Development of a novel lateral resistance measurement penetrometer for pipe soil interaction centrifuge model test

Transcription

1 Smart Infrastructure Networks: Sensing, Big Data and Mathematical Methods - Research Article Development of a novel lateral resistance measurement penetrometer for pipe soil interaction centrifuge model test International Journal of Distributed Sensor Networks 2018, Vol. 14(11) Ó The Author(s) 2018 DOI: / journals.sagepub.com/home/dsn Yu Zhang, Zhongtao Wang and Huafu Pei Abstract Offshore pipelines are exposed to potential submarine landslides. It is difficult to measure the impact forces exerted on a pipeline induced by submarine landslides because the upper seabed is very soft and an impact angle exists in practice. Current laboratory experiments are limited on measuring the normal force exerted on pipeline by the slides. This article describes the feasibility and performance of a novel penetrometer, which is designed to measure impact forces of submarine landslides on offshore pipeline including both the normal and frictional forces from variable impact angle in centrifuge test, termed as the lateral resistance measurement penetrometer. The calibration procedure for this particular version is illustrated in detail and the reliability and feasibility of the lateral resistance measurement penetrometer are preliminarily confirmed by an experimental study. Pipe soil interaction centrifuge tests were subsequently performed on a normally consolidated kaolin sample with 40g level conducted in Dalian University of Technology drum centrifuge to investigate the effect of incident angles on the impact forces exerted by submarine landslides on a pipeline. The impact forces deduced from the lateral resistance measurement penetrometer are analysed in comparison with published results. The lateral resistance measurement penetrometer is a potentially valuable device to measure the interaction force between submarine landslides and offshore pipeline, cables and other subsea facilities in small-scale centrifuge models. Keywords Penetrator, submarine landslides, offshore pipeline, impact force, soil resistance, strain gauge Date received: 12 March 2018; accepted: 30 October 2018 Handling Editor: Lalit Borana Introduction Offshore pipelines that carry the hydrocarbon product to shore are exposed to impact risk by submarine landslides because of their length and varied terrain through which they must pass. Normally, pipeline only interacts with the upper ;0.5 m of the soft seabed over very long linear distances, 1 and at these depths, the interaction forces between oblique submarine slides and pipeline are difficult to estimate. Critical issues are therefore what impact forces are exerted on a pipeline by submarine slides that is important for the design of pipeline. 2 The main emphasis of present studies is placed on the evaluation of impact forces from slide material with given rheological properties and moving State Key Laboratory of Coastal and Offshore Engineering and Department of Geotechnical Engineering, Dalian University of Technology, Dalian, P.R. China Corresponding author: Zhongtao Wang, State Key Laboratory of Coastal and Offshore Engineering and Department of Geotechnical Engineering, Dalian University of Technology, Dalian , P.R. China. zhongtao@dlut.edu.cn Creative Commons CC BY: This article is distributed under the terms of the Creative Commons Attribution 4.0 License ( which permits any use, reproduction and distribution of the work without further permission provided the original work is attributed as specified on the SAGE and Open Access pages ( open-access-at-sage).

