASB by a layer of 0.80 mm (20 gauge) polyethylene sheet with an intension to protect the ASB walls from any corrosion that may cause by this series of testing. Two more layers of same thickness polyethylene sheets were then placed with lubrication (AC Delco–Automotive Axle Grease) applied in between the two layers in order to eliminate the effect of friction between the soil and the ASB wall. Next, a 25 mm × 25 mm rubber seal, which had approximately 12.5 mm groove cut on the middle along the long direction, was pressed fit on the edge of the circular opening of the ASB. The ASB was then filled with layers of 150 mm soil up to the invert of rubber seal that covered the circular openings. Each layer of soil was compacted using a hand-held vibratory plate compactor; during the compaction operation, water as needed based on the Proctor test, ASTM D698 [33], for SC and S was added. As a protective measure to eliminate the friction between pipe surface and the rubber strip on the circular opening, the surface of the rubber seal was lubricated using the same AC Delco lubrication material prior to sliding of the pipe specimen through the circular opening. The pipe specimens were then placed inside the soil chamber and for each test the placing of pipe specimen followed the same protocol. Each pipe specimen was carried using a strap hanging from the fork of a backhoe ensuring no damage during carrying and the pipe end (with the pull head) was placed on the invert of the circular opening located on the west side of the ASB (Fig.5). Later, the 5 t (~4.54 ton) capacity overhead crane was used to lift the test specimens from the inside of the ASB and carefully pulled it (test specimen) forward toward the actuator head (east direction) until it reached the opening on the other side, where the already forwarded actuator head was hooked to the pull head using a 50 mm diameter connection rod. This pin joint, as shown in Fig.6, ensured no moment was transferred to the pipe specimens during the pulling action. The pipe specimen was then pulled inside the soil chamber at a rate of 12 mm/min (0.50 in/min) ensuring no damage on the coating and maintaining same overhang length on both sides.

Afterwards, the ASB was filled up to a depth of 100 mm (4 in) above the crown of the pipe and the EPCs were placed following the plan as shown in Fig.7. In S and SC, the EPCs were laid right on the soil. Although placements of EPCs in S and SC were fairly straightforward, extra precautions were needed for PG. The EPCs in PG were placed inside an encased wooden box filled with dry S and covered with geo-textile (Fig.8) on the top and bottom surface to minimize the probability of recording any localized stress caused by PG and to prevent any damage to the EPCs during testing.

Then, the soil box was filled with layer of soil and compacted to 150 mm thick layer using the hand-held vibratory compactor (see Fig.9) until the ASB was filled up to the top (Fig.10) with soils (SC, S, or PG) and sealed following the procedure mentioned in the Subsection 2.4 (Fig.11).

As proper sealing of the ACU was vital for the success of the test, a low-level air pressure (7 kPa) was applied in the ACU and soap water was sprayed on the seal (see Fig.12) to check for any leakage at the beginning of the experiment. After successful sealing of the ACU, the test pressure was subsequently increased, which then transmitted the desired OBP to the soil inside the ASB. The assembled setup is shown in Fig.13.

3 Discussion on experimental results

The study was conducted in two phases. In the initial phase, behavior of coated steel pipes was investigated for different soil types, coating types and overburden depths in terms of resistance force due to friction and rigid body movement. In addition, stress in soil in the vicinity of the pipe due to the pipe’s movement was also observed through utilization of EPCs. In the 2nd phase, a new analytical method to predict friction resistance force was proposed based on the experimental results. Moreover, the performance of the proposed analytical method was compared with the other two analytical approaches developed by previous studies [24,25]. The observation and related discussion of the first phase of the study is presented in this part of the article.

