shear capacity analysis of proposed piles for the...

Shear Capacity Analysis of Proposed Piles for the Mühleberg Dam

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Report No. 2012008.00

10 July 2012

LS-DYNA Shear Capacity Analysis of Proposed Piles for the Mühleberg Dam

Prepared for

BKW FMB Energie AG Kemkraftwerk Mühleberg

CH-3203 Mühleberg Switzerland

Prepared by

10 July 2012

10 July 2012

Table of Contents 1. Introduction 1

2. Description of Pile Model 1

3. Material Properties 2

3.1 Rock Properties 2

3.2 Concrete Properties 2

3.3 Steel Pipe Properties 5

3.4 Steel-concrete bond strength 8

4. Material Models 8

4.1 Concrete Constitutive Model 8

4.2 Steel Constitutive Model 8

5. Method of Analysis 9

6. Analysis Results 9

7. Median Capacity and Variability Results 12

8. Conclusion 15

References 16

APPENDIX A A-l

List of Tables Table 1. Finite-element model statistics 2 Table 2. Rock properties 2 Table 3. Median and variability of concrete compressive strength 3 Table 4. Median and variability of concrete tensile strength 4

Table 5. Median and variation of steel yield and ultimate strengths 5 Table 6. Median and variability of steel fracture strain 7 Table 7. Summary results of all runs 11 Table 8. Summary of averaged shear caapcities 11 Table 9. Normal Distribution Fit 13 Table 10. Combined Results 14

List of Figures Figure 1. Plan view of Turbine Building showing piles as green circles 17 Figure 2. Turbine Builkding profile showing location and depth of piles 17 Figure 3. Weir plan showing location locaiton of piles in brown circles 18 Figure 4. Weir profile showing location and depth of piles 18 Figure 5. Complete finite-element mesh with concrete-filled steel pile at the center 19 Figure 6. Model cross section through centerline 19 Figure 7. Details of Concrete-filled steel pile 20 Figure 8. More details of concrete-filled steel pile 20 Figure 9. Idealized stress-strain curve for S460 steel provided by BKW 21 Figure 10. Estimated triaxiality factor for shell elements S30048 and S11004 22 Figure 11. Meridians and the cross sections of the failure surface 23 Figure 12. Elastic-plastic behavior with isotropic and kinematic hardening 23 Figure 13. Velocity-controlled displacement loading from 0 to 10 cm in 10 second 24 Figure 14. Contours of pile displacement with concrete cracking before and at failure 24 Figure 15. Contours and history of effective plastic strain for shell Element S30022 25 Figure 16. Contours of pile displacement at failure 25 Figure 17. Force-displacement plots for all cases analyzed 26 Figure 18. Force-displacement plots for median and median minus standard deviation cases 27 Figure 19. Force-displacement plots for median and median plus standard deviation cases 28 Figure 20. Force-displacement plots for median and/'c± standard deviation cases 29 Figure 21. Force-displacement plots for median and/ ' t± standard deviation cases 30 Figure 22. Force-displacement plots for median and/y ± standard deviation 31

Figure 23. Force-displacement plots for median and £u ± standard deviation 32

Pile Shear Capacity Analysis July 10. 2012

Shear Capacity Analysis of Proposed Piles for the Mühleberg Dam

1. Introduction

Concrete-filled steel pipe piles have been proposed to improve the Mühleberg Dam performance under seismic loading and reduce the risk the dam poses on the Mühleberg Nuclear Power Plant. A preliminary design prepared by BKW indicates that this can be accomplished by stitching the slip surface beneath the dam using a total of 48 piles under the Turbine Building and 24 under the Weir section. The Turbine Building piles will be distributed equally among the eight turbine units, 6 piles per turbine or per 11.5-m width. The Turbine Building piles will be installed along the downstream toe of the structure within the outlet openings (Figures 1 and 2). The Weir piles will be distributed 4 each in five of the upper arch openings and 2 each in the upper arch openings on either side of the separator wall (Figures 3 and 4). The piles will be 18 m deep and will be designed using a 1500-mm-diameter borehole with a 1200-mm-diamter steel pipe. The boreholes will be filled with concrete and the 22-mm-thick steel pipes will be vibrated in place to create a composite concrete-filled steel pipe pile.

The preliminary design of the piles is based on code procedures and a shear capacity in pure shear that ignores interaction with the surrounding rock. For computation of shear capacity using code procedures refer to Appendix A. We believe that the actual shear capacity of the piles is influenced by the relatively soft surrounding rock and the slip surface that passes along the bottom of the dam shear keys. The purpose of this study is to estimate the median and variability of the pile shear capacity under the field condition using an LS-DYNA model of a single pile that includes the pile, the surrounding rock, and the slip surface. The pile fragility obtained in this manner will be used subsequently to evaluate seismic fragility of the dam with the piles.

2. Description of Pile Model

A single pile with the surrounding rock is modeled in LS-DYNA and subjected to velocity-controlled lateral displacements up to failure to obtain its shear capacity. Figure 5 shows the complete finite-element mesh with boundary supports and the direction at which lateral displacements are exerted. The rock surrounding the pile is modeled as two parts: a fixed lower part, and a moving upper part. This is intended to simulate potential movements along a slip surface observed beneath the dam, by allowing the upper part sliding on top of the lower part and loading the pile to failure. The surrounding rock is modeled using elastic 3D solid elements with properties consistent with the top 10-m rock layer beneath the dam. The length of the pile and depth of the surrounding rock is set to 10 m to simulate both bending and shear responses of the pile. The 1200-mm-diamter steel pipe is represented by shell elements using plastic-kinematic material properties (Figures 6 to 8), which allows yielding, plastic deformation, and rupture when the steel reaches its ultimate strain. The concrete inside the pipe and in the annulus between the pipe and the rock is modeled using Winfrith [1] nonlinear concrete model, which permits tensile cracking with shear transfer across the crack due to aggregate interlock. The model includes four contact surfaces: 1) between the pile and rock to simulate pile separation from the rock, 2) between the concrete core and steel pipe to model steel-concrete bond strength, 3) between the upper and lower rock to permit sliding along the slip surface, and (4) through the pile at the slip surface to obtain pile shear forces. Table 1 summarizes

Page 1


the finite-element statistics in terms of number of nodes, elements, and contact surfaces used in the model.