2 2 International Journal of Distributed Sensor Networks at a given velocity. The general situation is indicated in Figure 1. 3 In the literature, studies of the effect of the incident impact angle on the resulting normal and axial (or frictional) tractions imposed on the pipeline have tended to be conducted with analytical solutions 3 5 and numerical analysis 4,6 8 while fall short in physical laboratory experiments. Flume tests 9 and centrifugal modelling tests were performed to investigate the impact force of submarine slides normal to the pipeline axis in which the axial forces were supposed to be negligible. The lack of experiment verification leads to failure in providing a comprehensive method to estimate the oblique submarine slides impact forces on pipelines. Therefore, in this article, a novel device is developed, which could measure the normal and axial forces acting on the pipeline model at the same time, named by the lateral resistance measurement penetrometer (LRMP) and also an experimental programme is designed and conducted. The origin of LRMP is the vertically oriented penetrometer (VOP) which was designed to assess the shallow strength of soft seabed over continuous horizontal profiles, in which four pairs of strain gauges were mounted on a column for measuring the bending moments to infer the soil resistance. 14 The VOP is convenient to use for inferring the force magnitude and position of application, while it is not easy to determine the force orientation if an incident impact angle exists in practice. In this article, we develop a new device and propose that the LRMP can potentially be used as a means of determining the impact forces on offshore pipeline by submarine landslides. The process can be done by first vertically installing the LRMP with pipeline model mounted at the end to a specified total embedment depth, z t (measured from the mudline to the pipeline middle height) and subsequently dragging the LRMP horizontally along the mudline. In different tests, the pipeline models were mounted via an adjustable screw bolt at various angles with the direction in which the LRMP was travelling. During the process, the four pairs of LRMP strain gauges located at two perpendicular faces above the embedded cylinder portion will measure the bending moments generated due to soil resistance. The bending moments can then be used to infer the impact forces using the same concepts that are applied to assess the active slide-pipeline loadings in soft clay. 10 Compared to conventional penetrometers, the LRMP has the potential to measure soil resistance on the pipeline along continuous horizontal profiles and determine the accurate impact angle, as opposed to fixed direction measurement. The LRMP is simply to operate with low cost and is also easy to extend to infer the interaction forces between submarine landslides and other subsea facilities, like fixed Figure 1. Schematic representation of interaction between submarine landslide and pipeline. 3 platforms and cables by changing structure model at the end. In this article, centrifuge validation tests with four types of pipeline models embedded at the depth of 2D pipe in a normally consolidated (NC) kaolin sample are reported. All tests involved laterally dragging LRMP along the mudline at a constant horizontal translation velocity of 4.6 mm/s to assess the effect of incident impact angle on interaction forces. Impact forces derived from the LRMP are compared to those obtained from the existing model tests in which the incident impact angle equals to 90 to demonstrate the potential of the LRMP and validate the interpretation procedure. The effect of incident angles on the impact forces exerted by submarine landslides on a pipeline is also discussed. Experimental apparatus The LRMP The LRMP, as shown in Figure 2, is a column made from 6061 T6-grade aluminium. For this particular version, the lower part is cylindrical with an outer diameter of 8 mm, as an embedded portion of ;60 mm maximum. The upper part is square in cross section with a side length of 6 mm, and has a 120 mm length for providing a relative large plan where strain gauges can be glued in place. Four pairs of strain gauges, labelled a, b, c and d in Figure 2, are placed on two orthogonal faces and located at 110 and 165 mm, respectively, from the LRMP tip and remained above the soil surface. The metal foil strain gauges are coated with epoxy resin to avoid water ingress. During testing, the lower ungauged part of the LRMP with the model pipe mounted at the end is penetrated to a target depth within the soil and then translated horizontally. The top of the LRMP has a fixed connection to the actuator and the LRMP acts as a cantilever. The strain gauges provide a profile of bending moment above the soil, which can be used to infer the net horizontal force and its point of action as well as orientation.

3 Zhang et al. 3 Figure 2. Schematic representation of LRMP (unit: mm). Figure 3. Photograph of the model pipeline (unit: mm). Dalian University of Technology drum centrifuge A more straightforward approach for simulating the forces exerted by sliding materials impact on pipeline is to move a model pipe at a fixed velocity in a soil sample. Other test parameters such as the soil density and undrained shear strength can easily be varied by conducting test at different stages of consolidation. 10 The centrifuge testing programme described in this article was conducted in the Dalian University of Technology (DUT) drum centrifuge in a NC kaolin sample. At model scale, the channel containment area has a width of 370 mm (measured vertically) and a depth of 240 mm (measured radically). The DUT drum centrifuge has a full diameter (measured to the base of the channel) of 1.4 m and can rotate at up to 875 r/min. A complete description of DUT drum centrifuge and relevant hardware and software upgrades tailored for the high-velocity tests are described by Wang et al. 15 Model pipeline Four model pipes used in the centrifuge tests have the same diameter D pipe of 20 mm (0.8 m diameter in prototype) and were placed at different angles u in the horizontal direction (i.e. the direction the LRMP was travelling), as shown in Figure 3. Both ends of the pipeline were cut into a horizontal plane and polished to eliminate the friction force exerted by slides flow. The results from the additional tests to study end effects are not presented in this article, in which end effects were proven to be negligible for those sizes of pipes. The forces within the flow width of 40 mm shown in