3.1 Effect of coating types on resistance force

Initial investigation showed that in all soil types, the CM coated steel pipes exhibited the highest resistance force in comparison to the steel pipe specimens coated with PT-I and PPT materials. Fig.14 shows the variation in resistance force for different types of coating of steel pipe buried under overburden depth of 4.8 m for SC and S and overburden depth of 3.6 m for PG. It is apparent from Fig.14 that CM coated pipes had around 113% and 100% higher friction resistance force than that of PPT coated pipes under PG and S, respectively. The same CM coated pipe specimens exhibited about 84% and 73% greater resistance force as compared to PT-I coating when buried under PG and S, respectively. Likewise, CM steel pipes buried under SC showed about 79% and 28% higher resistance force than their PPT and PT-I counter parts, respectively. It is, therefore, appeared that PPT and PT-I coatings are less effective irrespective of soil types in comparison to CM coated steel pipe specimens.

It was also observed that PPT and PT-I coated steel pipe specimens experienced almost similar resistance force under S and PG type soil. On the other hand, under SC soil, PT-I coated steel pipes experienced about 40% more friction resistance force than that of PPT coated steel pipes. Such behavior supported that PT-I coating is relatively more effective under cohesive soil as compared to pipes with PPT coatings. Similar trend was also observed for all coated steel pipes under other different overburden depths considered in this study.

3.2 Effect of soil types on resistance force

The effect of types of soil on friction resistance force for overburden depth of 3.6 m is shown in Fig.15. PG had the highest resistance force as compared to corresponding pipes buried under SC and S. Similar higher resistance forces were observed under PG soil for all overburden depths. For CM coating, the pipe under PG soil experienced about 104% and 86% higher resistance force, respectively than its S and SC counterparts. However, an increase of about only 10% was observed for CM pipes when soil changed from S to SC. The pipes with PT-I coating under PG showed about 100% and 46% increase in resistance force as compared to pipes buried under S and SC, respectively. Similar trend was also observed for pipes with PPT coating. It was also evident from the experimental outcomes that all coated steel pipes exhibited similar relationship between friction resistance force and rigid body movement for all overburden depths. However, it was found that the difference in the peak friction resistance forces between SC and S reduced with higher overburden depths for all coating types. In general, the degree of resistance by soils was found to be in the order of PG > SC > S for all overburden depths and coating variations.

3.3 Effect of overburden depth on resistance force

Plots of friction resistance force vs. rigid body movement of the CM coated pipe specimens buried in SC, S and PG for four different simulated overburden depths are shown in Fig.16. The overburden depths ranged between 1.2 and 4.8 m. As expected, all pipe samples exhibited increased resistance force with the increase in overburden depth. For SC, the friction resistance forces were found to be increased by about 35%, 27%, and 38%, due to gradual increase in overburden depth from 1.2 to 4.8 m, with an interval of approximately 1.2 m, respectively. In the case of S, it was observed that the increment of the friction resistance force was more substantial with increase in overburden depth in comparison to other two soil types. The overburden depth of 1.2 m did not produce significant friction force. However, it was observed that friction resistance forces were increased by around 113%, 63%, and 50% when simulated overburden depth increased from 1.2 to 2.4 m, 2.4 to 3.6 m, and 3.6 to 4.8 m, respectively. Fig.16 also shows that the overburden depths of 3.6 and 4.8 m provided almost similar friction resistance for PG. Friction resistance forces increased at a decreasing rate by around 58%, 42%, and 7% for the same simulated overburden depth. In general, the rate of increase of resistance force exhibited a decreasing trend with increasing overburden depth, which could be due to the compaction of soil caused by the elevated overburden depth producing an arching effect.

Pipe specimens under SC and S experienced an initial axial rigid body movement prior to experience the resistance generated by soil friction. On the contrary, PG produced frictional resistance force from the beginning of the pulling, as the elevated overburden depth caused by the applied pressure had been acting on the individual components of PG. The resistance provided by particles of PG on the surface of the pipes prohibited any initial movement of the pipe. Similar behavioral pattern was also observed for other pipe specimens coated with PT-I and PPT buried under three types of soils with four overburden depths.