Table 1. Finite-element model statistics.

No. of nodal points

No. of elastic 3D solid rock elements

No. of 3D solid Winfrith nonlinear concrete elements

No. of nonlinear plastic-kinematic steel shell elements

No. of contact surfaces

32,218

7,700

5,828

2,048

4

3. Material Properties

Two concrete and two steel input parameters were judged to significantly influence the shear capacity of the concrete-filled steel pipe piles. These include compressive and tensile strengths of the concrete with yield strength and fracture strain of the steel. The choice of these parameters is reasonable since they are the primary input parameters characterizing the constitutive models discussed in Section 4. Only these four parameters will be varied to estimate variability of the pile shear capacity. All other parameters will be kept unchanged at their median level.

3.1 Rock Properties

The basic input median parameters for the top 10-m rock layer used in the analysis are the same as the values used in previous analyses [2], as summarized in Table 2 below.

Table 2. Rock properties.

Elevation (m)

460-448

Unit Weight (kN/m^)

23.5

Shear Modulus

(MPa) 1,100

Poisson's Ratio

0.46

Modulus of Elasticity

(MPa) 3,212

3.2 Concrete Properties

The basic input parameters for the Winfrith concrete model includes: initial tangent modulus of concrete, Poisson's ratio, uniaxial compressive strength, uniaxial tensile strength, crack width at which tensile stress goes to zero, and the aggregate size for shear transfer.

A median weight density of 2500 kg/m'', a Poisson's ratio of 0.2, and a maximum aggregate size of 32 mm were assumed for the concrete. Variability of these parameters on the shear strength of the pile was assumed not to be significant. The concrete compressive strength and tensile strength were selected as the two significant parameters that could influence the shear strength of the pile. The concrete modulus of elasticity varies proportionally to square root of the compressive strength and is not considered as an independent variable.

Page 2


Table 3 summarizes estimates of the median and variability of compressive strength of the concrete from the specified 28-day minimum and median values for the SIA262 Concrete. The specified 28-day median cylinder strength of 38 MPa is increased by a factor of 1.20 to obtain a long-term median cylinder strength value of 45.6 MPa. The median cylinder strength is divided by 0.85 to obtain median cube compressive strength of 54 MPa for input to LS-DYNA.

The unconfmed compressive strength input to Winfrith is 54 MPa with a strength ratio of 0.06 if,'lfc' = 3.19/54), a density of 2500 kg/m3, containing aggregate of 32 mm diameter, and specified to have a crack width of 0.1mm when no tensile force exists (controls tensile softening). The strain rate effects are turned off

A unit cube was modeled and tested in LS-DYNA to verify that the cube compressive strength and not the cylinder compressive strength is the input to LS-DYNA. The model boundary conditions consisted of prescribed axial displacement on the top of the unit cube with the lateral surfaces traction free, while the bottom surface was constrained against only axial motion. The results indicated that the cube develops a vertical crack and fails at a displacement consistent with the unconfmed compressive strength of 54 MPa, which is the same as the cube strength.

Table 3 . Median and variability of concrete compressive strength.

SIA262 Concrete

28-day minimum cylinder compressive strength (95% confidence),/,,,«,,

28-day median cylinder compressive strength,y .,„

Long-term cylinder median compressive strength (/ .„, = 1.2 x 38 = 45.6)

Concrete median modulus (£"„„ = 4700 V45.6 = 31,738)

Median concrete aggregate size

Compressive Strength

30 MPa

38 MPa

45.6 MPa

31,738 MPa

32 mm 1

28-day median cube compressive strength (fcuhe.m = 38/0.85= 45)

Long-term median cube compressive strength (= 45.6/0.85)

45 MPa

54 MPa

Lognormal standard

ß^ = In — 1.65 1 38 j

deviation (SD) for compressive strength

= 0.14

Lognormal SD for aging, ß„ (from NUREG/CR2320, median age factor 1.2)

Lognormal SD for uncertainty in compressive strength

/? = V(0.14)'+(0.l) ' =0.17

0.14

0.1

0.17

1

16"'-percentile cube compressive strength for fragility (54x e"*"'' = 45.56)

84*-percentile cube compressive strength (54x e"'^ = 46.00)

45.56 MPa

46.00 MPa

Pages


The median and variability of the concrete tensile strength are summarized in Table 4. A 28-day median tensile strength of 2.9 MPa was specified for the concrete consistent with the SIA262 Specifications. However, considering that tensile strength of the concrete is proportional to the square root of its compressive strength, the long-term age factor for the tensile strength was taken as the square root of the 1.2 factor used for the compressive strength. The lognormal standard deviation for tensile strength aging was assumed to be one-half of the 0.1 used for the compressive strength aging. The lognormal standard deviation for the tensile strength was estimated from division of the specified standard deviation of 0.6 MPa by the specified 28-day median strength of 2.9 MPa specified by BKW.

Table 4. IVIedian and variability of concrete tensile strength.