4 4 International Journal of Distributed Sensor Networks Figure 3 were analysed during the simulation; thus, the length of each model pipe was decided. The practical use and interpretation for LRMP The LRMP was first carefully calibrated prior to the application for model test. The top of the LRMP was tightly fixed to a steel square plate through which it was installed on the vertical load wall as a horizontally placed cantilever. The steel square plate was reinstalled at each step by rotating it clockwise at intervals of around 10 0, which consequently changed the angles between the strain gauges and the gravity, as shown in Figure 2. The responding coefficients of each strain gauge, which is defined as the ratio of voltage increment and the load increment, can be easily obtained with stepwise loading method by hanging weights at the end of the LRMP. After a round of calibration, the suspension point was changed to a new position at a distance of 20 mm and the above calibration process was repeated. The four strain gauges form a full-bridge Wheatstone circuit, so the relationship between the responding coefficient of each strain gauge and the calibration load satisfies a sine function. For the first calibration load F 1, the best-fitted expressions (R 2 = 0:97) for the coefficients of strain gauges a and d could be given as follows 8 20:3462 >< k a = ½sinð1:0073 u + 0:2154ÞŠ ð1þ 12:1055 >: k d = ½cosð1:0147 u 1:4359ÞŠ The results from the calibration tests indicates the ratio of the responding coefficients of two strain gauges at the same position is not influenced by the application point when subjected to a fixed force, but the ratio will change with the variation of force direction and the relationship will satisfy a tangent function. In the subsequent analyses, the average of the ratios k a =k c and k d =k b at the two strain gauges glued positions, respectively, is adopted to represent the ratio for a higher precision simulation. The measured variations of the ratios are plotted against the incident loading angles in Figure 4. The ratio can be conveniently approximated by the expression (R 2 = 0:98) (Figure 4) l u = 1:2975 tanð 0:9158u + 1:2746Þ ð2þ which fits the measured results closely and is subsequently used to determine the incident loading angle associated with each pipe test. Also, it is observed that the l u shows a sharp change during the resultant force Figure 4. Calibration data of resultant force angle equation. angle changing from 140 to 180, which will have an influence in the estimation precision. It is suggested to reinstall the LRMP appropriately at a different angle to estimate the inclined angle if the force angle falls into this range. For practical application, the measured response of four strain gauges was recorded when the LRMP is subjected to the lateral loading. The voltage difference of each gauge from the initial value to the steady value was used together to calculate the ratio. It is possible to estimate the incident impact angle directly from l u (equation (2)) by substituting the calculated ratio into equation (2), which yields u = arctan l u, calculated 1:2975 0:9158 1:2746 ð3þ Then, the magnitude and application point of the impact force can be calculated together with the iteration method. First, a hypothetical application point is chosen adjacent to the suspension point in the calibration process. The corresponding coefficients of two strain gauges, k a and k d, for this supposed action point can be suitably assumed to the product of the original coefficients (equation (1)) and the ratio of hypothetical distance to calibration distance. Then, the backcalculated coefficients are used to estimate the bending moments, respectively. The net horizontal force from the soil resistance can be calculated by dividing the bending moment by the distance between the strain gauge and the hypothetical application point. The assumed application point is correct if the net horizontal forces deduced from the measurements of two strain gauges are very close that the difference is within the range of 3%; otherwise, a new application point is assumed and the above procedure is repeated until the

5 Zhang et al. 5 Table 1. Verification test results. Verification test 1 Verification test 2 Verification test 3 F v (N) u ( ) l (mm) F v (N) u ( ) l (mm) F v (N) u ( ) l (mm) Target value Predicted value Error 2.45% 0.15% % 1.27% % 1.99% 21.5 ultimate accurate application point is found. This iteration is proven to be convergent and not difficult to implement in practice. Verification tests were conducted to evaluate the feasibility and performance of the LRMP. A 12.5 N weight (F v ) was hung at the end of the LRMP located at a distance of 88 mm from the strain gauge as shown in Figure 2, and the force direction was changed by rotating the LRMP to be 25:5 8, 35:7 8, 56:2 8, respectively. The verification tests show that the predicted magnitude (F v ), application point (l) and direction of force (u) deduced from the measuring values by LRMP are very close to the target value measured by a highprecision digital ruler and protractor, as shown in Table 1. Thus, the reliability and feasibility of the LRMP are preliminarily confirmed by experimental study. Sample preparation The centrifuge tests were carried out using the UK kaolin clay which allows to conduct a series of tests with good sample consistencies and it was convenient to compare the test results with other centrifuge tests which used kaolin clay such as the work by Sahdi et al. 10 The kaolin clay has the mechanical properties