It was observed that SC, due to its better cohesion, provided more enhanced resistance than was the case for S. On the other hand, each particle of PG provided a concentrated force on pipes, and eventually, cumulatively, provided better resistance against pipe movement. Such individual action of PG particles resulted in significantly higher resistance force as compared to SC and S. Therefore, PG can be recommended for application in cases of critical circumstances where higher friction resistance is required for counteracting thrust force.

3.4 Effect of coating type, soil type and overburden depth on earth pressure

Fig.17 and Fig.18 show the changes in stress in soils in the vicinity of the steel pipes with respect to coating types and soil types, respectively. The stress was monitored through two EPCs located above the crown of the pipes (as shown in Fig.7). The changes in stress in soils, shown in Fig.17, were observed for overburden depth of 3.6 m whereas Fig.18 depicts stress in EPCs for overburden depth of 2.4 m. The EPCs in SC and S recorded similar pattern of stress behavior for all types of coating, as is evident from Fig.17 and Fig.18. Considerable decrease in stress values was observed at a displacement of around 3 to 5 mm for all pipes under SC and S. The values of decrease in stress, due to rearrangement of soils resulting from movement of pipes, were found to range between 5 and 20 kPa. Rearrangement of soil was caused by the movement of a mass of soil along with the pipe. Such rearrangement of soils causes instability of soils at pipe surroundings and, eventually, can result in formation of sinkholes, which can cause significant damage to above ground structures. Therefore, ensuring adequate friction resistance of buried pipes is essential in case of SC or S soil types to ensure safety of both buried pipes and surface structures.

On the other hand, EPCs in PG registered increase in stress values with the movement of pipes. The particles of PG rearrange themselves individually due to pipe movement in a similar way to behavior of course aggregates in vibration. Such rearrangement of PG particles makes them more confined and eventually, results in higher stress. Confinement effect of PG particles were also evident from images of pipe taken after the experiment as shown in Fig.19. The pipe samples showed partial perforation caused by confining effect of PG particles around the pipe. It is, thus, evident that PG exhibited less potential for instability due to movement of pipes. Therefore, PG can be used as back-filling materials under critical conditions to ensure required friction between steel pipes and soils. The EPCs installed for steel pipe with PT-I coating in PG did not exhibit any usable data probably due to installation error so have been excluded from Fig.17(c) and Fig.18(b).

Similar trend was also observed for other overburden depths for all soil and coating types considered in the study. Both SC and S experienced a considerable decrease in stress due to pipe movement, and hence exhibited susceptibility to instability if adequate friction resistance could not be attained between pipe and surrounding soils. The authors believe that the outcomes of the study are significant in understanding the behavior of surrounding soil due to movement of coated steel pipes. Also, the results can be used for conducting further numerical and finite element analysis for quantification of surrounding soil behavior of moving steel pipes.

4 Analytical procedures

Based on the experimental data, three approaches were utilized as analytical procedures for calculating the surface frictional force between buried coated steel (BCS) pipes with different backfill materials. The first approach was based on modified Coulomb’s equation, with modifiers for the cohesion and soil friction angle coefficients as originally proposed by Potyondy [8]. This approach, termed as “PL” in this article, assumed that behavior at the pipe-soil interface is similar to that at a soil-soil interface, but with reduced friction angle values. The second approach, proposed by a previous study [34], also utilized a modified Coulomb’s equation. However, a semi-empirical expression was proposed for the internal friction angle of the soil to account for stiffness of the pipe, overburden pressure, and nature of the bedding and pipe zone backfill material. The new analytical method, proposed in this study, is a third approach, utilizing the concept of using the term Z as pipe resistance coefficient. The Z is a dimensionless factor representing the average resistance to motion around the pipe circumference for a specific soil type and coating type. Predictions from the three approaches were then compared with the experimental data to provide recommendations for future installation use. The predictions may serve as the foundation for further study.

