Suction effects during uplift of steel pipes buried in compacted soil

Abstract

This paper presents an experimental study on quantifying the effects of soil suction on the resistance offered by compacted unsaturated backfills to uplift of buried steel pipes and identifying the mechanisms that contribute to increased resistance compared to similar pipes buried in dry sand. This is achieved by means of 1-g physical model experiments, with the pipe buried in sandy loam–Kaolin soil beds of varying water content (suction), compacted to the same dry unit weight. The main experiments are supplemented by benchmarking experiments performed in dry sand of similar grain size distribution, as well as in compacted soil beds inundated with water to achieve conditions close to full saturation. The experiments are supported by a detailed characterisation study of compacted sandy loam–Kaolin mixtures and mini-CPT tests performed to evaluate the uniformity of the soil beds. Measurements of the reaction developing on the pipe as function of its uplift displacement are co-evaluated together with images of the failure mechanisms obtained using particle image velocimetry and continuous measurements of soil matrix suction. We conclude with a simplified method to predict the peak reaction to pipe uplift that allows considering the contribution of suction and the tensile–shear failure mechanism observed during the experiments.

1 Introduction

Pipelines are commonly buried in the ground, which provides protection and support. However, ground movements due to seismic fault rupture, slope instability, ground subsidence, tunnel excavation, etc. will induce additional stresses on pipe segments, which may impact their serviceability or result in failure. Verification of pipe integrity against such ground movements requires quantifying the reaction developing on a pipe as function of the relative soil–pipe displacement. This reaction depends on several factors, including the magnitude and the direction of the relative displacement, the pipe burial depth, as well as the properties of the pipe and of its surrounding soil. Numerous studies have resulted in methods for estimating the reaction force developing on a pipe as function of the mentioned problem parameters (e.g. [2, 3, 10, 11, 28, 33, 35, 38, 39]). Most of those are limited to the case of pipes buried in dry or fully saturated soil. This is reflected in the current guidelines for the design of pipelines crossing unstable soil deposits (e.g. [1, 19, 23]). These guidelines recommend the use of beam-on-nonlinear Winkler foundation models for the stress analysis of buried pipes and provide methods for calculating the properties of Winkler springs for dry or fully saturated cohesive or cohesionless backfill soil (e.g. [31, 41]). However, the backfill around buried pipes laid in trenches is commonly compacted after laying of pipe segments and will most likely remain unsaturated (instead of dry or fully saturated) during the lifetime of the pipeline [24]. Ignoring the unsaturated nature of the backfill, i.e. the effect of soil suction, suggests that Winkler spring parameters may underestimate soil strength and stiffness, and thus the reaction that would develop on a pipe during a relative movement episode. While this may be on the safe side for many geotechnical engineering applications, including the estimation of the upheaval buckling potential of buried pipes subjected to temperature loads, this is not the case when it comes to the analysis of buried pipes subjected to differential ground movements. Due to the prescribed displacement nature of this problem, the higher the soil reaction, the higher will be the pipe strains. Thus, it may be unconservative to ignore the effect of backfill suction when estimating the properties of Winkler springs.

Nevertheless, less attention has been paid in the past to investigating the effect of suction on the reaction developing on buried pipes during relative movement episodes, owing perhaps to the fact that physical and numerical modelling of this problem is challenging. Most of the available studies in the literature resort to numerical modelling to study this problem [14, 25, 26, 29] while a few researchers have attempted to obtain experimental measurements [20, 21, 35]. Notably, Olson [21] and Robert and Soga [24] have conducted large-scale physical model experiments to shed some light on the effects of moisture content of sandy backfills on soil–pipeline interaction. Robert and Soga [24] found that the resistance developing during lateral dragging of a pipe buried in unsaturated Tokyo Gas sand was significantly higher (about × 2.5 times) compared to the resistance measured when the pipe was buried in dry sand. On the contrary, results of experiments conducted by Olson [21] using Cornell Filter sand suggest that the degree of saturation of the backfill had negligible effect on the lateral reaction on the pipe. These contrasting findings are attributed to the different backfill grain size distribution, which largely controls its water retention capacity [24]. Recent numerical studies [14, 25, 26, 29] describe the use of elastoplastic constitutive soil models to simulate unsaturated soil–pipe interaction. These studies have documented that backfill matrix (capillary) suction may have an important, detrimental effect on the soil reaction developing on a pipe during a relative displacement episode. However, it is still unclear how backfill suction, which will potentially change as result of relative pipe movement, affects the magnitude of the reaction that develops on a pipe and how suction alters the failure mechanism that develops in the backfill as result of pipe movement. Arguably there is also a lack of high-quality experimental data to benchmark methods for deriving properties of Winkler springs for compacted backfill materials, where soil suction would be introduced as a parameter, and thus to consider its effects in pipeline engineering practice. An exception is the recent study of Wong et al. [36], who investigated the effect of the uplift rate on the reaction developing on pipes buried in compacted Regina clay and provide insights on the failure mechanism that developed in the compacted backfill. However, Wong et al. [36] have not studied parametrically the effect of the soil water content (i.e. soil suction) of the backfill material or of the pipe embedment depth on the magnitude of the developing soil reaction. Moreover, they have not measured how much initial suction increases during pipe uplift, to establish the value of suction that needs to be considered when estimating the peak reaction on the pipe.

The aim of this paper is to contribute to closing the abovementioned gaps, by presenting the results of a comprehensive experimental investigation on the effects of soil suction on backfill–pipe interaction. The core of the study comprises 1-g physical model experiments, modelling uplift of a rigid steel pipe buried at different depths in a soil bed representative of backfill materials used in practice. A total of 13 experiments were conducted under both saturated and unsaturated conditions where the backfill material was compacted according to piping specifications at different initial moisture contents (matrix suctions). We present detailed measurements from these experiments, including the reaction developing on the pipe as function of the applied uplift displacement, the variation in soil matrix suction (hereafter suction) during the development of a failure mechanism in the backfill, and illustrations of this mechanism captured with the aid of particle image velocimetry (PIV) and close-range photogrammetry [30]. Supplementary experiments performed with the pipe buried in dry sand are presented and used for benchmarking purposes. We conclude with the presentation of a simplified method for predicting the peak normalised uplift reaction (uplift factor) developing on rigid steel pipes, which can be used to determine the input parameters Winkler-type pipe stress analysis models.