described by Lu et al. 16 To prepare the sample, dry kaolin clay powder was first mixed with water at three times the liquid limit (155%) under vacuum in a customized clay mixer. The well-mixed slurry was then transferred to the whole drum channel while the centrifuge was spinning at an acceleration level of 40g (where the Earth s gravitational acceleration, g = 9.81 m/s 2 ) until primary consolidation was effectively completed. It took 3 days to make soil consolidate and the final clay sample was 125 mm decreased from the initial height of 280 mm which could be monitored by a digital camera fixed on the actuator. The settlement of the soil sample can be feasibly used to derive a rough scope of soil density, consolidation degree and soil strength through the empirical formula summarized by Lu et al., 16 in order to obtain a highly consistent, repeatable experimental condition available. After the primary consolidation was completed, a T- bar with diameter of 5 mm and length of 20 mm Figure 5. Pipe soil interaction drum centrifuge test set-up. was used to measure the shear strength of soil sample at a 0.2 s 21 strain rate. The shear strengths inferred from an initial T-bar penetrations s u in at a depth of z = 2D pipe are represented by the equation s u in = 0: :0138z. And then, the LRMP connected with pipe model was fixed in the front of the actuator for the further test, as shown in Figure 5. Centrifuge testing procedure The LRMP, together with the fixed model pipe, was attached rigidly to an actuator, which can be controlled by the software named EASI-V, capable of a maximum horizontal velocity of rad/s relative to the drum channel (Figure 5) when the centrifuge was spinning at an acceleration level of 40g. All pipe soil interaction tests were conducted by first embedding the pipe model vertically to the desired soil depth of 2D pipe at a penetration rate of 1 mm/s and then dragging the LRMP along the mudline at a constant horizontal translation

6 6 International Journal of Distributed Sensor Networks Table 2. Test programme. Test reference Type of test Pipe embedment (mm) Impact angle ( ) LRMP embedment (mm) Test velocity (mm/s) Strain rate (s 21 ) PS-1 Pipe test PS-2 Pipe test PS-3 Pipe test PS-4 Pipe test S-1 shaft test LRMP: lateral resistance measurement penetrometer. velocity of 4.6 mm/s. The measured response of four strain gauges was recorded during all the pipe model tests. After completion of soil pipe interaction tests, the LRMP without pipe model mounted will be immediately displacing horizontally at the same velocity and the same tip embedment, and the horizontal load from the LRMP itself will be subtracted from the measured load in the soil pipe interaction test. As the interval time of these two types of tests is very short (less than 0.5 h), the soil sample is regarded as maintaining the same properties. Test programme An overview of the test programme is presented in Table 2. The programme involved four pipe tests and one additional so-called shaft test. In the shaft test, only the LRMP itself was embedded at a depth equivalent to the shaft length exposed to the soil during pipe tests and translated laterally. The purpose of the shaft test was to measure independently the forces acting on the connecting shaft under the same conditions as the pipe tests, so the forces acting on the pipe can be isolated. To avoid potential boundary effects, all these tests were conducted at a minimum distance of 5D pipe from the edge of drum channel. Also, a spacing of at least 4D pipe was maintained between test sites to avoid the influences from previously formed footprints. Results of centrifuge tests Resultant force Figure 6 shows a typical example of the force displacement and resultant force angle displacement profiles. It is observed that force acting on pipeline model increases rapidly with the increase in horizontal displacement in the initial stage. The reason is that the moving velocity was relatively small, and the speed of actuator reached stability in a very short time. The force value shows a slight increase with the horizontal displacement increase from 0.2D pipe to 1.5D pipe. This should be caused by the soil around pipe model which was disturbed by the penetration of pipe model. The force due to the soil resistance became almost unchanged when the horizontal displacement exceeded a critical value in the later stage. For subsequent analyses, only the steady force and angle values are considered. These values are extracted, ignoring the initial build-up and decay of force and any initial peak in resistance. The action position of resultant force of pipe tests is approximately located at the middle line of pipe section with an error of 6 2 mm. The reason is that the soil strength of the upper layer of the seabed was almost homogeneous within the scope of the pipe height, although the soil strength increased slightly with the increase in depth. The centrifuge test results are more easily compared with other published results under normalized conditions. The normal force and axial force are normalized through N H = F H s u A H f a = F a s u A a ð4þ ð5þ where N H is the normal coefficient, f a is the axial coefficient, F H is the measured normal force, F a is the measured axial force, A H = L pipe *D pipe /sinu is the normal force acting area, A a = p*d pipe *L pipe /sinu is the axial force acting area and s u is the undrained strength of soil at 2D pipe embedment depth. All pipe soil interaction test results are listed in Table 3. The normal factor, calculated by 90 test data, is 8.83, which is within the scope of 6 10 calculated through centrifuge data proposed by Sahdi. 20 However, the presented N H is lightly higher than the best fitting data 7.35 proposed by Sahdi. 20 It is may be due to the couple effect influenced by the longitudinal flow of slides along the pipe surface that will change the flow mechanics of slides against the pipe model. In addition, the axial force measured in this test is tiny, which can be ignored, meaning that the resultant force angle is 90.