Coulomb’s equation for calculating the internal shear strength of soil, f, is expressed as:

(1)f=C_{\mathrm{s}}+{\sigma }_{\mathrm{r}}\mathrm{t}\mathrm{a}\mathrm{n} \varphi ,

where C_s is the cohesion of soil, σ_r is total radial stress, and ϕ is soil friction angle. Values of C_s and ϕ for tested soil types are listed in Tab.3. Values of σ_r can be calculated using the Eq. (2) given by Höeg [34] as provided below:

(2){\sigma }_{\mathrm{r}}= {\sigma }_{\mathrm{o}}+ {\sigma }_2\mathrm{c} \mathrm{o}\mathrm{s}2\theta ,

where {\sigma }_{\mathrm{o}} and {\sigma }_2 are uniform and non-uniform components of stresses, and \theta varies from 0° to 360°.

It is assumed that the frictional resistance acting on a buried pipeline can be determined using the Eq. (3) given by EBAA Iron, Inc. [3] as follows:

(3)F=\text{π}{OD}_{\mathrm{p}}{L}_{\mathrm{p}}{C}_{\mathrm{s}}{f}_{\mathrm{c}}+ W\mathrm{t}\mathrm{a}\mathrm{n}\left(f_{\varphi }\varphi \right),

where OD_p and L_p are the pipe outer diameter and buried length, respectively, and W is approximated for steel pipe as the total normal force per unit length acting on the pipe and given by Eq. (4).

(4)W={(2W}_{\mathrm{p}\mathrm{l}}+W_{\mathrm{p}}+ W_{\mathrm{f}})R,

where W_f, W_p, and W_pl are the weights of the fluid, pipe and prism load above the pipe, respectively.

(5)R=\frac{2+\mathrm{s}\mathrm{i}\mathrm{n}\varphi }{2}.

The first part of the right side of Eq. (3) indicates the skin friction between the soil and pipe surface. The second part of the right side of the equation is the reaction forces causing gripping action surrounding the pipe. This reaction force was generated by the contribution from the soil prism load above the pipe, self-weight of the pipe, and weight of the fluid inside the pipe. Two modifier coefficients, f_c for cohesion and f_ϕ for friction angle, were introduced in Eq. (3) based on work by Potyondy [24], and are listed in Tab.3.

As an alternate to the friction angle modifier coefficients, f_ϕ poposed by Potyondy [24], a previous study [25] proposed a new dimensionless soil friction angle modifier coefficient, δ_t, to measure friction resistance force that is termed as “TTCL” in this study. The coefficient δ_t accounts for: 1) the pipe stiffness, PS; 2) ring stiffness coefficient of the pipe, RSC; 3) multiplication factor, Ψ (Ψ is 1.0 for fine grain soils and 1.5 for gravel to account for localized strain concentration) [35]; 4) overburden pressure, q_o; and 5) the earth load coefficient, C_d [36], as shown in Tab.3. These parameters are similar to those listed by the ASCE [37], due to their role in controlling the normal stress distribution around the pipe. Therefore, the proposed equation by Ref. [25] for friction resistance force, F has been expressed as follows:

(6)F=\text{π}{OD}_{\mathrm{p}}{L}_{\mathrm{p}}{C}_{\mathrm{s}}{f}_{\mathrm{c}}+ W\mathrm{t}\mathrm{a}\mathrm{n}\left({\delta }_{\mathrm{t}}\varphi \right),

where δ_t is given by Eq. (7) and all other parameters were defined previously.

(7){\delta }_{\mathrm{t}}= \frac{{\displaystyle \frac{PS}{RSC}}}{{\mathrm{e}}^{\frac{{\mathrm{C}}_{\mathrm{d}}}{q_o}}+{\displaystyle \frac{RSC}{PS}}}\mathrm{\Psi },

(8)PS=\frac{6.66E_{\mathrm{p}}{I}_{\mathrm{p}}}{{\left({\displaystyle \frac{{OD}_{\mathrm{p}}-2t_{\mathrm{p}}}{2}}\right)}^3},

(9)RSC=\frac{252E_{\mathrm{p}}{I}_{\mathrm{p}}}{{\left({OD}_{\mathrm{p}}-2t_{\mathrm{p}}\right)}^2},

where E_p is the modulus of elasticity of pipe material, I_p is the moment of inertia of pipe’s cross-sectional area, and t_p is the wall thickness of the pipe.