2 Experimental methodology

2.1 Testing rig

Figure 1 depicts an overview of the testing chamber, the reaction and loading frames, the model pipe used in the experiments, and of the loading and data acquisition systems. A detailed description is given in Wu et al. [38]. The chamber has inner dimensions of 1050 mm (length) × 450 mm (width) × 825 mm (height). Its bottom and cross walls are made of 25 mm-thick aluminium plates, while the two 20-mm-thick annealed glass sidewalls allow observing soil movement and capturing images with a DSLR camera during testing. Ten pressure sensors (KDF-PA type, manufactured by Tokyo Measuring Instruments Laboratory Co. Ltd.) are used to measure vertical and horizontal stresses. A total of 48 10-mm-diameter nozzles facilitate drainage of water when full saturation is required. The locations of the pressure sensors and of the drainage holes are shown in Fig. 1b.

Fig. 1

a Main components of the rig used in the physical modelling experiments. b Arrangement of pressure sensors and of the drainage system

The chamber is mechanically clamped on a reaction frame of dimensions 1800 mm (length) × 2600 mm (height) × 500 mm (width) that is anchored to the strongfloor. A second steel frame is housing the loading system used to performed pull-out and lateral drag displacement-controlled experiments. The model pipe is a rigid 3 mm-thick stainless-steel tube (self-weight 36 N) with outer diameter 73 mm. The length of the pipe is approximately 450 mm, as its ends are fitted with HDPE ring caps. A 1-mm-thick piece of felt is attached to each cap, to reduce pipe-glass friction and prevent soil particles from becoming trapped between the pipe and the glass windows. The pipe is attached to two parallel threaded rods that are connected to two horizontal steel beams, to allow pulling the pipe vertically while preventing its rotation. The loading system comprises a 1.5 t electric winch mounted on the loading frame, a pulley clamp mechanism, and a 3-mm-diameter high-strength steel cable connected to the winch that is used to pull the pipe upwards. The cable is attached to the horizontal steel beams via an eyebolt and a D-shackle, to prevent imposing any kinematic constraints on pipe movement. The winch allows applying pulling rates between 1 and 200 mm/h. A pulling rate of 120 mm/h was applied in all the experiments presented in this study, consistent with previous tests performed in our laboratory [2]. The described setup guarantees that plane strain conditions are achieved during pull-out and lateral drag tests, as the bending stiffness of the pipe is sufficiently high and pipe deformation during testing is negligible. This is compatible with standard beam-on-nonlinear-Winkler-spring stress analysis models, where the properties of springs are considered constant along the length of the pipe. Still, the setup cannot account the effects of pipe bending or section deformation on the developing reaction to pipe uplift or lateral drag.

The reaction force is measured with S-type tension–compression load cells of varying capacity, depending on the magnitude of the expected reaction force. Pipe displacement is measured with precision of 0.1 mm using a string potentiometer connected to the horizontal steel beam. As the beams used to connect the pipe to the cable are sufficiently rigid, any slack in the measured displacements is minimal. Four button load cells of capacity 1 t each, mounted on the steel reaction frame beneath the testing chamber, provide continuous measurement of the weight of the chamber during sample preparation and testing. Two low-range tensiometers (T5 type, manufactured by METER Group Inc., USA) with range −85 to  + 85 kPa and precision of 0.1 kPa, allow measuring pore water pressure u_w in the soil bed around the pipe. Assuming zero relative air pressure within the soil (u_a = 0), the pore water pressure measured by the tensiometers can be converted into matrix suction as: s = u_a−u_w = −u_w. All the instruments are connected via a data logger to a data acquisition unit, which features custom software to record and monitor measurements in real time.

Finally, a custom-built mini-CPT rig is used to evaluate the uniformity of compacted soil beds inside the chamber (see [2, 38]). The diameter of the mini-cone is 16 mm and the cone tip angle is 60°. Tip resistance is measured using a 2-kN mini load cell housed inside the cone, while the cone tip displacement is measured by a string potentiometer attached to the shaft of the actuator.

2.2 Material tested

According to Australian Standards pertinent to buried pipelines [4,5,6], the backfill material placed above the pipe crown that provides resistance to pipe uplift is commonly in situ (ordinary) fill produced during excavation of the trench. This material should be properly compacted, to provide support to the pipe during its design life. To replicate backfill conditions commonly encountered in the field, an artificial sandy loam–Kaolin mixture was used in this study. Ye et al. [40] used sandy loam from the same commercial source and found that moisture uniformity would be affected under the influence of gravity when the degree of saturation was higher than 20%, due to its relatively low water retention capacity. As such, 20% by mass Q38 Kaolin was mixed with 80% sandy loam to increase the water retention capacity of the backfill. The particle size distribution of pure sandy loam and of the sandy loam–Kaolin mixture is presented in Fig. 2, in comparison with the particle size distribution of Stockton Beach sand (STK sand) used in the benchmarking experiments in dry sand. These three soils are all classified as poorly graded silty sand according to ASTM D6913 [7]. The specific gravity of the mixture, measured with a gas pycnometer, is G_s = 2.65. Results of standard proctor compaction tests shown in Fig. 2 suggest that the optimum water content of the mixture is 9.5% and the corresponding optimum dry unit weight is 19.2 kN/m³. According to Melbourne Retail Water Agencies [18] and Howard [13], silty pipe backfill materials in non-trafficable areas must be compacted to 90% of the maximum Standard Proctor dry unit weight. As such, the target dry unit weight of the sandy loam–Kaolin mixture in all the physical model experiments presented in following sections is γ_target = 17.3 kN/m³.

Fig. 2

Physical soil properties: a Particle size distribution of pure sandy loam, Stockton Beach (STK) sand and sandy loam–Kaolin mixture. b Standard Proctor compaction test results for sandy loam–Kaolin mixtures. Suction s of the mixture specimens in their as-compacted state are also presented

Figure 3 presents the pore size distribution (PSD) and the water retention curve (WRC) of the sandy loam–Kaolin mixture compacted at γ_target. The PSD was estimated from mercury intrusion porosimetry (MIP) tests [27] using specimens compacted at the optimum water content. The influence of the compaction method on the PSD is presented in Fig. 3a as the soil beds in the physical model experiments were compacted dynamically, whereas statically compacted specimens were used in the laboratory characterisation tests described below. The very good agreement between PSDs indicates that the compaction method has no effect on soil fabric, allowing the use of small-scale laboratory results in the analysis of physical model data. The sandy loam–Kaolin mixture has a bimodal PSD composed by micro pores (0.01–20 µm) and macropores (40 up to 400 µm, the maximum detectable pore size in the MIP test). Dominant micro- and macropores are observed at 0.65 µm and between 150 µm, respectively.

