A Simple Soil-Structure Interaction Model for Indirect ...

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A Simple Soil-Structure Interaction Model for Indirect Damage Assessment of Segmented Concrete Pipelines During PGD A.S. Bradshaw1, A.M. ASCE, P.E., R.A. Green2, M. ASCE, P.E., J.P. Lynch3, M. ASCE, R.L. Michalowski4, F. ASCE, J. Kim5, S.M. ASCE, S. O'Connor5, S.M. ASCE, M. Pour-Ghaz6, S.M. ASCE, S. Nadukuru5, S.M. ASCE and W.J. Weiss7, M. ASCE 1

Assistant Professor, Department of Civil and Environmental Engineering, University of Rhode Island, Kingston, Rhode Island 02881; PH (401) 874-2680; email: [email protected] 2 Associate Professor, Charles E. Via, Jr. Department of Civil and Environmental Engineering, Virginia Tech, 120B Patton Hall, Blacksburg, VA, 24061; PH (540) 231-9826; FAX (540) 231-7532; email: [email protected] 3 Associate Professor, Department of Civil and Environmental Engineering, University of Michigan, 2380 G.G. Brown, Ann Arbor, MI, 48109-2125; PH (734) 615-5290; FAX (734) 764-4292; email: [email protected] 4 Professor, Department of Civil and Environmental Engineering, University of Michigan, 2364 G.G. Brown, Ann Arbor, MI, 48109-2125; PH (734) 763-2146; FAX (734) 764-4292; email: [email protected] 5 Graduate Research Assistant, Department of Civil and Environmental Engineering, University of Michigan, 2340 G.G. Brown, Ann Arbor, MI, 48109-2125 6 Graduate Research Assistant, School of Civil and Environmental Engineering, Purdue University, 1284 Civil Engineering Building, West Lafayette, IN 47907 7 Professor and Associate Head, School of Civil and Environmental Engineering, Purdue University, 1284 Civil Engineering Building, Room G215, West Lafayette, IN 47907; PH (765) 494-2215; FAX (765) 496-1364; email: [email protected]

ABSTRACT This paper describes a simple soil-structure interaction model of a buried segmented concrete pipeline that can be used for indirect health monitoring during Permanent Ground Deformation (PGD). Buried pipelines are difficult to inspect visually, and thus accurate health monitoring systems can improve the efficiency and effectiveness of repair efforts immediately following an earthquake. A Winkler pipeline model is developed for indirect health monitoring that incorporates the two primary modes of failure observed in pipeline experiments, namely telescoping and rotation at the joints. Very approximate estimates of the model parameters are made, and the model results are compared to experimental results. In general the model captures both the magnitude and patterns of joint deformation. However, the model yields axial forces that are two orders of magnitude higher than the measured values. This suggests that the first order approximation of the joint as an elastic beam is inaccurate. Structural

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testing of the joints both in axial compression and rotation will provide more accurate refinement of the joint model. INTRODUCTION Permanent Ground Deformations (PGD) from an earthquake can adversely affect buried pipelines. Buried pipelines are difficult to inspect visually, and thus accurate health monitoring systems can improve the efficiency and effectiveness of repair efforts immediately following an earthquake. Health monitoring of pipelines can be accomplished through smart sensors mounted on or near the pipelines. However, another concept is to utilize indirect damage assessment. In this approach a soilstructure interaction model is developed for the pipeline of interest. The postearthquake ground displacement in the field is measured and this information is input into the model to estimate the loads and deformations in the pipeline. Damage is evaluated by comparing the calculated loads or deformations to the ultimate limit state of the pipeline. The objective of this study was to develop a simple numerical model that can be used for indirect damage assessment of buried segmented concrete pipelines under PGD. Large-scale experiments were performed on a buried pipeline and are described herein, and the results are used to identify the primary failure modes. A simple Winkler pipeline model is developed of the pipeline that captures the major system components and failure modes. Very approximate estimates of the model parameters are made and are used to calculate the deformations and loads that are then compared to the results from the pipeline experiment. PIPELINE EXPERIMENTS Before developing the pipeline model it was necessary to identify the primary failure modes of the pipeline subjected to PGD. The authors have performed three experiments to date on buried segmented concrete pipelines at the NEES Lifeline Experimental and Testing Facility at Cornell University, shown in Figure 1. The experiments involved burying instrumented segmented concrete pipeline in the test basin and subjecting the pipeline to PGD. The experiment completed in 2009 was the first performed on full-scale concrete segmented pipeline. The 2009 test results are briefly summarized herein, and additional details can be found in Kim et al. (2010). The test pipeline consisted primarily of five sections of 2.44 m long segments having an inside diameter of 30 cm and an outside diameter of 41 cm. The pipe segments had bell and spigot type joints that were assembled and grouted in place in the test basin. The pipeline was instrumented with an array of sensors, including strain gages, load cells, LVDTs, and concrete damage sensors. The pipeline was buried in uniform sand backfill with a depth of cover of 81 cm. The backfill properties were carefully controlled and measured using a nuclear density gage. The average total density for the 2009 experiment was determined to be 1,756 kg/m3, and the dry density was