In this study, a simplified approach for calculating the friction resistance force, F, was proposed, given in the form of Eq. (11), which uses the parameter Z. This method is termed as “ZL”, where the values of Z for different soil and coating types with respect to overburden depth of backfill materials were evaluated through experiments. Initially, from the experimental results, the relation between experimental pulling force (F) and overburden depth (h) for different soil and coating types was established using the power law as shown in Eq. (10):

(10)F=A\times h^B,

where A and B are constants for different soil and coating types. The values of A and B were evaluated by fitting the data point to minimize the error. The values of B should be less than unity, representing long-term arching effect of overburden depth on friction resistance.

The proposed equation for friction resistance force, F, incorporating the Z parameter is provided below as Eq. (11). This approach considered the arching effect of overburden soil height, soil type and coating type of the pipe, which made the approach using Eq. (11) significantly different from the first two approaches proposed in Eqs. (3) and (6).

(11)F=\text{π}{OD}_{\mathrm{p}}{L}_{\mathrm{p}}h {\gamma }_{\mathrm{s}\mathrm{o}\mathrm{i}\mathrm{l}}Z,

where OD_p is the outside diameter of the pipe in m, h is the overburden depth of the back fill materials (vertical distance from the ground surface to the crown of pipe) in m, {\gamma }_{\mathrm{s}\mathrm{o}\mathrm{i}\mathrm{l}} is the unit weight of soil, and L_p is the length of pipe also in m.

Equations (3) and (6) are semi-empirical in nature and can be utilized for any soil type, for which cohesion and friction angle modifier coefficients are available, while Eq. (11) is purely empirical and based on experimental results.

Based on Eq. (10) and on the relations proposed in Eq. (11), the correlations between Z and h (soil depth above the pipe, m× h = overburden depth in meter) were developed and shown in Eq. (12). Values of the constants, c₁ and c₂ are provided in Tab.4.

(12)Z=c_1{h}^{-c_2}.

The parameter Z incorporates the effect of pipe coating, soil characteristics, and arching effect on the pipe-soil interaction. Hence, Eq. (11) can offer enhanced prediction of friction resistance force. Although, values of Z are limited to the soil and coating types, they can be measured through the experimental program mentioned in Subsection 2.6.

5 Comparison of experimental and predicted values

The equality charts for the analytical approaches for calculating the frictional force between a restrained BCS pipe and its surrounding soil envelope are shown in Fig.20–Fig.22, where the predicted friction resistance forces using Eqs. (3), (6), and (11) were compared with experimentally observed frictional forces measured during each test. Data points falling above the equality line represent non-conservative predictions while data points falling below the equality line represent conservative predictions. The equality charts (Fig.20–Fig.22) showed the comparison between predicted and experimental resistance force values for coating types CM, PT-I, and PPT, respectively. It is evident that friction resistances forces predicted from the Z value concept exhibit significantly enhanced agreement with the experimental outcomes.

It was also observed that the other two methods, PL and TTCL, showed inconsistencies in predicting friction resistance force for different soil types and coating variations. Predictions made using the PL method were found to be in good agreement with the experimental data for fine grain soils (SC) and CM coating but underestimated the friction forces for PG and CM coating and PG and PT-I coating. On the other hand, PL method overestimated the friction resistance force for PPT and PT-I coated pipes buried in SC soil. The PL method considers surface friction of the soil, which is a function of soil cohesion and friction angle. However, PG soil particles do not behave as one rigid body (like S and SC) and hence, PG particles act as multiple point loads that provide enhanced resistance.

The TTCL method significantly underestimated the resistance force with all types of coatings under S and PG as it used a reduction factor with soil cohesion and soil friction angle. On the other hand, like the PL method, the TTCL method overestimated the friction resistance force for PT-I and PPT coated pipes buried in SC soil.

