drilled shafts paper jee suarez kowalsky

8/8/2019 Drilled Shafts Paper Jee Suarez Kowalsky

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4 Suarez V, Kowalsky M

This equivalent model has been developed to render all the information required forthe application of the DDBD method. Most of the model has been devolved from simpleelastic beam theory and geometry and has been calibrated to account for the nonlinearsoil-interaction effects using the results of a parametric study described at the end of thissection.

Some of the parameters used in the model are: The target displacement D which isthe maximum expected lateral displacement that occurs under seismic attack at the top of the column and is the sum of a yield displacement y, that is assumed elastic, and aplastic displacement p (Eq. 3.1). Plastic displacement results from plastic rotation p once a plastic hinge has developed. It is assumed that p is concentrated at the center of the plastic hinges. The ratio between p and plastic curvature p at the point of maximum moment is the plastic hinge length L p. At a section level the targetcurvature D is the maximum expected curvature and it is the sum of yield curvature y

and plastic curvature p . The yield curvature y can be approximated using Eq. (3.2) asa function of the yield strain of the longitudinal steel bars y and the diameter of the shaftD (Priestley et al, 1996). Displacement ductility is the ratio between D and y andcurvature ductility is the ratio between D and y.

p y D += (3.1)

D y

y

25.2= (3.2)

Two parametric studies were performed to study the response of pinned and fixed headcolumn-soil systems. The first study looked at the response under static lateral loads andthe second study focused on the response under earthquake loading. For both studies,nonlinear single column-soil parametric models were built in OpenSees (McKenna et al,

2004). In these models the column was modeled as a series of frame elements of lengthsequal to one quarter of the diameter. The embedded length of the column was set as longas 30 column diameters and it was verified during the analysis that the tip displacementswere insignificant. The Hysteretic Bilinear (McKenna et al, 2004) section responsemodel was assigned to the column section with pinching coefficients of 0.7 for curvatureand 0.2 for moment. These coefficients were set to match the Modified TakedaDegrading Stiffness hysteresis rule (Takeda et al., 1970) (previously used in equivalentdamping investigations by Dwairi, 2005). The elastic modulus of concrete was E c= 27200Mpa. The cracked moment of inertia I cr was assumed equal to 50% of the gross momentof inertia. This value is adequate for concrete columns with 2% reinforcement ratio andsubjected to an axial load equivalent to 20% the capacity of the section Caltrans (2004).The yield curvature y was obtained from Eq 3.2.The column diameter ranged from 0.3mto 2.4m and the above ground height varied between two and ten diameters of thecolumn. The parametric matrix is presented as Table 1.

The soil was idealized as a uniform layer of either sand or soft clay with the watertable at ground level. The OpeenSees module PysimpleGen (Brandenberg,2004) wasused to generate P-y elements along the embedded length of the column. The PySimple1


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Seismic Design of Drilled Shaft Bents with Soil-Structure Interaction 5

material model (Boulanger, 2003) was utilized to model the soil. For clay, the P-yelements were set to match Matlocks P-y model for soft clay under water(Matlock,1970). For sand, the P-y elements were set to match the API P-y model forSand (API, 1987). Table 2 summarizes the soil properties used for each soil type in theparametric study, where su is the undrained shear strength for clays, 50 is the strain atwhich clay develops half of its compressive strength, w is the total unit weight, is theeffective friction angle and k is the rate at which the subgrade modulus increases withdepth in sands.

Pinned head drilled shafts

In the proposed model, the nonlinear soil-column system is replaced by a cantilevercolumn with equivalent length L e that is fixed at its base (Fig. 2). The point of fixity islocated at the point of maximum moment in the soil-column system. The yield

displacement of the equivalent system is calculated with Eq. 3.3. where is a coefficientthat amplifies the yield displacement of the equivalent cantilever and accounts for elasticrotation that exists at the underground point of maximum moment and the larger areainside the curvature pattern in the nonlinear soil-shaft system.