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1,686 kg/m3. The effective friction angle of the soil was about 40 (O’Rourke et al. 2008).

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at this density

Figure 1. Pipeline testing basin at Cornell University. The pipeline was subjected to compressive and shear loads by moving one half of the test basin along a fault that was oriented at 50 degrees to the longitudinal axis. The movable half of the basin was displaced along the fault in 12 steps, 2.5 cm each, with a short waiting period after each step. At the completion of the test, the pipeline was excavated to record the observed damage. As shown in Figure 2 structural failure occurred at the joints, with the majority of the damage occurring at the joints closest to the fault line. The modes of joint failure included telescoping, where the spigot pushed into the bell, and rotational type failure.

(a)


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(b) Figure 2. Photographs showing the (a) deformed pipeline after ground rupture and excavation, and (b) telescoping and rotational failure of a joint nearest the fault. WINKLER PIPELINE MODEL The pipeline experiments indicated that the damage was confined to the joints, with no damage to the body of the pipe segments (Figure 2). Therefore, a Winkler pipeline model was developed to focus on the telescoping and rotational failure modes at the joints, as shown in Figure 3. Simple models of this type have been used previously to analyze buried pipelines (e.g., O’Rourke et al. 2003). In the model used herein, the pipe segments were treated as elastic columns connected by pins. Rotational stiffness of the joint was modeled by rotational springs having stiffness kθj, and the axial stiffness of the joints was modeled by axial springs having stiffness kaj. The soil reaction was modeled by axial springs having stiffness ksx and lateral springs having stiffness ksy. fault line ksx

δx ke δy

ksy

kθj

Figure 3. Winkler pipeline model used for segmented concrete pipe. Note that the boundary conditions include displacement of the left side of the test basin shown as δx and δy in Figure 3. The equations for this model are given in the Appendix. In this study, it was assumed that all springs are linear, but the model can also be modified and used for nonlinear analyses. The bodies of the pipe segments did not show any structural damage and thus are modeled as elastic beams having axial and bending stiffness, respectively, of:

kap =

(AE) p l

(1)


krp =

3(EI) p l3

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(2)

where (AE)p = axial stiffness of pipe, (EI)p=rotational stiffness of pipe, l=length of pipe segment. The elastic modulus of the pipe was estimated from the compressive strength of the concrete specified by the pipe manufacturer. The configuration of the joint is complex, but as a first approximation, it is modeled as an elastic beam having axial and rotational spring stiffness, respectively, of:

kaj =

kθj =

(AE) g lg (EI) g

(3)

(4)

lg

where (AE)g=axial stiffness of grout ring in joint, (EI)g=rotational stiffness of grout ring, and lg=length of grout ring. The elastic modulus of the grout was estimated from the compressive strength measured on specimens tested in the laboratory. The soil spring constants were estimated from existing p-y and t-x curves from ASCE (1984). The axial soil resistance per unit length of pipe is estimated from the following:

t u = πDHγ

1+ K 0 tan δ 2

(5)

where D=outside diameter of pipe, H=depth of soil above the center of the pipeline, γ=average moist unit weight of soil, K0=lateral earth pressure coefficient at-rest, and δ=interface friction angle. The soil spring constant corresponding to half of a segment of pipe is determined from the following expression:

ksx =

tul 2Δ t

(6)

where Δt=mobilizing displacement in the axial direction. Since the soil was compacted, K0 was assumed to be 1.0. For dense sand Δt was assumed to be 3 mm. The maximum lateral resistance per unit length of pipe (pu) is given by:

pu = N qhγ H D

(7)

where Nqh=horizontal bearing capacity factor for sand. Nqh depends on friction angle of the soil and the ratio D/H and was estimated to be 15.6 for the test conditions. The mobilizing displacement in the lateral direction is given by:

⎛ H D⎞ Δ p = 0.03⎜ + ⎟ ⎝2 4⎠

(8)


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For the test, Δp was calculated to be 1.8 cm. The lateral soil spring constant for half of a pipe segment is given by: ksy =

pu l 2Δ p

(9)

COMPARISON OF RESULTS

The model was used to calculate the rotation and compression of the joints and the load at the ends of the pipeline in the 2009 experiment. These quantities were measured in the pipeline experiment and therefore could be directly compared to the model results. The measured and modeled joint rotations are shown in Figure 4, the measured and modeled joint compressions are shown in Figure 5, and the measured and modeled axial forces at the pipeline ends are shown in Figure 6. To simplify the figures, only selected actuation steps (i.e. 2, 4, 6, 8, and 10) are shown in the figures. The modeled joint rotations shown in Figure 4 compare very well to the measured rotations, specifically at the joints closest to the fault line (Joints 2 and 3). The agreement was not as good at the joints further from the fault line (Joints 1 and 4) as the modeled joints showed a significantly stiffer response than the measured response.

Figure 4. Comparison of modeled and measured joint rotations. The measured joint compression data in Figure 5 clearly shows the complex behavior of the pipeline joints during PGD. The absence of a clear trend in the measured data


is the result of progressive joint failure and load redistribution within the pipeline during each actuation step. Note that significant damage was observed beginning at about the fifth actuation step. However, the model results show joint compressions that are the same order of magnitude as the measured results.

Figure 5. Comparison of measured and modeled axial compression of the joints. The modeled axial forces at the ends of the pipeline, shown in Figure 6, are significantly higher than those measured in the experiment. The modeled forces were two orders of magnitude higher and thus are shown on a log scale in Figure 6. The deformations shown in Figures 4 and 5 are consistent between the model and experiment, yet the forces in Figure 6 are different by orders of magnitude. This suggests that the axial stiffness of the model pipeline is much too high. It is likely that the body of the pipe segments remained in the elastic range during testing and thus the elastic beam model accurately represents the axial stiffness of the bodies of the segments. However, given the complex behavior of the joints, a simple elastic beam model is not robust enough to accurately model the observed joint behavior. A more accurate assessment of the joint stiffness both in the axial and rotational modes could be made through structural testing of the joint. Once the model is refined and calibrated it is anticipated that it can be used for indirect structural health monitoring. This can be accomplished by predicting the load (moments) or deformation (rotation) at the joint and comparing to those required to reach the ultimate limit state (i.e. failure) of the pipeline. Failure for water distribution pipelines may be defined as leakage that would occur from cracks in the pipeline structure. Given that the boundary conditions are specified as displacements, it may

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be appropriate to use deformation limit states (i.e. joint rotation or joint compression at failure) as a means to evaluate the level of damage. Again, these deformation limit states would have to be evaluated through structural testing of the joint.

Figure 6. Comparison of modeled and measured forces at the ends of the pipeline. CONCLUSIONS

This paper presented the concept of indirect damage assessment of buried segmented concrete pipelines subjected to permanent ground deformation. The method relies on an accurate soil-structure interaction model. Before the model was developed, pipeline experiments were performed and then used to identify the major failure modes. These modes were incorporated into a simple Winkler model that is summarized in the Appendix. The model was used to estimate the rotation and compression of the pipeline bell and spigot joints, as well as reaction forces at the ends of the pipeline. In general the model captured both the magnitude and patterns of joint deformation. However, the model yielded axial forces that are two orders of magnitude higher than the measured values. Structural testing of the joints both in axial compression and rotation will provide more accurate refinement of the joint model. Assessment of the limit states of the pipeline joints, in particular the rotation and compression at failure, will allow the model to be used as an indirect structural health monitoring tool.