Both PL and TTCL equations weight the cohesion component more than the friction portion for SC soil, due to its low friction angle value. But, in this study, this behavior was not found for CM coated pipe buried in SC soil, as the CM provides additional frictional resistance due to its rough surface in comparison to PPT and PT-I coating. This additional frictional resistance force compensates the over estimation by the equations of PL and TTCL in comparison to the values obtained from the experimental study.

As expected, predictions from the ZL method using Eq. (11) showed excellent agreement with the experimental data since this method incorporated the effect of coating and soil types on soil friction as well as the arching effect of overburden depth of back fill soils. Fig.23 shows the mean percent of error resulted from difference between predicted and experimental force values for three different approaches. The error bars in Fig.23 represent the standard deviations of mean percent of error. It is apparent from mean percent error values that the concept of the Z parameter has significant potential in accurately estimating the friction resistance force. Nevertheless, it is important to note that the usage of the Z concept is limited for soil and coating type conditions for which coefficients for Z were developed (Tab.4).

6 Conclusions

A full-scale experimental program was undertaken for measuring the frictional force at the soil-pipe interface for direct coated buried pressurized steel pipes pulled along the axial direction. The testing program included 36 different tests that covered a range of soil types, coating types and overburden depths. In the first phase of the study, the behavior of buried steel coated pipe under different conditions (variation in soil types, coating types and overburden depths) was investigated with respect to friction resistance force, RBD, and pressure in surrounding soil, through full-scale experiments. In the second phase, an analytical approach was used for predicting the friction resistance force of the steel pipes based on experimentally measured results. The experimental resistance forces for different pipes under investigation were also predicted using two previously developed/proposed analytical approaches. Finally, the performance of the proposed new analytical approach was evaluated by comparing the predicted friction resistance forces obtained through the three approaches with the experimental outcomes. Based on the study performed, the following conclusions can be drawn.

The steel pipes with CM coating experienced the highest resistance force as compared to the PT-I and PPT coated pipes. The PT-I coating was found to be more effective in providing friction resistance force in cohesive soil as in comparison to pipes with PPT coatings.

Significant influence of soil types on friction resistance of buried coated pressurized steel pipes subject to motion was observed. The following order of resistance by soils to pipe movement in terms of soil types was found for all overburden depths: PG > SC > S.

It appeared from the experimental outcomes that particles of PG acted as a concentrated force on pipes and, thus, resulted in significantly higher resistance against pipe movement. Therefore, PG has good potential in cases where higher friction resistance is required to counteract thrust force.

A decreasing trend in resistance force was observed with the increase in overburden depth for all types of soil and coated steel pipes. This phenomenon was due to the arching effect caused by compaction of soil resulted from elevated overburden depth.

Considerable decrease in soil stress values in SC and S at the vicinity of the steel pipes were observed due to rearrangement of soils resulting from movement of pipes. Such rearrangement can form sinkholes and thus, can cause significant damage to above ground structures. On the contrary, PG showed increase in soil stress with the movement of pipes. The movement of pipe rearranged the PG particles individually, resulting in better confinement and consequential higher stress in soil.

The simplified analytical approach for calculating the friction resistance force proposed in this study exhibited significantly enhanced agreement with the experimental outcomes as compared to the other two previously developed analytical models. The other two methods exhibited inconsistencies in predicting friction resistance force for different soil types and coating variations.

The new analytical approach was based on the parameter Z named as pipe resistance coefficient. The term Z is a dimensionless parameter, depending on specific soil and coating types and overburden depth. This new approach considered the arching effect of overburden soil height, soil type and coating type of the pipe in estimating friction resistance force, which made it significantly different from the other two previously developed approaches.

It is apparent that the analytical approach with the concept of Z parameter has significant potential in accurately estimating the friction resistance force. Although, the application of Z concept is limited to the soil and coating types, the parameter Z can be evaluated for different soils and coatings through an experimental program and finite element analysis. Therefore, future work should include experimental evaluation of soil-pipe interaction characteristics for a range of bedding and coating materials, to develop a holistic guideline.

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