Fig. 3

a PSD curves; b S_r−s relationship of sandy loam–Kaolin mixture compacted at dry unit weight γ_dry = 17.3 kN/m³

The water retention curve of the sandy loam–Kaolin mixture (γ_dry = 17.3 kN/m³), which defines the variation in the degree of saturation S_r with suction s, is presented in Fig. 3b. Suction values below 85 kPa were measured using the tensiometers described above. Higher suction values were measured with a psychrometer WP4C (METER Group Inc., USA). Although the WP4C measures total suction, which combines the contribution of matrix and osmotic potentials, the influence of the osmotic component in the sandy loam–Kaolin mixture is negligible so that matrix suction could be taken equal as the total suction. A total of 11 soil samples were statically compacted to the target γ_dry and various water contents, ranging from w = 3 to 15%. Grey circles indicate the measured suction values, whereas the solid line represents the WRC estimated via fitting using the van Genuchten model [34]:

$${S}_{\mathrm{r}}={\left[1+{\left(\frac{s}{{P}_{0}}\right)}^{\frac{1}{1-\lambda }}\right]}^{-\lambda }$$

(1)

where S_r is the degree of saturation, s is soil suction, whereas P₀ and λ are fitting parameters. The WRC depicted in Fig. 3b corresponds to P₀ = 2 kPa, λ = 0.275. The air entry value (AEV) estimated from the van Genuchten model is around s_e = 1 kPa. Figure 3b includes the range of suction associated with macro and micro pores, obtained from the MIP data assuming the pores are capillary tubes [27]. Macropores are mainly responsible for suction values below 35 kPa, whereas micropores control suction values are above 150 kPa. Considering the low suction measured at the optimum water content (Fig. 2), the suction response described in following sections is dominated by soil macro porosity, which also controls the soil’s hydraulic conductivity. From a constant-head permeability test on saturated compacted sandy loam–Kaolin mixture, we estimated the saturated water conductivity to be k = 2.5 × 10^–7 m/s.

Shear strength parameters of the mixture were estimated using a modified direct shear apparatus. Two low-capacity tensiometers were installed at two locations within the specimen to measure suction during tests (Fig. 4). Tests were performed on unsaturated and saturated specimens, which were statically compacted inside the direct shear box to γ_dry = 17.3 kN/m³. For unsaturated tests, the compacted specimens were left to cure inside sealed plastic bags for about 12 h to achieve moisture equilibrium before testing. In saturated tests, the cured compacted specimens were soaked in tap water for over 12 h prior consolidation. After placing the specimens in the direct shear apparatus, tensiometers were installed through the loading plate with their shaft tip located close to the expected shear plane (~ 5 mm above the mid-plane), to measure suction changes during shearing. All specimens were sheared at a horizontal displacement rate of 0.0005 mm/s. Note that additional tests (not shown here for brevity) have been performed to investigate the effect of the rate of shearing. The maximum rate of shearing was 0.05 mm/s and was of the same order of magnitude as the pipe pulling rate. Results of these tests suggest that shearing rate effects for the particular material were practically negligible.

Fig. 4

Schematic of the modified direct shear apparatus: Top view a and side view b. Dimensions in mm

A total of 18 direct shear tests (9 on unsaturated and 9 on saturated samples) were conducted to estimate the shear strength parameters of the mixture. Specimens were compacted to three initial water contents (w = 6.5, 8 and 9.5%) to match the nominal water content of the physical model experiments. The tests were performed under relatively low normal stress levels (σ_n = 12.5, 25 and 50 kPa), relevant to the study at hand. Figure 5 shows representative results obtained from specimens compacted at w = 6.5%, and sheared under normal stress σ_n = 25 kPa. Observe that the unsaturated specimen exhibits post-peak softening, while the saturated specimen exhibits hardening and reaches much lower peak shear stress. Accordingly, the unsaturated specimen exhibits dilative behaviour, whereas the saturated specimen contracts. Suction increases during shearing as the soil undergoes dilation, a phenomenon that has been reported before for different soils (e.g. [22, 31]). As expected, zero suction was measured during saturated tests.

Fig. 5

Results of direct shear tests on an unsaturated and a saturated specimen prepared at initial water content w = 6.5% and sheared under normal stress σ_n = 25 kPa. Results include the variation with shear displacement of a Shear stress. b Vertical displacement; and c Normalised suction

A summary of the direct shear tests is presented in Fig. 6. Results obtained by Ansari et al. [2] from tests on dense STK sand are also included for comparison. The peak shear stress increases as the as-compacted water content decreases (i.e. suction increases), while the initial water content has negligible effect on the behaviour of saturated samples. The dilation angle ψ_p at peak shear stress estimated from the ratio of vertical and horizontal displacements ψ_p = tan⁻¹(δ_y/δ_x) is shown in Fig. 6b. The tendency of unsaturated samples to dilate decreases as the water content and the normal stress increases, while saturated samples exhibit contractive behaviour across the whole normal stress range. The variation in peak shear stress and suction is shown in Fig. 6c. The linear trend observed in this figure indicates that, for the range of suction measured in the experiments, the peak shear stress increases with suction at a rate dτ/ds ≈ 0.23 kPa/kPa.

Fig. 6

a Failure envelope of dense STK sand, and of unsaturated and saturated sandy loam–Kaolin specimens. b Dilation angle at peak shear stress. c Peak shear stress against the measured suction at peak shear stress

The shear strength parameters of the sandy loam–Kaolin mixture are estimated using the Mohr–Coulomb effective stress equation proposed by Bishop and Blight [8]:

$$ \tau = (c^{^{\prime}} {\mkern 1mu} + \sigma_{n}^{\prime } {\mkern 1mu} {\text{tan}}\varphi ) + \left( {\chi s{\text{tan}}\varphi } \right) $$

(2)

where τ is the shear strength, ${\sigma }_{n}^{^{\prime}}={\sigma }_{n}+(\chi s)$ is the effective normal stress, φ is the effective friction angle, c′ is the effective cohesion, s is the soil suction at peak strength, and χ is a parameter that depends on the degree of saturation. Khalili and Khabbaz [15] proposed to determine the parameter χ using Eq. (3):

$$ \chi = \left\{ {\begin{array}{*{20}l} 1 \hfill & {\;\;s < s_{{\text{e}}} } \hfill \\ {\left( {\frac{{s_{{\text{e}}} }}{s}} \right)^{r} } \hfill & { \;\;s \ge s_{{\text{e}}} } \hfill \\ \end{array} } \right. $$

(3)

where s_e is the air entry value from the Van Genuchten model, s is again the suction at peak strength, and the parameter r ranges from 0.4 for clayey soils to 0.65 for sandy soils. Here we take r equal to 0.45 and accordingly we estimate c′ = 1.3 kPa and φ = 28.5º.

2.3 Preparation of physical model experiments

2.3.1 Preparation of moist sandy loam–Kaolin beds

The sandy loam was first oven-dried and then sieved using a 2-mm-aperture sieve to remove large particles. Accordingly, the sandy loam was dry mixed with Q38 Kaolin clay at a 80:20 mass ratio, using a concrete mixer. The mixture was then blended with the required amount of water to achieve the nominal (target) water content w_nom. The moist mixture was stored in sealed barrels for more than 24 h to achieve moisture equilibrium.