SIA262 Concrete

Specified 28-day median tensile strength

Age factor for long-term tensile strength

is taken as vl -2 = 1.1, since/? is proportional to y / J

Long-term median tensile strength /; = 2.9x l.l = 3.19

Tensile Strength

2.9 MPa

1.1

3.19 MPa

1

Lognormal SD for tensile strength aging use 1/2 ofthat for compressive strength (0.1/2 = 0.05)

Lognormal SD for tensile strength (Coefficient of Variation = 0.6/2.9)

Lognormal SD for uncertainty in tensile strength

^ = V(0.05)' + (0.2l)' =0.22

0.05

0.21

0.22

1

16*- percentile tensile strength (3.19xe-°22 = 2.56)

84* - percentile tensile strength (3.19xe°-'2 = 3.97)

2.56 MPa

3.97 MPa

Page 4


' i p e tics

The basic input parameters for the steel pipe include the modulus of elasticity, Poisson's ratio, yield strength, slope of strain hardening, and failure strain. Typical values of 7.85 kg/m^ for mass density, 2.0E+08 kN/m^ for elastic modulus, and 0.3 for Poisson's rafio were used. The minimum and median values of the yield and ultimate strengths were provided by BKW in accordance with EN 10204 specificafions, as summarized in Table 7. Assuming a lognormal distribution, the strength variability was estimated from the minimum and median strength values. The specified minimum values were at 95% confidence interval with a 5% chance of being lower. Based on computed lognormal standard deviations of 0.06 for the yield strength and 0.02 for the ultimate strengths, the 16% and 84% non-exceedance probability (NEP) strengths are also shown in Table 7.

The ultimate strength is not an independent variable. Its effect is reflected in the slope of strain hardening needed as input to LS-DYNA (see Section 4.2). The slope of strain hardening was determined by idealizing the specified stress-strain curve (Figure 9) into a bilinear stress-strain curve similar to Figure 12. This was achieved by connecting the median yield point (490 MPa) in the stress-strain curve to the median ultimate strength (560 MPa) at corresponding \6% strain and measuring the slope.

Table 5. Median and variation of steel yield and ultimate strengths.

Steel P460 NL2 or S460 NL according to EN 10204

Minimum yield strength (95%) confidence) -/>.,„„„

Median yield strength -fy,„

Lognormal SD for une

ß„ = In ' 1.65 U90v

ertainty in yield strength

= 0.06

16*-percential yield strength (490xe-°°'' = 460.6)

16th-percential yield strength (490x6""^ = 520.30)

Steel Strengths

445 MPa

490 MPa

0.06

461.46 MPa

520.30 MPa

1 Minimum ultimate strength (95% confidence),/,,,,,,,,

Median ultimate strength, f,,,,,

lognormal SD for unct

ß„ = In 1.65 U60J

;rtainty in ultimate strength

= 0.02

16*- percentile ultimate strength (560x6-"°^ = 548.91)

84* - percentile ultimate strength (560xe°°' = 548.91)

540 MPa

560 MPa

0.02

548.91 MPa

548.91 MPa

Page 5

Pile Shear Capacity Analysis July 10,2012

The median and variability estimates of the fracture strain are given in Table 6. Only the minimum uniaxial fracture strain of 16% was specified in EN 10204. The median uniaxial strain at fracture was assumed to be 18.4%, or 15% higher than the minimum. For three-dimensional analysis the uniaxial fracture strain should be further adjusted for the effects of as-built configuration (i.e., welds, fabrication, etc.) and triaxial state of stress, which are known to reduce the strain magnitude at failure.

In the literature, a factor in the range of 1 to 1.25 is reported for the effects of as-built configuration. We use the larger factor of 1.25 to obtain a reduction of 0.8 (1/1.25=0.8) for the configuration effects.

For reduction due to triaxial state of stress, we use Davis' triaxiality factor adapted by Manjoine [3]:

TF--(T, + (Tj -1- (T3

2 [ (^1 - Ö-2 ) ' + (ö-2 - 0-3 ) ' -f (C73 - Ö-, ) ' (1)

Where CTI, 0-2, and 03 are the first, second, and third principal stresses at critical points expected to undergo large plastic deformations. TF for the steel pipe was estimated for two shell elements S30044 and SI 1004 located where plastic deformation and rupture of the steel was expected (Figures 10a and 10b). This was accomplished by extracting principal stresses for these elements from the LS-DYNA pile analysis for median values and substituting them in Equation 1 above. The resulting TF's for the entire duration of the analysis are plotted in Figures 10c and lOd. Based on these results, a median triaxiality factor of 1.8 with a maximum value of 2.0 was conservatively estimated. According to Manjoine the strain reduction factor due to triaxiality is given by:

reduction factor — ,2'-"'-TF (2)

Substituting TF=1.8 in the above equation gives a TF reduction factor equal to 0.566. Applying the configuration (0.8) and triaxiality (0.556) reduction factors to the median uniaxial strain of 18.4% results in a median fracture strain of 8.2% for the 3D pile analysis.

Variability for the uniaxial strain is estimated from the specified minimum value (16%) with a 5% NEP and the median value (18.4%) using lognormal distribution, as shown in Table 6.

Variability for the as-built configuration reduction factor is estimated from factor of 1.0 having a 1% NEP and median factor of 0.8, as shown in Table 6.

Variability for the triaxiality factor is estimated from the maximum TF of 2.0 with 5% NEP and median TF of 1.8, as shown in Table 6.