3

2e y

y

L = (3.3)

Figure 3 shows design values for and Le as a function of the above ground height L a,diameter D of the column and soil type. These charts resulted from the parametric studydescribed early in this section. The plastic displacement is calculated with Eq. (3.4)where L p is plastic hinge length that can be estimated from Eq. (3.5) (Chai, 2002a).

e p p p L L = (3.4)

D L

D L a p 1.01 += D6.1 (3.5)

Application of DDBD requires the calculation of the displacement ductility. If theperformance is specified in terms of a target top displacement, D is obtained directlywith Eq. (3.6). If performance is given as a target curvature in the section then D isobtained from Eq. (3.7).

y

D

= (3.6)

y

e p y D L L

+=

)(1

(3.7)

Fixed head drilled shafts

The fixed-head drilled shaft is replaced by a column of equivalent length L e that is fixedat its based and supported on rollers at the top so the rotation is restrained (Fig.2). L e is


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the same as for a pinned head column but different values of is used to match the yielddisplacement. Both parameters can be found in Fig. 3 and result from the parametricanalysis described earlier. The yield displacement is calculated from Eq. (3.8).Displacements beyond yield consist of a combination of elastic displacement and plasticdisplacement due to plastic rotation at the top hinge. As the displacement continues toincrease, the underground moment will reach the yield strength of the column and secondplastic hinge will develop underground. This behavior can not be captured by theequivalent column in which both hinges develop at the same time. However the plasticdisplacement after the top hinge is formed can be estimated as the product of the plasticrotation at the hinge and a fraction of the equivalent length L e as shown in Eq. 3.9. In thisequation is a coefficient that affects L e. The parametric study suggested = 1.68 for thecolumns in sand and = 1.54 for columns in clay without a particular trend with respectto above ground height and column diameter.

6

2e y

y L = (3.8)

e p p p L L = (3.9)

The plastic hinge length L p for the column connecting the cap beam can be calculatedfrom Eq. (3.10) (Priestley M.J.N., 1996 ). In this equation Li is the distance from theplastic hinge to the point of contraflexure, f y is the yield strength of the reinforcementsteel in MPa, and d bl is the longitudinal bar diameter in meters. Approximate values for Li were determined in the parametric study described before and are presented in Fig. 4along with the location of soil reaction for pinned head columns. In Eq. (3.10), the firstterm represents the spread of plasticity resulting from variation in curvature with distancefrom the critical section, and assumes a linear variation in moment with distance. The

second term represents the increase in effective plastic hinge length associated with strainpenetration into the cap beam.

bl yi p d f Ll 022.008.0 += (3.10)

If performance is given in terms of a target curvature for the section, is obtained fromEq.(3.11) . This equation does not account for the formation of a second plastic hingeunderground since if has been found that for fixed head columns in soft soil, the secondplastic hinge starts to develop after significant damage has occurred in the first hinge.

y

e p y D L L

+=

)(1 (3.11)

Comparison with experimental data

The proposed equivalent model is used to predict the yield displacement and ductility inan RC pile embedded in sand. The comparison is made to a pile lateral load testconducted by Chai and Hutchison (2002b). The test involved the application of a cycliclateral load and a constant axial load at the top of a 0.4 m diameter RC pile partiallyembedded in sand with an effective friction angle of =37 . The column head was free


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and the normalized above ground height was L a /D= 6. From the data recorded in theexperiment, the yield displacement of the pile was 0.11m. Also at different levels of displacement ductility, the curvature ductility at the plastic hinge location was calculatedas shown in Fig. 5.

The application of the proposed equivalent model to this problem is as follows: Theequivalent length of L e /D= 8.4 is obtained from Fig. 3 by entering with L a /D=6, Also,from the same charts the yield displacement coefficient is = 2.2. The yield curvature forthe pile section is approximated using Eq. (3.2). Then, using Eq. (3.3) the yielddisplacement is calculated, y= 0.11m . The plastic hinge length from Eq (3.5) isLp=0.65m this value is used with Eq. (3.7) to find the displacement ductility for differentlevels of curvature ductility with results plotted in Fig. 5.