Dynamic moist tamping compaction (e.g. [9]) was used to prepare beds of uniform density and moisture content, using an electric percussion hammer fitted with stiff steel pads of different dimensions (100 mm × 100 mm and 100 mm × 448 mm). We performed trial compaction tests using a rigid steel box (dimensions 245 mm × 245 mm × 180 mm), and we found that a compacted layer thickness of 50 mm was sufficient to achieve the target dry unit weight (γ_dry = 17.3 kN/m³) for all the nominal water content values (w_nom = 6.5%, 8% and 9.5%). However, as discussed later, the compacted layer thickness in the testing chamber was reduced to 20 mm, as beds comprising 50 mm layers did not exhibit the desired uniformity. To compact the material inside the chamber, we laid a predetermined quantity of moist mixture and carefully levelled the surface of the layer. The thickness of each layer was controlled using markers on the glass sidewalls of the chamber as reference. Prior to compacting a new layer, the bed surface was thoroughly incised to about 5 mm depth, to facilitate interlocking between successive layers and increase bed uniformity. The pipe was carefully placed on the bed surface after preparation of the first two layers (40 mm thick), and the process was then repeated while threading additional rods to the pipe (Fig. 1), until the desired pipe embedment was reached. The mixture was carefully compacted by hand in the vicinity of the pipe and of the threaded rods. After each experiment, the material was removed from the chamber, oven dried and recycled in subsequent experiments.

The two tensiometers (S1 and S2) were installed after the desired bed thickness was reached, at the locations shown in Fig. 7. The tensiometer S1 was installed directly above the centreline of the pipe, 50 mm below the surface. The tensiometer S2 was located 200 mm away from the centreline of the pipe and 100 mm below the surface. After installation, the tensiometers were left to equilibrate for about 12 h, during which suction was monitored continuously.

Fig. 7

Schematic of the experimental setup. Dimensions in mm

2.3.2 Inundation of compacted beds in saturated tests

Considering the large macro porosity observed in Fig. 3a and the relatively high water conductivity of the compacted mixture, to achieve saturated conditions we applied 100 mm of water column on the surface of the bed, and percolated tap water through the soil (Fig. 7). A 2-mm-thick geotextile placed at the bottom and sides of the chamber prior to compaction facilitated the saturation process. Moreover, water was continuously re-circulated using a low-capacity electric pump connected to the bottom drainage line, so that the water level at the bed surface was kept constant. This procedure was maintained for 7 days before tests for pipe embedment depth H/D = 1.5 and 14 days before tests for H/D = 3 and 4; D = 73 mm is the pipe diameter and H the pipe burial depth measured from the bed surface to the pipe centreline.

2.4 Miniature cone penetration testing (mini-CPT)

Cone penetration tests were performed only in the thicker soil bed with water content w_nom = 9.5%, as the resistance measured during tests in beds compacted at lower water contents exceeded the capacity of the system. The locations of the mini-CPTs, carried out before pipe uplift, are shown in Fig. 8. The locations were selected to avoid side boundary effects [38] while also avoiding the area near the pipe. Penetration was halted when the tip reached about 50 mm from the base, to avoid damaging the load cell. Figure 8 presents the tip resistance profiles measured at locations A, B, and C. The profiles suggest that the uniformity of the compacted soil bed is excellent, and there is no indication of any layering effects. It is worth observing that the tip resistance measured at a depth of about 250 mm is approximately 2 times higher compared to the tip resistance measured by Wu et al. [38] at the same locations in very dense sand (D_r = 93%, γ_dry = 17 kN/m³). This increase in the tip resistance, mainly attributed to soil suction, is consistent across the full penetration depth.

Fig. 8

a Comparison of tip resistance profiles from tests in compacted material with water content w_nom = 9.5%, and in dense STK sand (γ_dry = 17 kN/m³, D_r = 93%) measured by Wu et al. [38], b Locations of mini-CPT tests (plan view). Dimensions in mm

3 Benchmark uplift experiments in dry sand

The results of six uplift experiments performed in dry STK sand [2, 3, 38, 39] are presented to establish a baseline for the experiments with the pipe buried in compacted soil beds. The experiments were performed with the pipe buried in loose (relative density D_r = 27%, dry unit weight γ_dry = 15.15 kN/m³) to dense (D_r = 93%, γ_dry = 17 kN/m³) sand in shallow depths H/D = 1.5 and H/D = 3 to match the embedment depths of experiments on compacted sandy loam–Kaolin. The sand was deposited in the testing chamber using the automatic air pluviation system described in Wu et al. [38].

Measurements of the reaction force versus pipe displacement are summarised in Fig. 9. In addition, in Fig. 10 we present the shape of the failure mechanism that developed in sand when the peak reaction on the pipe was reached, depicted via incremental shear strain contours and displacement vectors. These were obtained from the analysis of images captures during the tests using the PIV technique. The reaction stress per unit length of the pipe F_vu/DL in Fig. 9 is normalised against the mean geostatic stress acting on the pipe centreline γ_effH, which was measured during deposition via pressure sensors to account for any arching effects [38]. The dimensionless parameter N_vu = F_vu/γ_effHDL is commonly used in the relevant literature to normalise the reaction force on pipes with regards to their diameter. Note that F_vu is the net reaction force, excluding the weight of the pipe and the friction force developing between the pipe ends and the glass walls of the chamber. The latter was measured via “friction tests” (see [2]) to be of the order of 8–10 N for the setup at hand, i.e. it is considerably less that the reaction developing due to the resistance offered by sand to pipe uplift. In addition, the pipe uplift displacement δ_vu is normalised against the pipe diameter D. Notice that softening is observed during tests in dense sand, while the reaction force converges to a residual value at large pipe displacements. The failure mechanism governing the development of the peak reaction force changes from a flow-around mechanism associated with loose sand and deep embedment depths to a wedge-type mechanism in dense sand and shallow embedment depths.