Finally, the total variability due to all three reduction factors is obtained from the square-root-of-the-sum-of-the-square (SRSS) of individual variabilities. This results in a total variability of 0.14 from all sources, which produces a 16* -percentile and 84* -percentile failure strains of 7.1% and 9.5%, respectively.

Pages


Table 6. Median and variability of steel fracture strain.

Steel P460 NL2 or S460 NL according to EN 10204

Minimum specified elongation strain at fracture, £f,min

Median elongation strain at fracture, Efm Estimate median is 15% higher than the min. ( 1.15xQ. 16 = 0.184)

Assumed median strain capacity reduction for configuration (fabrication, welds, etc.) F„m

Triaxiality reduction factor

Median effective strain capacity (0.184x0.80x0.556 = 0.138)

Lognormal SD for uniaxial strain at fracture

1 f i ^ ß = In =0.085

1.65 U-15J Lognormal SD for

ß = In — 2.33 V0-8J

Lognormal S

ß = ^ \n 1.65

Dfor r2.o^

the strain capacity reduction for welds

= 0.096

triaxiality factor

= 0.064

Lognormal SD for uncertainty in fracture strain

ß = 7(0.085)' + (0.096)' + (0.064)' = 0.14

16*-percentile effective strain (0.82xe"'"'' = 0.071)

64* -percentile effective strain (0.82x6°''' = 0.095)

Strain at Fracture

16%

18.4%

0.80

0.556

8.2%

0.085

0.096

0.064

0.14

7.1%

9.5%

Page 7


3.4 Steel-concrete bond strength

A median shear and tensile bond strength of 2.5 MPa was used for the steel-concrete interface. This value was recommended by^^^^ fHj j j ^HHj and is consistent with anchorage bond test results obtained for plain round steel bars by Snowdon [4].

The median friction coefficient between the steel pipe and concrete for input to LS-DYNA analysis was obtained from tests conducted by Rabbat and Russell [5]. The average effective coefficient of friction from these tests varied between 0.57 and 0.70 for dry and wet interfaces. In this study a conservative coefficient of friction of 0.60 was used.

4. Material Models

4.1 Concrete Constitutive Model

The Winfrith concrete model is based on the shear failure surface proposed by Ottosen [6]:

F{L,J , ,cosW) = a ^ ^ + X ^ ^ - + b h - \ (3)

This is a four-parameter constitutive model, where a and b control the meridional shape of the shear

surface, and /l = A (cosiO) varying in the range of -1 < cosiO <+\ for triaxial compression to triaxial

extension control the shape of the shear failure surface on n- plane. In addition to an explicit dependence

on the unconfmed compressive strength, f , the constants a and b also depend on the ratio of the

unconfmed tensile strength, / , to the unconfmed compressive strength. Figure 11 shows the meridians

and the cross sections of the failure surface. In the above equation, /y is the first invariant stress tensor, and J2 and Jj are the second and the third invariant deviatoric stress tensor. The third deviatoric stress invariant is used in definition of cos3ö :

3 V 3 ^ J

cosW = ^ - ^ (4) 2

The angle 9 is often referred to as the Lode Angle.

4.2 Steel Constitutive Model

The elastic plastic with isotropic hardening material model was used for the steel pipe. Figure 12 shows the stress-strain curve for the model. In addition to mass density. Young's modulus, E, and Poisson's ratio, the input data also include yield strength, hardening tangent modulus, E,, and steel strain at rupture for failing the element.

Pages

Pile Shear Capacity Analysis July 10, 2012

5. Method of Analysis

A three-dimensional nonlinear static pushover analysis procedure was adopted to evaluate the median and variability of the pile shear capacity. First, an elaborate model of the pile and surrounding rock including all significant potential nonlinear mechanisms observed in previous dam analyses was developed (Section 2). The model is very complex and employs 5 nonlinear mechanisms that interact with one another. They include: 1) tensile cracking of the concrete, 2) yielding and rupturing of the steel pipe, 3) separation and sliding of the concrete against steel pipe, 4) separation of concrete from rock, and 5) sliding of the surrounding rock along an observed slip surface. Second, the top rock layer above the slip surface was subjected to incrementally increasing lateral displacement according to pattern shown in Figure 13. The velocity-controlled displacement pattern starts slowly to allow for mobilization of various pile components and then increases almost linearly to a maximum of 10 cm in 10 seconds. As the lateral displacement increases incrementally, the pile undergoes various nonlinear response behaviors numerated above until it is unable to resist any further load and fails. The main output of the analysis is a plot of shear forces induced in the pile and tracked during the analysis versus the applied lateral displacements. The resulting nonlinear force-displacement is indicative of various nonlinear response mechanisms discussed above followed by a total failure of the pile shortly after the pile reaches its shear capacity. The peak of the force-displacement curve represents the shear capacity or the maximum shear force that the pile can resist.

The analyses were performed in two stages: 1) median deterministic analysis using median input values to confirm median shear strength of the piles to finalize the pile design, and 2) probabilistic analysis to esfimate variability of shear capacity for the subsequent dam fragility analysis. The probabilistic analysis was carried out using the Separation-of-Variable Method with four significant parameters including compressive and tensile strengths of concrete with yield strength and rupture strain of steel pipe. The probabilistic analysis included numerous runs and considered both input parameters variability and model sensitivity to numerical convergence. In each run a median minus standard deviafion or median plus standard mediation was assigned to one of the four parameters while median values were used for others; then the same run was repeated for different values of a numerical convergence parameter, discussed later. The results of these runs are used to determine the actual median value and variability of the pile shear capacity, as discussed in Section 7.