The predicted yield displacement was found to be essentially the same as the valueobtained during the test. Also in Fig. 5 it is observed that the relationship between

displacement ductility and curvature ductility predicted by the new model is in goodagreement with the experimental results of Chai and Hutchinson (2006b).

Effect of longitudinal steel ratio

In the parametric study that rendered trends for L e , and (Fig. 3), the amount of longitudinal reinforcement was not varied for each column section. As explained before,the cracked section moment of inertia assigned to the different columns was taken as 50%of the gross inertia assuming a longitudinal reinforcing ratio of 2%. In this section of thepaper, the results of nonlinear lateral (pushover) analyses of RC shafts with the samediameter but with different longitudinal steel ratios are compared to the values predictedusing the proposed equivalent model. The purpose of this comparison is to determine theeffect of the amount of longitudinal steel on the values of the yield displacement andductility demand in the column.

The pushover analyses were performed using the program MultiPier (BridgeSoftware Institute, 2000). The diameter of the selected drilled shaft is 0.6m, the aboveground height is 4.8m, and the total length is 25m. The compressive strength of theconcrete was assumed equal to 28MPA and the elastic modulus equal to 24800 MPA.The yield strength of the steel was 450MPA and the elastic modulus is 200000MPA. Theconcrete cover was 0.07m. The water table was set at the ground level. The soil wasassumed to be clay with a total unit weight of 16 kN and undrained shear strength of 20kPA and it was modeled using the P-y model for soft clay under water (Matlock,1970). The rotation of the columns head was fixed. Four pushover analyses wereperformed varying the amount of longitudinal reinforcement from 1% to 4%.

From the information presented above, the yield displacement and ductility can beestimated using the equivalent model as follows: From Fig. 3 for a fixed headed column

in clay with L a /D = 8, L e /D = 11.9 , = 2, =1.54. Using Eq.3.8 the estimated yielddisplacement is 0.14m. Also, using Eq. 3.11 the displacement ductility demand iscalculated for curvature ductility values ranging from 1 to 18. These results are shown inFig. 6 and 7 along with the results of the pushover analysis.


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Figure 6 shows the force deformation response for the four columns with differentsteel ratios. In each curve the yield point is defined from the results of the pushoveranalysis as the lateral displacement at which the moment at the top of the column reachedthe value of the effective yield moment found for that section on a separate momentcurvature analysis. Also shown in Fig. 6 is the yield point calculated using the equivalentmodel. It can be seen that the value predicted with the equivalent model is close to yieldpoint of the column with 2% steel ratio and not very distant from those of the columnswith 3% and 4%. It can be concluded that the yield displacement is not very sensitive tothe strength of the column and that the equivalent model gives a reasonable prediction.

Fig. 7 compares the levels of curvature ductility at the plastic hinges with thedisplacement ductility of the system for the four levels of reinforcement. The same figurealso shows the prediction using Eq. 3.11. It can be observed that there is good agreementwith the values obtained from the pushover analysis. Again it seems that the strength of

the section has little influence in the relation between curvature and displacementductility. It is interesting to notice from this example that the curvature ductility demandand therefore the level of damage at the hinge in the top of the column can reach largevalues before a second hinge develops underground. This is typical of fixed headcolumns in soft soils (Suarez, 2005).

3.2. Equivalent Viscous Damping

During earthquakes, energy is dissipated by inelastic deformation in the soil and plastichinging in the shafts. DDBD uses the concept of equivalent viscous damping to modelthe energy dissipation in the structure and so far several studies have been conducted tofind equivalent damping-ductility-period relations for concrete members (Jennings, 1968;Dwairi, 2005; Priestley and Grant, 2005). However; to the knowledge of the authors noprevious research on equivalent viscous damping for soil-column systems has beenconducted. Therefore, in order to implement DDBD, a parametric study was conducted toinvestigate the response of single soil-column systems under earthquake loading with thegoal to identify trends that relate hysteretic damping to displacement ductility.