Fig. 9

Normalised reaction–pipe displacement response measured during uplift experiments in dry STK sand beds

Fig. 10

Incremental shear strain contours and displacement vectors corresponding to the pipe displacement δ_vu,peak where the peak reaction was measured. Results for nominal initial pipe embedment H/D = 1.5 and H/D = 3 and experiments in loose, medium and dense sand

4 Uplift experiments in compacted backfills

4.1 Testing procedures

Uplift experiments on unsaturated and saturated sandy loam–Kaolin soil beds were performed for nominal pipe embedment depths H/D = 1.5, 3, and 4, covering common embedment depths of buried pipes laid in trenches. Key information about the experiments is summarised in Table 1. The average dry unit weight of the compacted soil beds γ_dry was calculated using the button load cell measurements, and the water content w_measured was determined from six soil samples retrieved after each experiment. Note that generally the measured average dry unit weight of the compacted soil bed was close or higher than the target dry unit weight γ_dry = 17.3 kN/m³ (90% of the maximum dry unit weight as mentioned earlier), except in test #6 where the average dry unit weight reached 88% of the maximum dry unit weight. This is attributed to issues encountered with the compaction equipment during preparation of that experiment.

Table 1 Summary of the initial conditions of uplift experiments and key results

The target initial conditions of test #10 matched those of test #4, with the latter performed to assess the effect of compacted layer thickness on the reaction force developing on the pipe. The average dry unit weight of the soil bed in test #10 was γ_dry = 16.89 kN/m³, which is less than the average dry unit weight γ_dry = 17.3 kN/m³ achieved when the layer thickness was reduced to 20 mm. Key results from these two tests are compared in Fig. 11. The peak reaction that developed on the pipe was of the order of 20% less in test #10 (Fig. 11a) and the suction during pipe uplift is lower in test #10 (Fig. 11b). One could attribute suction differences to the minor difference in the achieved dry unit weight, but the difference in the measured reaction suggests that the soil adjacent to the pipe was not properly compacted in test #10, particularly at the haunch zone. This is evidenced by the fact that the initial stiffness of the soil–pipe system is almost identical for both tests, but the cracks developing at the haunch zone near the peak reaction (see Fig. 11c, d) propagate through the interface of the two layers in test #10. These cracks, which denote mobilisation of the failure prism in the soil bed above the pipe, originate at the springline in test #4 and a different, wider mechanism is formed. The effect of the thickness of the compacted layers becomes less important at large pipe displacements, when a similar wedge-type mechanism is fully formed (see Fig. 11e, f), and the reaction on the pipe converges to the same residual value. This suggests that backfill around small diameter pipes in the field should be compacted in thin layers, to ensure backfill homogeneity. As result of the above, soil beds were compacted in 20 mm layers while preparing all the experiments presented in the following sections, and test #10 is not considered further.

Fig. 11

a and b Reaction–displacement response and suction measured during test #10 (compacted layer thickness h = 50 mm) and test #4 (compacted layer thickness h = 20 mm). Nominal pipe embedment H/D = 1.5 and water content w_nom = 8%; c and e Incremental soil displacement vectors and contours at the peak reaction (δ_vu,peak = 0.02D) and post-peak (δ_vu = 0.23D) during test #10; d and f Incremental soil displacement vectors and contours at the peak reaction (δ_vu,peak = 0.068D) and post-peak (δ_vu = 0.2D) during test #4

4.2 Reaction–pipe displacement response

Figure 12 presents the dimensionless reaction–pipe displacement curves for uplift displacements δ_vu up to 0.5D. Results are presented in terms of the normalised reaction force used in Fig. 9; however, as the soil bed is unsaturated, the expression providing the normalised resistance is modified as:

$$ N_{{{\text{vu}}}} = F_{{{\text{vu}}}} /HDL\gamma_{{{\text{dry}}}} \left( {{1} + w_{{{\text{measured}}}} } \right) $$

(4)

where F_vu is again the net reaction on the pipe, excluding the weight of the pipe and glass–pipe friction, while γ_dry and w_measured are listed in Table 1. Observe in Fig. 12 that, as expected, the peak reaction on the pipe increases with the embedment depth. Moreover, it increases further as the initial water content decreases (suction increases). The response is characterised by significant post-peak softening, which is more prominent at lower water contents. Not surprisingly, these observations are in line with findings of the experiments on dry sand (Fig. 9). Note that the reaction measured during test #6 (H/D = 4.1, w_measured = 7.97%) is lower than expected, and similar to the reaction measured in test #5 (H/D = 3.1, w_measured = 7.91%). As discussed earlier, this is attributed to issues with compaction equipment during the preparation of test #6.

Fig. 12

a–c Normalised reaction–displacement curves measured during experiments in compacted sandy loam–Kaolin mixtures with different water content. d Comparison of normalised reaction–displacement curves measured during experiments in dry dense sand and inundated compacted sandy loam–Kaolin mixtures

Of particular interest is the peak reaction developing on the pipe and the displacement required to mobilise that peak reaction, as these are used to define the properties of elastoplastic Winkler springs for stress analysis models. As such, we present in Fig. 13a the normalised peak reaction force (uplift factor) N_vu,peak and in Fig. 13b the relevant pipe displacement δ_vu,peak/D, as function of H/D and w. Figure 13 depicts for comparison the uplift factor N_vu,peak from the experiments on dense dry sand of similar dry unit weight (γ_dry = 17 kN/m³), and the results of the experiments where the soil bed was soaked after compaction. The uplift factor measured in compacted soil beds is significantly higher that the factor measured in dry sand, much higher than the × 2.5 increase reported by Robert and Soga [24] from lateral drag tests in dry and unsaturated Tokyo Gas sand. This finding has significant implications for practice, as it suggests that methods for calculating the properties of Winkler springs that are based on physical model experiments with the pipe buried in dry sand are not appropriate for the analysis of pipes which backfill is compacted according to standards, even if the backfill is classified as silty sand and features similar grain size distribution (Fig. 2). Note that the uplift factor is in the same range as the results obtained by Wong et al. [36] during uplift tests performed at different pulling rates on 150-mm- and 250-mm-diameter pipes buried in compacted Regina clay. The soil tested by Wong et al. [36] was compacted at 85–90% of its maximum dry unit weight (γ_dry = 12.75–13.5 kN/m³) and its water content was w = 30%, about 1.5% on the wet side of its optimum. According to the WRC presented by Wong et al., the initial suction in their experiments was approximately s = 100 kPa. Some insights on the mechanics behind these high values of uplift factor are provided in the following, from the analysis of further test results.

Fig. 13

a Normalised peak uplift reaction (uplift factor) measured during experiments in compacted sandy loam–Kaolin mixtures with different water content, and during benchmark experiments in dense dry sand. The range of measurements of Wong et al. [35] from uplift experiments in compacted Regina clay are also presented for comparison. b Pipe displacement required to mobilise the peak uplift reaction during experiments in compacted sandy loam–Kaolin mixtures with different water content, and during benchmark experiments in dry sand

The uplift factor measured during soaked experiments (#11–#13) appears to be consistent with the benchmarking experiments in dense dry sand, of similar dry unit weight (Figs. 12d, 13a). As mentioned earlier, the average degree of saturation of tests #11–#13 was determined from six samples retrieved from the soil beds after the experiments, and the average degree of saturation ranged from S_r = 87–88% for the deeper experiments (#12 and # 13) to S_r = 91% for the shallow experiments (#11). According to the WRC shown in Fig. 3, the suction associated with the degree of saturation achieved upon soaking is lower than the air entry suction. This suggests that air is still present only in the form of occluded bubbles, and hence, saturated conditions can be assumed.