6. Analysis Results

The pile shear capacity results for all cases are summarized in Table 7. The table also includes values of the four significant input parameters as well as modulus of elasticity of the concrete that varies with square root of compressive strength of the concrete. The last column shows legends used for the force-displacement graphs, discussed below. The median runs are assigned Case 0, median minus standard deviation Cases 1 to 4, and median plus standard deviafion Case 11 to 14. Each case consists of two or three runs with different hourglass factors, except Case 2 and 11 for which only one converged run could be obtained. In LS-DYNA, hourglass factor is a numerical parameter used to control hourglass or zero energy modes observed in Winfrith concrete model. For each case, whenever possible, two to three runs were performed to account for sensitivity of results to hourglass factor. The multiple shear capacities obtained for each case are then averaged and listed in Table 8 as representative values for each case.

Page 9


Figures 14 to 16 provide typical examples of nonlinear response behavior observed for one of the cases. Figure 14a is a snapshot of pile displacement at 2.46 cm before failure. Relative movement of the upper rock layer (yellow) with respect to lower rock layer (blue) is evident. The concrete between the steel pipe and rock shows cracking along the length of the pile. The concrete inside the pipe exhibits cracking within a diagonal band passing through the slip surface that separates the upper rock from the lower rock. Figure 14b depicts displacement contours at failure at 8.71 cm of lateral displacement. Again the relative movement of the upper rock (red) and respect to lower rock (blue) is evident. Additional color changes and distortion of pile immediately above and below the slip surface (i.e. orange and lighter below) indicate significant deformation and separation of the pile from the rock (on right side above the rock and on the left side below the rock). The concrete cracking inside the pile is now more pervasive along the diagonal band and elsewhere.

Figure 15 shows that as the pile deform and concrete cracks, the steel pipe yields and undergoes bending and shear deformations. Figure 15a exhibits a diagonal band of the steel pipe undergoing plastic deformation; red color indicating regions where the plastic strain of approaching or has reached 8.2% and will fail and removed from the analysis in the subsequent steps. For example, plastic strain history of shell element S30022 (Figure 15b) indicates that the plastic strain increase rapidly from 3.5 to 5 seconds reaching the rupture strain of 8.2% and then the element is removed at about 7.9 seconds.

Finally, Figure 16 shows displacement contours at failure where separation of pile from rock is evident on the left contours and failed and removed shell elements from the analysis on the right contours.

The results in the form of force-displacement plots for all cases including median and median plus and minus standard deviation are presented in Figure 17. The force-displacement plots characterize the behavior of the pile reasonably well. Nonlinear response behavior is reflected by slope the reduction of force-displacement curves as concrete cracking and steel yielding progress. However, the behavior is quite complicated due to interacdon among various nonlinear mechanisms and switching of dominant failure mechanism from one case to another. All cases indicate some form of diagonal shear failure which involve both bending and shear deformations, but cases with lower concrete compressive and elastic modulus exhibit tendency for direct shear. The force-displacement plots are also presented in Figures 18 to 23 for different subcases to facilitate visual examination of the effects of each significant parameter on the pile shear capacity.

Page 10


Table 7. Summary results of all

Concre te

(MPa)

31,738

31,738

f o (MPa)

54

54

(MPa)

3,19

3,19

Steel

fy (MPa)

490

490

Eu

(%) 8,2

8,2

runs

Case

0

0

Shear

Capacity

(MN)

19.37

18.89

Graph

Legend

Median O i l

IVIedian 012 1

29,152

29,152

29,152

31,738

31,738

31,738

31,738

31,738

31,738

31,738

31,738

45.56

45.56

45.56

54

54

54

54

54

54

54

54

3,19

3,19

3.19

2.56

2.56

2.56

3,19

3.19

3.19

3.19

3.19

490

490

490

490

490

490

461.46

461.46

461.46

490

490

8,2

8,2

8,2

8,2

8,2

8,2

8,2

8,2

8.2

7.1

7.1

1

1

1

2

2

2

3

3

3

4

4

22.0

20.7

22.3

16.5

* *

19.7

17.1

14.2

20.1

15.0

/'c-sigma_010

/'c-sigma_011

/',-sigma_012

/'t-signna_010

/',-sigma_011

/'t-sigma_012

/,-sigma_010

/y-sigma_011

/y-sigma_012

Eu-sigma_011

Eu-sigma_012 1

34,553

34,553

34,553

31,738

31,738

31,738

31,738

31,738

31,738

64

64

64

54

54

54

54

54

54

3.19

3,19

3,19

3.97

3.97

3,19

3,19

3,19

3,19

490

490

490

490

490

520.3

520.3

490

490

8,2

8.2

8,2

8,2

8,2

8,2

8,2

9.5

9.5

11

11

11

12

12

13

13

14

14

* *

14

16.4

21.8

22.0

23.2

21.3

20.1

/'j+sigma_011

/'£+sigma_012

/',+sigma_0125

/',-fsigma_010

/'t+sigma_011

/,+sigma_011

/i,+sigma_012

E„+slgma_011

Eu+sigma_012

* did not converge due to numerical instability

Red values indicate median minus or median plus standard variation values

Table 8. Summary of averaged shear caapcities.

Concre te

Ec (MPa)

31,738

(MPa)

54

r, (MPa)

3,19

Steel

fy (MPa)

490

Su

(%) 8,2

Case

0

Shear

Capacity

(MN)

19.13

Graph

Legend

Median 1

29,152

31,738

31,738

31,738

45.56

54

54

54

3,19

2.56

3,19

3,19

490

490

461.46

490

8.2

8,2

8,2

7.1

1

2

3

4

21.7

16.5

17.0

17.5

/'c-sigma

/',-Sigma

/,-Sigma

Eu-sigma 1

34,553

31,738

31,738

31,738

64

54

54

54

3.19

3.97

3,19

3,19

490

490

520.3

490

8.2

8,2

8,2

9.5

11

12

13

14

14.0

19.1

22.6

20.7

/'c+sigma

/',+sigma

/y+sigma

Ei,+sigma

Page 11


7. Median Capacity and Variability Results

Table 8 shows the averaged shear capacity estimates obtained from LS-DYNA for the following nine cases.