In the study, Nonlinear Time History Analyses (NTHA) were performed on singlecolumnsoil models that were built in OpenSees. The models were built as detailed in theprevious section with the parameters show in Table 1. A set of ten soft-soil earthquakeacceleration records were used (Miranda, 2003). Each record was applied to all thestructural models with ten different amplification factors, resulting in 100 NTHA permodel and 28,000 analyses in total.

From each NTHA the maximum top displacement and the correspondingdisplacement ductility and effective period were obtained. Then, the equivalent hysteretic

viscous damping was found as the viscous damping with which an elastic single degreeof freedom system would have the same maximum displacement as the inelastic system.Final values of equivalent hysteretic damping assigned to each column-soil model wereobtained as the average equivalent viscous damping from the ten earthquake records at


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each level of ductility. No viscous damping was added in the NTHA with the purpose of capturing hysteretic damping only. Fig. 8 shows the hyperbolic trends that best fitted theresults. The curve fitting was done using an optimization tool to minimize the sum of thesquared difference between the hysteretic damping predicted by the model and the resultsof NTHA.

Each of the trends shown in Fig. 8 corresponds to a type of soil and head restraint. Notrends were found between hysteretic damping and the height or diameter of the column.Fig. 8 shows higher levels of damping for columns with pinned heads and for columns insofter soils. This is expected since for the same level of displacement ductility, pinnedhead columns and columns in soft soils displace more, inducing larger deformation in thesoil and therefore resulting in more energy dissipation. Figure 6 also shows considerableamounts of hysteretic damping at ductility equal to one. This damping resulted from theenergy dissipated by the soil only and it is related mainly to the deformation in the soil.

Although for < 1, equivalent hysteretic damping exists and should be accounted for,insufficient data was collected from the parametric study as to give any trend that can beused in DDBD. A detailed description of the parametric study can be found in Suarez(2005).

It was mentioned before that although viscous damping exists in reinforced concretebents, it was not applied to the models in the study such that hysteretic damping could beisolated. This was done to give the designer the freedom of using any level of viscousdamping that is considered to be appropriate (2%-5% typically). Viscous damping v canbe combined with hysteretic damping eq,h to get a design value of equivalent viscousdamping eq using Eq. (3.12) and Eq. (3.13) (Priestley, 2005).

heqveqeq ,, += (3.12)

= vveq , (3.13)

3.3. Displacement-based design of a drilled shaft bent in clay

As an example, a drilled shaft bent (Fig. 9) partially embedded in clay is designed in thein-plane direction. The structure is designed for the AASHTO (2004) design spectrumwith peak ground acceleration A= 0.4g and soil coefficient S=2, without exceeding adamage control curvature in the columns with an upper displacement ductility limit of three. The bent has three columns with diameter D = 1.2m, the above ground height is L a = 8m and it is embedded in a clay with undrained shear strength s u = 40kPa. The bentsupports a weight P=2500 kN per column. In this example the damage control curvaturehas been calculated using Eq. (3.14) (Kowalsky, 2000). For an axial force in the columnP= 2500kN, compressive strength of concrete fc = 28MPa and the gross area of the

column A g and the diameter D, the damage control curvature

D is 0.05. From Eq. (3.2),the yield curvature for the section is y = 0.0038 1/m so the damage control curvatureductility is =0.05/0.0038=14


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D A f P

gc D

1068.0068.0 '

= (3.14)

The next step is to calculate the yield displacement. Since the design is in the in-planedirection, the yield displacement is going to be calculated for one of the columnsassuming fixed head conditions. Entering in Fig. 3 with L a /D=6.6, it is found that L e =11.63m and the yield displacement coefficient is 2.05. This information is then usedin Eq. (3.8) to find a yield displacement of y= 0.17m.