Finally, Fig. 13b presents the pipe displacement required to mobilised the peak reaction on the pipe δ_vu,peak. Observe that the response becomes stiffer as the water content decreases (suction increases). Nevertheless, values measured in compacted beds are generally higher than those registered in dry sand. According to ALA [1] for dry sands:

$$ \delta_{{\text{vu,peak}}} = \, 0.0{1} - 0.0{2}H\;\;{\text{for dense to loose sand }} < \, 0.{1}D $$

(5)

These results suggest that the above expression will provide realistic estimates of the displacement required to mobilise the peak reaction only for low water content values (high suction). Nevertheless, we can argue that the effect of suction on the initial stiffness of the reaction–pipe displacement response is rather small, compared to its effect on the uplift factor.

4.3 Failure mechanisms

The magnitude of the reaction force measured during experiments in compacted soil beds, compared to dry sand, arguably cannot be attributed only to the increased soil strength due to suction. To shed some light on the mechanics underlying this phenomenon, we present here the failure mechanisms developing in the soil bed at the peak reaction force and at large pipe displacements. Results depicted in Fig. 10, as well as in other relevant studies [2, 12, 16, 35, 37], demonstrate that the shape of the failure mechanism developing in dry sand during uplift is function of sand density and of the pipe embedment. Recently, Wong et al. [36] postulated that a tensile–shear failure mechanism developed during uplift tests in compacted Regina clay. This mechanism is characterised by the formation of tensile cracks at the pipe springline during the initial stages of pipe uplift, which lead to the formation of a soil beam as pipe displacement increases and cracks propagate towards the surface. Wong et al. explain that the cracks will stop propagating if the confining soil stress is sufficiently large to resist crack opening, and shear failure will develop to resist the increasing load on the soil beam from the pipe. As the load increases further, a tensile crack will appear on the soil surface above the pipe centreline, when the tensile strength of compacted soil is exceeded.

Results of the PIV analysis preformed during this study confirm Wong et al.’s postulation and the formation of the tensile–shear mechanism. These results are depicted in Fig. 14, where we present incremental soil shear strain contours from tests #4–#6 (w_non = 8%). Inclined cracks originating at the pipe springline developed when the peak reaction on the pipe was reached, but these cracks do not propagate to the soil bed surface (as in tests in dense dry sand, Fig. 10). The peak reaction is reached when a vertical tensile crack opens above the pipe centreline ([36], Fig. 15), regardless of test conditions (pipe embedment, water content). Formation of this vertical tensile crack is associated with transition to the softening part of the reaction–displacement curves (Fig. 12). At large pipe displacements, the cracks reach the soil bed surface and a wedge mechanism is formed. However, unlike tests in dry sand this mechanism is independent of the embedment depth (at least for the depths tested here) and is much wider. Therefore, it is not just the increased soil strength due to suction that results in increased resistance to pipe uplift, but also the formation of a different (and wider) failure mechanism. Note that failure mechanisms depicted via incremental shear strains are not always perfectly symmetric with respect to the vertical plane passing through the pipe axis, due to inevitable variabilities in the soil bed and in the imaging analysis method used to obtain incremental strains.

Fig. 14

Incremental shear strain contours developing in soil at the peak reaction δ_vu = δ_vu,peak a–c and at large pipe displacements δ_vu = 0.2D d–f. Results for nominal water content w_non = 8% and pipe embedment H/D = 1.6 (test #4, a, d), H/D = 3.1 (test #5, b, e) and H/D = 4.1 (test #6, c, f)

Fig. 15

Incremental displacement contours developing in soil at the peak reaction δ_vu = δ_vu,peak a–c and incremental shear strain contours developing in soil at large pipe displacements δ_vu = 0.2D d–f. Results for nominal pipe embedment H/D = 3 and nominal water content w_nom = 9.5% (test#8, a, d), w_nom = 8% (test #5, b, e) and w_nom = 6.5% (test #2, c, f)

This behaviour is better illustrated in Fig. 15, which presents results of tests #2, #5 and #8 corresponding to different nominal water contents, but for H/D = 3. Incremental displacement contours depict the failure mechanism at the peak reaction on the pipe, to clearly depict the mobilised soil mass. Incremental strain contours delimit the failure mechanism at large displacements. Notice that the failure mechanism at the peak reaction and at large displacements is independent of the water content (suction). In addition, the inclination of the wedge denoting the mobilised soil mass increases as the water content decreases. The parameters affecting the inclination angle are discussed in Sect. 5.

It is also interesting to compare the failure mechanisms observed in unsaturated soil against the failure mode obtained in soaked material, particularly in test #11 where the highest degree of saturation was achieved. This comparison is depicted in Fig. 16, which presents incremental shear strain contours developing in soil during tests #7 and #11, at the peak reaction and at large pipe displacements. Observe that the mechanism developing in test #11 (soaked) is much narrower compared to the mechanism observed during test #7 and is very similar to the mechanisms observed in dry dense sand for the same H/D (Fig. 10). This explains why the uplift factor measured during test #11 is much lower than that in test #7, and similar to the uplift factor measured during the test in dry dense sand (Fig. 13a).

Fig. 16

Incremental shear strain contours developing in soil at the peak reaction δ_vu = δ_vu,peak a, c and at large pipe displacements δ_vu = 0.2D b, d. Results for nominal pipe embedment H/D = 1.5 and soil degree of saturation S_r = 51.2% (test #7, a, b) and S_r = 91% (inundated test #11, c, d)

4.4 Suction measurements

Table 1 shows that the initial (as-compacted) suction measured with tensiometers S1 and S2 is quite consistent across all experiments, and compatible with the WRC shown in Fig. 3. However, as soil strains develop during uplift, suction does change (see Fig. 5c). Figure 17 shows an example of the evolution of suction during test #5, plotted together with the normalised reaction–pipe displacement curve. Note that as the pipe is pulled upwards, suction in both tensiometers increases. Suction at tensiometer S1, located above the pipe centreline, increases about 30% (13.6 → 18 kPa) before the peak tensile strength is reached. This coincides with the formation of a vertical crack at the surface, the formation of which causes a rapid decrease in suction at S1. Interestingly, suction at tensiometer S2, located in the vicinity of the expected shear plane where tensile stresses do not develop, continues to increase (14.8 → 21.6 kPa) until the peak reaction is reached. After a temporary drop in suction, as shearing continues and cracks propagate to the vicinity of S2, suction increases again. Whereas the secondary increase in suction at S2 may be due to shear straining that occurs along the shear plane, the possibility for the tip of the tensiometer to be detached from the surrounding soil (due to cracking) is also plausible. Hence, the discussion of the suction response is here focused on the pre-failure and peak conditions.