Case 0: All median properties

Cases 1, 11 : Minus and plus one standard deviation of concrete strength/'^

Cases 2, 12: Minus and plus one standard deviation of steel ultimate tensile strength/',

Cases 3, 13: Minus and plus one standard deviation of steel yield strength/

Cases 4, 14: Minus and plus one standard deviation of steel rupture tensile strain s,,

Assuming a normal distribution fit of these results. Cases 0, 1, and 11 can be used to estimate the mean

capacity and standard deviation based only on varying concrete strength f since these three cases have

essentially equal likelihood of occurrence (33.3% each). Table 9 shows the mean capacity C} and

standard deviation a\ estimated from these three cases. Based on Cj and Ci, the 16% and 84% NEP capacities are also shown in Table 9 to be 14.36 MN to 22.16 MN which are close to the one sigma bounds of 14.0 MN to 21.7 MN shown in Table 8 for Cases 0, 1, and 11. The assumed normal distribution one sigma bounds are skewed about 2.5% high which is considered to be acceptably close.

Similarly, Cases 0, 2, and 12 are used in Table 9 to estimate the mean capacity C2and standard deviation

G2 based only on varying the ultimate tensile strength/',. Based on Cjand oa, the 16% to 84% NEP capacities are shown in Table 9 to be 16.71 MN to 19.76 MN which are skewed about 2% high compared to the one sigma bounds of 16.5 MN to 19.13 MN shown in Table 8 for Cases 0, 2, and 12. Again, the normal distribution fit is acceptably close.

Cases 0, 3, and 13 are used in Table 9 to esfimate C3 and 03 based on varying/. The resulting 16% and

84% NEP capacities are 16.74 MN to 22.39 MN which are very close to the one sigma bounds of 17.0 MN to 22.6 MN shown in Table 8 for Cases 0, 3, and 13.

Cases 0, 4, and 14 are similarly used to estimate C4and G4 based on varying e„. The resulting 16% and 84% NEP capacities shown in Table 9 are 17.55 MN to 20.72 MN which perfectly match the one sigma bounds of 17.55 MN to 20.72 MN shown in Table 8 for Cases 0, 4, and 14.

Four different estimates of the median capacity (C,, C2, C3 , and C4 ) are thus obtained. These estimates

range from 18.23 MN to 19.56 MN. These four estimates are used in Table 10 to obtain the overall mean

estimate C , and standard deviation GUUR associated with the varying mean estimates. Lastly, the overall

standard deviation o is estimated in Table 10. Thus:

Page 12


C = 18.8 MN

o= 5.34 MN

Table 10 also shows the 5%, 16%, 84%), and 95% NEP capacities resulting from the estimated C and a.

The resulting normal distribution fits the Table 8 results reasonably good. However, the coefficient of variation (COV) computed by:

COV = o/C =0.28

is rather large. This large COV is significantly due to the 14.0 MN capacity esfimate for Case 11.

An identical approach was also followed using a lognormal distribution. The results did not fit the capacities tabulated in Table 1 as well as the results from the normal distribution fit.

1.

2.

3.

4.

Table 9. Normal Distribution Fit

Varying/'c Cases (0, 1, 11)

C, = 18.26

C,6o/., 1=14.36

Varying/', Cases (0, 2, 12)

Q = 18.23

C|6%,2 =16.71

Varying/Cases (0, 3, 13)

C3 = 19.56

C,6o/„,3= 16.74

Varying e„ Cases (0, 4, 14)

C4 = 19.13

C,6o/„,4= 17.55

Oi = 3.9

C84%,i = 22.16

02= 1.53

C84o/„,2 = 19.76

03 = 2.82

C84o/„,3 = 22.39

G4= 1.59

C84o/„,4 = 20.72

Page 13


Table 10. Combined Results (Normal Distribufion Fit)

From Table 9 Mean Values

- 18.26 + 18.23 + 19.56 + 19.13 ,__ C — — 10.8

OERR = 0.66

Combined a

[ 2 2 2 2 2 1" ' '

Ö-1 +(^2 +(73 +0-4 +fT^vi«J

o = 5.34

Capacity Variability

NEP

5%

16%

Mean

84%

95%

C

10.0

13.5

18.8

24.1

27.6

10 20 30

Pile Shear Capacity (MN) 40

Page 14


8. Conclusion

A single pile of as many as 70 concrete-filled steel-pipe piles designed to improve the seismic performance of Mühleberg Dam was analyzed using an elaborate LS-DYNA nonlinear model. The model included the pile and surrounding rock with five potential nonlinear mechanisms observed in previous analyses of the dam. The median and variability of pile shear capacity were evaluated by subjecfing the pile to an incrementally increasing displacement pattern until the pile was unable to resist any further load and failed. The resulting force-displacement plots characterizing the nonlinear behavior of the pile and its peak shear load capacity were developed for the median input parameters as well as for the median plus and minus one standard deviation of four significant parameters influencing the shear capacity. The parameters judged to significantly influence the pile shear capacity included compressive and tensile strengths of the concrete with yield strength and fracture strain of the steel.