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APPENDIX. PIPELINE MODEL

The equilibrium equations for the discretized concrete segmented pipeline system have the following general form:

{f } = [k ]{u}

(10)

where {f}=external applied force vector, [k]=stiffness matrix, and {u}=joint (i.e. node) displacement vector. If the stiffness matrix and external applied forces are known, the displacements can be determined:

{u} = [k ]−1{F }

(11)

The joint displacement vector is comprised of translation in the longitudinal x and transverse y directions:

{u} = {u1 u2 .. uN v1 v 2 .. v N } T

(12)

where ui = joint displacement in the x-direction at joint i, and vi=joint displacement in the y-direction at joint i, N = number of joints. The external forces result from the movement of the boundary conditions on the north end of the test basin that have the following general form:

{ F } = { ( ke + k sx ) δ x 2ksxδ x .. 0 k syδ y 2ksyδ y .. 0} T

(13)

where ke=spring constant of the end restraint, ksx= axial soil spring constant for ½ the pipe segment length, ksyi=lateral soil spring constant for ½ the pipe segment length, δx=displacement of boundary in longitudinal direction, δy=displacement of boundary in transverse direction. The displacements can be expressed in terms of the fault rupture length:

δ x = δ cosθ

(14)

δ x = δ sinθ

(15)

where δ=fault displacement, and θ=angle of fault line relative to longitudinal axis of pipeline. The general form of the stiffness matrix was assembled using the direct stiffness method:


⎡ k +k +k ⎢ e sx a ⎢ −ka ⎢ .. ⎢ 0 ⎢ [k]=⎢ 0 ⎢ ⎢ 0 ⎢ .. ⎢ ⎢ 0 ⎣

−ka

..

0

0

0

..

2ksx +2ka ..

0

0

0

..

.. 0

.. 0

.. ..

−kr

..

.. 0

.. .. .. ksx +ka+ke

0

..

0

ksy+kr

0

..

0

−kr

.. 0

.. ..

.. 0

.. 0

2ksy+2kr .. .. 0

.. ..

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⎤ ⎥ 0 ⎥ ⎥ .. ⎥ 0 ⎥ ⎥ 0 ⎥ 0 ⎥ ⎥ .. ⎥ ksy+kr ⎥ ⎦ 0

(16)

where ka=axial stiffness of pipeline considering pipe and joint stiffness, kt=rotational stiffness of pipeline considering pipe and joint stiffness. In the axial direction the joint spring and pipe spring are in series and therefore the equivalent axial stiffness is given by:

ka =

k aj kap k aj + k ap

(17)

where kaj=axial stiffness of joint, kap=axial stiffness of pipe segment. An equivalent rotational stiffness is calculated in the same manner:

kr =

krj krp k rj + krp

(18)

where krj=rotational stiffness associated with joint rotation, and krp=rotational stiffness of the pipe segment. The joint is modeled as a rotational spring and therefore:

krj =

kθj l2

(19)

where kθj=rotational stiffness of joint (in units of moment per radians). The axial forces and moments in the joint are calculated by the following: (20) (21) where Δu=change in the longitudinal displacement between adjacent nodes, Δu=change in transverse displacement between adjacent nodes. The joint compression (cj) and rotation (θj), respectively, are evaluated from the following:


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(22)

(23) Note that θj only accounts for the rotation on one side of the joint thus the total rotation at a specified joint is obtained by subtracting the rotations on each side of the joint. ACKNOWLEDGEMENTS

This study was supported by the National Science Foundation under Grant No. CMMI-0724022. This support is gratefully acknowledged. We also thank the Cornell University team and the Undergraduate Research Assistants from Merrimack College including Gail daSilva, Stephanie Kearns, and Richard Matson for their efforts on the project. REFERENCES

ASCE (1984). Guidelines for the Seismic Design of Oil And Gas Pipeline Systems. ASCE TCLEE Committee on Gas and Liquid Fuel Lifelines, ASCE, Reston, VA., 473 p. Kim, J., O'Connor, S., Nadukuru, S., Pour-Ghaz, M., Lynch, J.P., Michalowski, R.L., Green, R.A., Bradshaw, A. and Weiss, W.J. (2010). “Behavior of Full-Scale Concrete Segmented Pipelines under Permanent Ground Displacements.” Proceedings of SPIE Conference: Smart Structures/NDE 2010, San Diego, CA. O'Rourke, M.J., Gadicherla, V. and Abdoun, T. (2003). “Centrifuge Modeling of Buried Pipelines”, Sixth U.S. Conference and Workshop on Lifeline Earthquake Engineering, Long Beach, CA. O’Rourke, T.D., Jezerski, J.M., Olson, N.A., Bonneau, A.L., Palmer, M.C., Stewart, H.E., O’Rourke, M.J., and Abdoun, T. (2008). “Geotechnics of Pipeline System Response to Earthquakes.” Proceedings of Geotechnical Earthquake Engineering and Soil Dynamics IV, ASCE, Sacramento, CA, May, 2008.