Fig. 17

a Soil suction measured with the tensiometers S1 and S2 during pipe uplift, plotted against the normalised reaction force developing on the pipe. b Location of the tips of tensiometers S1 and S2 and soil cracks that developed when the pipe displacement reached δ_vu = 0.2D. Results from test #5

Suction measurements suggest that, as observed in the direct shear tests, its contribution to the reaction on the pipe is considerably higher compared to the initial suction of the soil bed. To quantify this, Fig. 18 shows the evolution of suction with increasing pipe displacements measured during the 9 unsaturated tests. To facilitate comparison, suction is normalised against the initial values s_1,initial and s_2,initial (Table 1). Potentially unreliable measurements at large pipe displacement are excluded here for clarity. The dashed lines in Fig. 18 denote δ_vu,peak, while the red triangle symbols denote the peak measured suction. Figure 18 confirms that suction at S1, near the soil bed surface above the pipe centreline, increases until the peak reaction is reached or a bit earlier, and then decreases to its initial value as the tensile crack at the surface opens. At relatively large pipe displacements, suction may drop below its initial value, due to the development of cracks that propagate at the vicinity of the shaft of the tensiometer. Peak normalised suction values plotted in Fig. 19 demonstrate that the increase in suction can reach 10–40% and is function of the initial water content, as in the direct shear tests (see Fig. 6), and of the H/D ratio. We postulate that this is associated with the increase in the dimensions of the failure wedge with the increase in H/D and the decrease in w_nom (Figs. 14, 15), leading to the accumulation of higher plastic strains at the vicinity of S1 before opening of the crack. This mechanism is compatible with trends observed for δ_vu,peak in Fig. 13.

Fig. 18

Variation in soil suction with pipe uplift measured with tensiometers S1 and S2 during tests #1–#9

Fig. 19

Variation in peak suction measured a with tensiometer S1 and b with tensiometer S2 during the uplift tests, with nominal water content and pipe embedment

Similar conclusions are drawn from measurements with tensiometer S2, installed to capture suction changes near the shear plane. As result of the different mode of soil deformation, suction at S2 reaches considerably higher peak values compared to S1 viz. 20–60% greater than s_initial. These values are consistent with the increase in suction at the peak shear stress measured during direct shear tests (Fig. 6). We should note here that the location of tensiometer S2 (100 mm from the soil surface and 200 mm from the pipe centreline) remained unchanged regardless of pipe embedment; thus, the measurements from different tests correspond to different locations along the shear plane.

In an attempt to quantify the contribution of suction to the uplift factor, Fig. 20 presents the variation in N_vu,peak against suction measured in the experiments. The N_vu,peak is plotted against: average initial suction measured with both tensiometers s_initial, s_1,peak measured with S1 and s_2,peak measured with S2. The nonlinear variation in N_vu,peak with suction observed in Fig. 20 can be mathematically represented with the following empirical expression:

Fig. 20

Variation in the uplift factor as function of a Initial suction of soil beds. b Peak suction measured at tensiometer S1, s_1,peak. c Peak suction measured at tensiometer S2, s_2,peak

$${N}_{\mathrm{vu},\mathrm{peak}}\left(s\right)=\frac{{F}_{\mathrm{u}-\mathrm{sat}}}{\gamma HDL}\left[1+{\left(\frac{s}{{s}_{\mathrm{ref}}}\right)}^{m}\right]$$

(6)

where F_u-sat is the net uplift reaction force for saturated conditions, s is soil suction, s_ref is a reference suction (1 kPa), γ = γ_dry(1 + w_measured), and m is a fitting parameter that varies between 0.40 and 0.44. Notice that a unique envelope seems to represent the behaviour for H/D = 3 and H/D = 4, while a slightly reduced value of m is required to capture the results for shallower embedment depth (H/D = 1.6). Figure 20 demonstrates that reasonable estimates of N_vu,peak can be obtained even when s_initial instead of s_peak is used. Thus, the calibration of expressions similar to Eq. (6) would require three physical model experiments on soil beds compacted to the same initial density, but different moisture contents: one bed prepared at the optimum moisture content, one bed prepared at a moisture content drier than optimum, and one bed prepared at the optimum moisture content and then soaked prior to testing. Only values of s_initial for these three tests would be required to calibrate the parameter m. It can be noted that only two experiments (saturated and as-compacted) would be required if a linear, more conservative N_vu,peak versus s relationship is assumed.

5 Simplified method for predicting the uplift factor for pipes buried in compacted backfills

As demonstrated above, methods for predicting the uplift factor developed for pipes buried in dry sand cannot be used directly to predict the uplift factor for pipes buried in compacted soil, even if the formula used to calculate the soil shear strength accounts for suction (Eq. 2). A method for predicting the uplift factor for pipes buried in compacted soil needs to account for the shape of the tensile–shear failure mechanism and, ideally, for the variation in suction during uplift. A simplified method, based on the model described in White et al. [35], is presented in the following. The considered tensile–shear failure mechanism is depicted in Fig. 21a. Although development of the failure mechanism commences with the formation of practically horizontal cracks at the pipe springline (see Fig. 15), we consider that the inclined shear planes (dashed lines in Fig. 21a) have been fully formed when the peak reaction force is reached. These shear planes are approximated with straight lines extending from the springline to the soil surface, and we assume that resistance to uplift pipe movement develops along their full length. The vertical tensile crack depicted in Fig. 21 is not considered in the analysis that follows, as we seek to predict only the peak reaction on the pipe, and not the softening part of the reaction–displacement curve.