The results show that the averaged shear capacity estimates grouped according to the four significant parameters correlate reasonably well with a normal distribution fit. These estimates range from 18.23 MN to 19.56 MN. The overall mean estimate C , and the overall standard deviation a for all cases are 18.8 MN and 5.43 MN, respectively. The 5%, 16%, 84%, and 95% NEP capacities resulting from the estimated C and a with a uniform distribution are:

NEP

5%

16%

Mean

84%

95%

C

10.0

13.5

18.8

24.1

27.6

Page 15


References

[1] Broadhouse, B.J. (1995). The Winfrith Concrete Model in LS-DYNA3D. Report: SPD/D (95)363, Structural Performance Department, AEA Technology, Winfrith Technology Centre, U.K.

[3] Manjoine, M. J., "Creep-Rupture Behavior of Weldments", Weld. Research Supplement (February 1982),pp. 50s-57s.

[4] Snowdon, L.C., "Classifying Reinforcing Bars for Bond Strengths," An edited version of Paper No. 223/70 prepared for the Building Research Station Seminar 'Deformed bars in concrete' and first given at Garston on 14 April 1970. Current paper 36/70, Building Research Station, Department of the Environment.

[5] Rabbat, B.G., and Russell, H.G., "Friction Coefficient of Steel on Concrete or Grout," ASCE Journal of Structural Engineering, Vol. II1, No. 3, March 1985.

[6] Ottosen, N.S., (1977) "A Failure Criterion for Concrete," Journal of tlie Engineering Mechanics Division, Volume 103, Number 4, July/August, pages 527-535.

Page 16


Figure 1. Plan view of Turbine Building showing piles as green circles.

VrtCW MtiMob«g. S!jmant»ge

• KW'FMB*

Figure 2. Turbine Builkding profile showing location and depth of piles.

Page 17


Figure 3. Weir plan showing location locaiton of piles in brown circles.

' m

NX'

f - . . \ \ \ \ x , \

''^ (^00

obi

/«f sMrtu^ <Jiitngrvnd vy M

PUni-lr 1010 3AOT«C1 3

Figure 4. Weir profile showing location and depth of piles.

Page 18


MÜHLEBERG DAM - Pile Capsclty

4—i—r Figure 5. Complete finite-element mesh with concrete-filled steel pile at the center

MUHLE

if jt.

BERG

—

—^

DAM

_j_ ^ s —

1 /— \ -

J-\

z_ X T~

y "Y-^

• P l l

—

' C

-

—

— --

-

z —

— _

opacity

fl 4P 4# "4fî Mr

j J_L l

Mrt # f f

. 1 M l

c 1 i-M T T

• MUHLEBERC OA' tt^j

1

1

1

m 1 1 1

! • 1 t •

• S

1 m

•f m 1 1 1 •

1 1 m c

1

1

S • K

: • m i

s

sa •+Z

-+-"+--I--* " r i _|_ -4— ztn

zjçz

i -4—1 - I -

i

i p

ss Sä

ï.

!Wf> • i k

- ; ^

- \ _y - l ^

/ ( 1

-75

ï: —f

î X .

- f - ^

I Rock Slip Surface

î \ i \ 1

i l ' '^•^^•^H Concrete ^ Rock

•

1

lube I

Figure 6. Model cross section through centerline.

Page 19


MUHLEBERC 0AM - Pll« Capacity

Pile ^ Cap

steel Tube

MUHLEBERC DAM - Pile Capacity

Inside

Concrete

Outside Concrete

Steel Tube

Figure 7. Details of Concrete- filled steel pile.

MUHLEBERC DAM - PILE CAPACITy

Outside Concrete

MUHLEBERC DAM • PILE CAPACITY

Inside Concrete

Figure 8. More details of concrete-filled steel pile.

Page 20


700

600

500

400 ra a. S It) w

200

100

0 0 10 15

strain % 20 25

Figure 9. Idealized stress-strain curve for S460 steel provided by BKW.

Page 21


MUHLEBERC DAM • PILE CAPACI Tim» " 0

a) Shell 530048 and 511004 used for TF calcs. b) Snap shot of 530048 and 511004 stresses

3 4 Time (sec)

c) Triaxiality factor for Shell 530048 from entire duration of analysis.

1 2 3 4 5

Time (sec)

d) Triaxiality factor for Shell 511004 from entire duration of analysis.

Figure 10. Estimated triaxiality factor for shell elements S30048 and S11004.

Page 22


P h

Compressive Mexidian (p,..) 0 = ii)

Figure 11. Meridians and the cross sections of the failure surface.

'•=() kinematic hardening

ß=l isotropic hardening

Figure 12. Elastic-plastic behavior with isotropic and kinematic hardening (lo and / are the uniformed and deformed length of uniaxial tension specimen)

Page 23


0.08-

£0,06 • c » E

^ 0.04 Q. M

>

0.02

0-

iwtUHLEBERG DAM - PILE CAPACITY (Displacement History)

•

«

y ^

/

/

/

'

Node no.

_â_36663

0 2 4 6 8 10

Time (sec)

Figure 13. Velocity-controlled displacement loading from 0 to 10 cm in 10 second.

MUHuréeriffoMw-picepAPJ T i m « - Ô. : . ; C o n t o u r « o f y . d i 3 p l à c « m e n t mir?=4),Ö'14527$, at ï iode i f l è s A

, m » l - 0 08? ) 3 * * , »t m K t * # 4 2 0 2 0 N u m b e r of e l emen ts c tac l<ed«355?