7 Zhang et al. 7 Figure 6. Force value and angle displacement profile for PS-3: (a) resultant force, (b) normal force, (c) axial force and (d) resultant force angle. Table 3. Results of centrifuge tests. Test reference Resultant force (N) Normal force (N) Axial force (N) Resultant force angle ( ) Normal factor, N H Axial factor, f a PS PS PS PS The resultant force angle, u, measured in 30, 45, 60 and 90 tests is shown in Figure 7. In general, resultant force angle decreases with the increase in impact angle u. It is observed that when the impact angle increases from 0 to 30, the resultant force angle decreases from 90 to about 40 sharply. Then, the decreasing trend of resultant force angle slows down with the further increase in impact angle. This trend agrees well with the existing computational fluid dynamics (CFD) results, 8 which shows a faster decrease in resultant force angle at the range of 0 to 30 impact angle. The N H results of different impact angle tests are drawn in Figure 8. When the impact angle is 0, the N H would be 0 in theory because the formal force acting on pipeline would not exist. Liu et al. 8 estimated impact

8 8 International Journal of Distributed Sensor Networks Figure 7. Resultant force angle versus impact angle. Figure 9. Axial factor versus impact angle. sufficient to establish a full-flow mechanism according to existing research results. 10,21 Figure 9 shows the axial factor, f a, of different impact angles, u, including CFD results by Zakeri 6 and Liu et al. 8 All these results show that the axial bearing capacity factor f a decreases with the increase in impact angle. The variation of f a and u can be expressed as follows f a = 1:55 cos ðuþ 1:5 ð7þ Figure 8. Normal bearing capacity factor versus impact angle. forces induced by landslides on pipeline using a CFD approach, and the variation of normal factor N H with the flow angle relative to the pipeline axis is also drawn in Figure 8. Both centrifuge test results and CFD results show a similar changing tendency. So the same estimate equation form is adopted and the best fitting of centrifuge test data can be expressed as follows N H = 9 sin ðuþ 0:85 ð6þ It is noted that the CFD data are bigger than centrifuge test data at the same impact angle. The reason is that in CFD calculation, the pipe is designed to be suspended and free from near-surface effects where a fullflow mechanism is expected to occur. In centrifuge tests, the pipe embedment is 2D pipe (from the top of soil surface to the mid-height of pipe), which is may be not Equations (6) and (7) can be applied to assess the impact force acting on pipeline at 2D pipe embedment condition. It should be noted that as the f a data seem a bit scattered, more tests are needed to modify these equations to give more reliable assessment. Conclusion The feasibility and performance of a novel device named LRMP are evaluated in this article, by means of both the conventional gravity test and centrifuge test in NC kaolin clay. In addition to being able to measure comparable net horizontal force and its associated moment arm with the conventional VOP device, the LRMP as an improved version can be used to determine the incident impact angle generated from the soil resistance when simulating the slides pipe interaction. The oblique load deduced from the LRMP verification test exhibits good agreement with the target values. The limitation of this novel device is that the response of the LRMP is too sensitive when the inclined angle falls into the range of , which will be improved further. At this situation, the LRMP will have to be reinstalled appropriately at a different angle to repeat the model