Next, the displacement ductility that corresponds to the damage control curvatureductility is calculated using Eq. (3.11) with =1.54. The calculated displacement ductilityis = 3.8. Since an upper limit of 3 was specified, the target displacement is D= 3x0.17=0.51m. This value can be also expressed as a drift, 0.51/11.63= 4.3%

Knowing the ductility demand on the system, the corresponding equivalent viscous

damping can be estimated. The equivalent viscous damping eq has two components thatmust be added together. The hysteretic damping component eq,h is found from Fig. 8 andthe viscous damping component eq,v is calculated from Eq. (3.13). Assuming that theviscous damping is v= 5%, the viscous damping component for DDBD is eq,v= 8.6% .From Fig. 8 the hysteretic damping component is eq,h= 11.4%, so the total equivalentviscous damping is eq=20%. The next step requires entering the displacement responsespectra that corresponds to the design earthquake with 20% of damping with D=0.51mto find the required effective period for the equivalent elastic system. Alternately, Eq.(3.16) has been developed from the AASHTO acceleration response spectra Eq.(3.15) tocalculate the effective period T eff . The term with the square root comes from theEurocode (1988) and scales the spectra to the desired level of damping.

32

2.1

T

ASSaD = (3.15)

(3.16)

In Eq. (3.16) all the parameters have been previously presented with the exception of g which is the acceleration of gravity. From this equation an effective period T eff = 2.8s isfound. With knowledge of the period and the weight on top the column, the design baseshear acting on one column can be calculated from Eq. (3.17). The first term on the rightside of this equation is the required effective stiffness for the system.

DgT W

V = 224 (3.17)

Equation 3.17 yields a required lateral strength of V= 687 kN per column. This force isequivalent to 28% of the supported weight. The total design base shear for the bent is thesum of the required strength for the three columns, that is V t = 2061 kN. The next step isto build a model and analyze the structure under the application of the base shear force to

75.2

7

2

2.14

+= eq Deff ASgT


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find the internal forces for member design. To do this, analysis software such asMultiPier, (2004) or Lpile (2003) could be used. Alternately, knowing that for in-planedesign, the plastic hinges are located at top of the column, the design moment at thosepoints can be estimated as the product of the base shear force and the distance betweenthe top of the column and the point of inflection. This distance, taken from Fig. 4, equals0.57L e, therefore the design moment for the column is M u= 687x0.57x11.6=4552 kN-m .Finally it was found that a reinforcement-area ratio of 1.8% is needed such that themoment capacity of the section at the damage control curvature limit is at least equal tothe design moment M u. Shear reinforcement in the columns and the reinforcement of capbeam should be designed according to capacity design principles (Paulay and Priestley,1993).

Design verification

An Incremental Dynamic Analysis IDA (Vamvatsikos and Cornell, 2002) was carried toverify the performance of the drilled shaft bent designed with DDBD in the previoussection. IDA is a parametric analysis method that involves applying to a nonlinear modelone or more earthquake records, each scaled to multiple levels of intensity. The result isone or more curves that relate the first-mode spectral acceleration S a (or any othermeasure of intensity) to maximum displacement (or any other measure of response). IDAis recommended for performance verification in DDBD (SEAOC, 2003). The IDA wasperformed as follows:

(i) A structural model of the bent and surrounding soil was built in OpenSees. Fig. 10shows the moment curvature response of the column section as designed and alsoshows the bilinear response integrated to the bilinear hysteretic section model inOpenSees. The soil was modeled using P-y elements as previously described.

(ii) A nonlinear static (pushover) analysis was performed to determine the force-displacement response and yield point for the structure.