MUHIÊ8EI TJm#= A CohtOMTS of min=J)0O66^

- m a x - « 0246 N u m b e r o f el

y y X

4r~ \^

' • • • •

/ ^ ~ • • •

1-

K''

t C D m Jpite

ncerrtehl

MW.j tnoäeJiS

'ment

•ùS 1 î m r < : rBcke<f= t8 l i '

I-- ! 1 \ r

; - -

\

^ .''-'

1 y

1 r ' t :E

'1 1

<, 1 1 '

L

J -XX^

z: —

—

1

- „

--

a

z

j

t • • •

fi

i

S tffî ì. 1 fflffliwl

-^^ \\' r-\ C i

i .-H ..

- J

— _ r: -

S

1

M - n

_

-""

} \ J^ - f ' ' J , ^

4 1 ,--•

1

T ^ 1 -.. [•

> + "T

i ' î

Fr

lU- l ' - - -

nge t e v «

L462*-Û2

L l 4 a f t . û 2

f ^ f ì

^ 1 1 * * 2

UX l imJX l

*.03

h63< v<09^

l.««^«-03

/

" • • •

\ •

1

ZT"

S

^

a) Before failure at 2.46 cm displacement b) At failure at 8.71-cm displacement.

Figure 14. Contours of pile displacement with concrete cracking before and at failure.

Page 24


MUHLEBERC D A M . PILE CAPACH Tinie= 7 8 Contours of Effer:tive Plastic Strain nia)( ipt, value min-0, Bt nodelr 10002 max=0,082, at node» 10773

Pring* Levels

8,200e.02

7380eJ)2

G,5G0<42

6,74ae4)2

4 9 a ) e «

4 .100è^

3.28M42

IMOtJa 1.64ll#«2

8.200e4)3

OOOOeWO

MÜHLEBERG DAM - PILE CAPACITY

z

0.1-

0.08

è lo.oe

1 OC 0)

0

' '

'—-A J

A

f 1

/ 7

A

' , >

min=0 max=0.082

a) Contours of plastic strain

2 4 6 8

Time

b) History of plastic strain

Figure 15. Contours and history of effective plastic strain for shell Element S30022.

MUHLEbERG DAM - PIBE CA)»»(QrWJÌI|ttj|i' T«"t- 1 ; - ^ ! ' . l l l i i l l l ! ' Contours of'rMjispUcement nl(fï-,0,0fl452?9, atno(fell4638 !

:—m«i-0,ob713Ìi.ali iode*42020 {

MUHLEBERC D A M - PILE CAPAt ] Time » 9 Contours of Y-displacenient mln"^.0t46279, at node! 16638 max4,0871364, at node! 42020

Fringe Levels

8,714e02

7,697e«2

eeeoem 6664e,02

4.647e02

36300O2

2,ei4e«2

1,697eœ

6806e<)3

J,362e03

-1,463e02.

J

Z

Figure 16. Contours of pile displacement at failure.

Page 25


25,000

20,000

15,000

« 10,000 V

5,000

10 20 30 40 50 60 70 80 90 100

Displacement (mnn)

Figure 17. Force-displacement plots for all cases analyzed.

Page 26


25,000

20,000

9- 15,000

V

5 10,000

5.000

Figure 18. Force-displacement plots for median and median minus standard deviation cases.

Page 27


25,000

20,000

5- 15,000

Ì 01 5 10,000

5,000

Figure 19. Force-displacement plots for median and median plus standard deviation cases.

Page 28


25,000

20,000

z

15,000

n> 10,000

5,000

Median Oi l

Figure 20. Force-displacement plots for median and f'c ± standard deviation cases.

Page 29


25,000

20,000

15,000

« 10,000

5,000

Figure 21. Force-displacement plots for median and f't ± standard deviation cases.

Page 30


25,000

20,000

15,000

ra 10,000 V

5,000

Figure 22. Force-displacement plots for median and f^± standard deviation.

Page 31


25,000

20,000

15,000

ra 10,000 w

J S (A

5,000

0 10 20 30 40 50 60 70 80 90 ICO Displacement (mm)

Figure 23. Force-displacement plots for median and EU ± standard deviation

Page 32


APPENDIX A

Nominal shear capacity of pile according to code procedure

The nominal shear capacity of the concrete-filled pipe pile can be obtained from:

V„=K+Vc

Where V and Vc are steel and concrete contributions to shear capacity of the pile.

The shear capacity of the 1200-mm-diamter steel pipe with wail thickness of 22 mm is given by:

V..= ( A M L ^

\ ^ J vV3y

0.083 490

1.732 = 11.7 MV

The shear capacity of the 1.5-m diameter concrete can be estimated from:

V = 0.166-(fÌA^f^ = 0.166(V45^)(0.9xl .7?) = 1.8 iW/V

So the total shear capacity of pile is equal to:

F„= 11.7+1.8 = 13.5 TW/V

Note that the code procedure used above is for pure shear. The field condition and behavior of the pile is expected to be different due to flexibility of the surrounding rock. The piles are expected to undergo both bending and shear deformation.

LS-DYNA computation of capacity for pure shear

The LS-DYNA model was also used to estimate capacity under pure shear deformation. This was accomplished assuming the surrounding rock is rigid so the pile could be deformed under shear without any bending. The LS-DYNA pure shear capacity analysis resulted in a shear of 15 MN, which is only slightly higher than code value and confirms validity of LS-DYNA model.

Page A-1


25,000

20,000

15,000

t

ra 10,000 V

JS

5,000

13,500

- Medijn 012

- Pure Shea'

-Code Value

10 20 30 40 Displacement (mm)

50 60 70

Figure A1. Comparison of LS-DYNA computed pure shear with field-condition median force-displacement and code estimated capacity.

Page A-2

shear capacity analysis of proposed piles for the...

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