Fig. 21

a Simplified tensile–shear failure mechanism. b Mohr’s circles of soil element on the shear planes

The peak reaction force F_vu,peak can be split into two parts: The weight of the mobilised soil prism F_w and the mobilised shear resistance along the two shear planes F_s. The former results from the geometry of the problem as:

$${F}_{\mathrm{w}}={\gamma }_{\mathrm{dry}}(1+w)\left({H}^{2}\mathrm{tan}\theta +\gamma HD-\frac{\pi \gamma {D}^{2}}{8}\right)L$$

(7)

where θ is the inclination of the shear planes with respect to the vertical. To calculate F_s, we need to estimate the normal stress acting on the shear planes, and for that we embrace the concept introduced by White et al. [35]: The normal stress σ_n on a soil element along the direction of the shear planes defined by θ remains unchanged as the at-rest vertical stress σ_v0 = γ_dry(1 + w)z + χs increases during pipe uplift (Fig. 21b), and is calculated as:

$${\sigma }_{n}=\frac{1+{K}_{0}}{2}{\sigma }_{v0}-\frac{1-{K}_{0}}{2}{\sigma }_{v0}\mathrm{cos}(2\theta )$$

(8)

where z is the depth measured from the soil bed surface and K₀ is the earth pressure coefficient at-rest for unsaturated soil calculated according to Lu and Likos [17] as:

$${K}_{0}=\frac{v}{1-v}-\frac{1-2v}{1-v}\frac{\chi \mathrm{s}}{{\sigma }_{v0}}$$

(9)

where v is the Poisson’s ratio of the compacted soil, taken equal to v = 0.4. Then, we can calculate the shear resistance F_s by integrating shear stresses as:

$$ F_{{\text{s}}} = \left( {2\mathop \int \limits_{0}^{{H/{\text{cos}}\theta }} \tau {\text{ds}}} \right)L $$

(10)

where τ is the shear strength calculated according to Eq. (2) for c′ = 1.3 kPa and φ = 28.5°.

There are two undetermined parameters in the above equations: The inclination angle θ and suction s. As mentioned earlier, White et al. [35] take θ to be equal to the dilation angle of soil, a reasonable assumption for pipes in dry sand (see also [2]). However, it is clear from the results depicted in Fig. 15 that this is not the case for compacted soil, as θ is grossly higher than the dilation angle measured during the direct shear tests (Fig. 6), and depends on H/D and w_nom (suction). In lack of a more robust method to estimate the inclination of the shear planes, Eq. (11) provides θ as function of H/D and of the initial suction s_initial. Equation 11 results from fitting θ values estimated from the analysis of images captured during the experiments with PIV (Table 2).

$$ \begin{aligned} \theta & = {\rm A}{\text{ln}}\left( {H/D} \right) + B \\ A & = - 0.{\text{48s}}_{{{\text{initial}}}} + {2}.{9} \\ B & = 0.{\text{96s}}_{{{\text{initial}}}} + {3}0.{6} \\ \end{aligned} $$

(11)

Table 2 Input parameters required to estimate the peak reaction to pipe uplift and associated predictions

In addition, in line the with experimental measurements, the suction used to estimate the peak shear strength of soil with Eq. (2) has been taken as the peak suction measured at tensiometer S2, which is 1.2 to 1.6 times the initial suction (Table 2). The lower bound corresponds to shallow embedment depths and the upper bound to deeper embedment depths and relatively low initial suction values.

Outcomes of the simplified prediction method are presented in Table 2 and Fig. 22. Note that the predicted peak reaction values in Table 2 were obtained while using the shear plane inclination angle θ inferred from PIV together with Eqs. (7) and (8). With the exemption of test #6, where issues with the compaction equipment resulted in relatively lower average dry unit weight (Table 2), the predicted values are within 95–105% of the measured ones (Fig. 22). This suggests that possibly higher suction values developed in the shear plane deeper than the location of tensiometer S2. Predictions of the reaction forces measured by Wong et al. [36] for different pipe pulling rates are also included in Fig. 22. Note that use of Eq. (11) to predict the angle θ observed in Wong et al.’s [36] experiments results in unrealistically high values, if the suction from the WRC of Regina clay near the optimum water content is used as input. Therefore, to obtain the predictions depicted in Fig. 22 we set θ = 37º, i.e. the inclination inferred for test #8, as the water content of the soil bed in that experiment was close to the optimum. In this case, the prediction method appears to reasonably capture the results presented in Wong et al. [36], apart perhaps from those tests performed at very slow pulling rates.

Fig. 22

Comparison of predicted and measured peak reaction to pipe uplift

Unquestionably, the above can only be considered as a preliminary attempt towards a practical method for predicting the uplift factor for pipes buried in compacted soil as e.g. Eq. (11) that provides the inclination angle of the shear planes has not been extensively validated against experiments on different backfill materials, different dry unit weight values, or pipes of varying diameters. Still, considering that the observed failure mechanism (Fig. 21) remarkably resembles the mechanism described by [36], who tested larger pipes backfilled with compacted Regina clay, future research efforts should focus on:

• The development of general methods to estimate the inclination of shear planes that are based on (unsaturated) soil mechanics principles and not on fitting of PIV data as Eq. (11),

• The derivation of formulas for predicting the increase in soil suction during pipe uplift in different backfill materials,

• The investigation of diameter scale effects.

6 Concluding remarks

We have presented extensive evidence that suction strongly affects the soil reaction to uplift of pipes buried in compacted backfills. Although this is not an unexpected finding, results obtained during this study suggest that the peak reaction can be up to eight times the reaction that develops on the same pipe initially embedded at the same depth, in dry or saturated soil of similar density and grain size distribution. Such a behaviour has not, to our knowledge, been reported in the literature, and highlights the implications of the outcomes of this study for practice. Specifically, the influence of soil suction on the parameters of Winkler springs for pipe stress analysis should be explicitly accounted for, as our results suggest that current methods are applicable only to pipes backfilled up to the surface of their trench with coarse-grained clean sand, where suction effects are negligible. It is worth noting that the suction values that resulted in the measured high reaction values are in fact quite low, considerably less than 50 kPa. This suggests that even compacted backfill materials classified as silty sands, as the one used in this study, would not fall under the range of application of current methods for determining Winkler spring properties. Using current methods that are based on experiments in dry dense sand would result in underestimating strains on pipes affected by ground movements or overestimating the potential for upheaval buckling of pipes subjected to temperature gradients.

We have also shown that the effects of suction are not limited to increasing the backfill shear strength, but also result in altering the failure mechanism developing in the backfill as result of uplift pipe movement. This means that we cannot simply use existing analytical or semi-analytical models for predicting the uplift factor and modify the soil strength criterion to account for suction. New methods are required that will account for the tensile–shear failure mechanism observed during the experiments and for the increase in suction along the shear planes during pipe uplift as result of soil dilation. A first attempt to formulate such a method for rigid continuous steel pipes, for which the effect of pipe bending on the developing pipe reaction can be ignored, has been presented in this paper. Nevertheless, certain input parameters such as the inclination of the shear planes and the increase in suction along the shear planes have been calibrated on the results of the experiments at hand, and further work is required to validate their application for different pipe sizes and different backfill materials. While repeating the presented experiments for different backfill conditions and pipe sizes would be particularly laborious, this gap could be covered with numerical simulations. In fact, the rationale behind the very detailed presentation of the experimental procedures and results is to allow calibration of numerical modelling techniques on the presented experiments and facilitate further studies on pipe-unsaturated soil interaction.