9 Zhang et al. 9 test to re-estimate the inclined angle for a better precision. The effect of incident angles on the impact forces exerted by submarine landslides on a pipeline was investigated through a series of pipe soil interaction centrifuge tests. Results show that the predicted normal bearing capacity factor and axial factor inferred from model tests have a similar tendency with the published numerical analysis results. The difference is maybe explained by the different measuring means for the soil strength or the different flow mechanics. But it is very possible that those two factors suggested in the literature are overestimated, and more tests need to be conducted in the future for providing a more reliable assessment. This study only shows the usage of the LRMP as a novel device to measure the impact forces by slides on a pipeline; actually, it could be extended to measure the interaction force between submarine landslides and offshore pipeline, cables and other subsea facilities in small-scale centrifuge models by changing the models at the end of LRMP, which makes the LRMP potentially attractive for future use to evaluate the interaction forces and which is important for the design of offshore structures that interact with the shallow seabed. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by National Nature Science Foundation of China under grant nos , and ORCID id Zhongtao Wang References 1. White DJ, Gaudin C, Boylan N, et al. Interpretation of T-bar penetrometer tests at shallow embedment and in very soft soils. Can Geotech J 2008; 47(2): Jeanjean P, Liedtke E, Clukey EC, et al. An operator s perspective on offshore risk assessment and geotechnical design in geohazard-prone areas. In: Proceedings of the international symposium on frontiers in offshore geotechnics, Perth, WA, Australia, 9 21 September 2005, pp Taylor & Francis Group. 3. Randolph MF and White DJ. Interaction forces between pipelines and submarine slides a geotechnical viewpoint. Ocean Eng 2012; 48(7): Boukpeti N, White DJ and Randolph MF. Analytical modelling of the steady flow of a submarine slide and consequent loading on a pipeline. Ge otechnique 2012; 62(2): Yuan F, Li L, Guo Z, et al. Landslide impact on submarine pipelines: analytical and numerical analysis. J Eng Mech 2015; 141(2): Zakeri A. Submarine debris flow impact on suspended (free-span) pipelines: normal and longitudinal drag forces. Ocean Eng 2009; 36(6 7): Zakeri A, Høeg K and Nadim F. Submarine debris flow impact on pipelines part II: numerical analysis. Coast Eng 2009; 56(1): Liu J, Tian JL and Yi P. Impact forces of submarine landslides on offshore pipelines. Ocean Eng 2015; 95: Zakeri A, Høeg K and Nadim F. Submarine debris flow impact on pipelines part I: experimental investigation. Coast Eng 2008; 55(12): Sahdi F, Gaudin C, White DJ, et al. Centrifuge modelling of active slide pipeline loading in soft clay. Ge otechnique 2014; 64(1): Oliveira JRMS, Almeida MSS, Almeidam MCF, et al. Physical modeling of lateral clay-pipe interaction. J Geotech Geonviron Eng 2010; 136(7): Zakeri A, Bloem H and Chi K. Drag forces caused by submarine glide block or out-runner block impact on suspended (free-span) pipelines. Ocean Eng 2013; 67(4): Cheuk CY and Bolton MD. A technique for modelling the lateral stability of on-bottom pipelines in a small drum centrifuge. In: Proceedings of the 6th international conference on physical modelling in geotechnics, Hong Kong, China, 4 6 August Taylor & Francis Group. 14. Sahdi F, White DJ, Gaudin C, et al. Laboratory development of a vertically oriented penetrometer for shallow seabed characterization. Can Geotech J 2016; 53: Wang ZT, Xu B, Luan MT, et al. An introduction to a new drum centrifuge at DUT. Appl Mech Mater 2012; : Lu S, Fan N, Nian TK, et al. Experimental approach for strength of ultra-soft clay by using rheometer. Chin J Geotech Eng 2017; 39(Suppl. 1): (in Chinese). 17. Stewart DP and Randolph MF. A new site investigation tool for the centrifuge. In: Proceedings of the international conference on centrifuge modelling, Boulder, CO, June Rotterdam: Balkema. 18. Stewart DP and Randolph MF. T-bar penetration testing in soft clay. J Geotech Eng 1994; 120(12): Zhu H and Randolph MF. Numerical analysis of a cylinder moving through rate-dependent undrained soil. Ocean Eng 2011; 38(7): Sahdi F. The changing strength of clay and its application to offshore pipeline design. PhD Thesis, The University of Western Australia, Perth, WA, Australia, Martin CM and White DJ. Limit analysis of the undrained bearing capacity of offshore pipelines. Ge otechnique 2012; 62(9):