(iii) The fundamental period of the structure was found by performing modal analysis.This is the first mode period based on initial/elastic properties of the bent and soil.Then, a set of eight soft-soil earthquake records was made compatible with thedesign spectrum within periods ranging from the fundamental period T 1=1.54s to aperiod slightly longer that the effective period found in design T eff =2.8s. Thecompatibility was achieved by using wavelet decomposition (Montejo, 2004)

(iv) NTHAs were conducted. Each of the earthquake records was applied with 12different scale factors ranging from 0.1 to 1.2. After each analysis was performed,the maximum top displacement and maximum moment at the top of the columnswere extracted from the output.

(v) Finally two IDA plots where made. In Fig 11, the X axis shows the maximum top

displacement and the Y axis the spectral acceleration S a that corresponds to theamplification level used with the earthquake. An amplification factor of 1corresponds to the fundamental period spectral acceleration found with Eq.3.15equal to S aD=0.73g. With the maximum top displacement values recorded from theNTHA and the yield point found in the pushover analysis, the maximum


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displacement ductility demand for each NTHA was calculated. This is shown in Fig

12 where the X axis shows the displacement ductility and the Y axis the spectralacceleration S a. In both figures, each dotted line corresponds to the results of NTHAswith a particular earthquake. Both figures show the 16%, 50% (mean) and 84%fractile curves as a summary of the eight IDA curves. Fig 11 also includes a capacitycurve that was derived from the pushover analysis.

In Fig. 11 and 12 there is a point that shows the intended performance of the structure.During the application of DDBD, the target displacement was D=0.51 m. This value isvery close to the average displacement of 0.53m predicted by IDA (Fig 11). Thepushover analysis shows a yield displacement equal to 0.19m which is 12% more thanthe yield displacement estimated during design. The difference between the values of yield displacement is reflected in the displacement ductility demand plot shown in Fig.12. In this figure it is observed that the average ductility demand is 2.7, which is lower

than the design limit of three. It is also observed that the probability of having a ductilitydemand higher than three is almost 16%. With this information, one can conclude thatthe design using DDBD was appropriate.

In PBSE more than one performance level must be satisfied. If that is the case,DDBD should be applied for the different performance levels, then the reinforcement isdesigned for the governing case and IDA could be used for verification. One importantfeature of IDA is that in a single plot the performance of the structure for differentseismic intensity levels can be checked. Another important feature is that the IDA plotsgive an insight into the behavior of the bent. For example, Fig. 11 shows that the IDAcurves depart from the capacity curve at displacement as low as 0.05m. This point marksthe onset of inelastic behavior and energy dissipation and it is only at 25% of the yielddisplacement. The yield displacement y=0.19m indicates that the effective yield

curvature has been reached in the columns. An average force reduction factor R can becalculated at this point or at any level of displacement ductility by dividing the ordinateof the 50 th fractile curve into the ordinate of the capacity curve. The reduction factor atthe yield point is R =1.7, at this point the displacement ductility demand is =1. At thetarget displacement, R=2.5 and corresponding to a displacement ductility demand =2.8approximately. Therefore it can be concluded that the equal displacement approximationdoes not apply in this case and also that the force reduction factor of R=3 (ATC, 1996)commonly used for all bents without consideration of the soil-structure interaction effectsmight not be achievable. Furthermore the reduction in force reached in this exampledepends on whether or not a top displacement of 0.53m can be accommodated withoutcausing damage to the superstructure or connections.

4. Summary and Conclusions

DDBD has been implemented for seismic design of drilled shaft bents. This has requiredthe development of an equivalent model to predict displacement and ductility whileaccounting for soil-structure interaction effects and also, the development of relations for


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the estimation of the equivalent viscous damping at different levels of ductility and fordifferent soils and boundary conditions. These tasks have been accomplished by applyingexisting knowledge on DDBD and by performing parametric studies to identify trends inthe response of this type of structure. The verification analyses included in this paperdemonstrate that the proposed design procedure captures the behavior of bents and istherefore suitable for the application of PBSE. However it is recognized that the approachhas some limitations:

(a) The bents are assumed to be embedded in a single layer of sand or soft clay.Multilayer profiles must be transformed to an equivalent single layer.

(b) The soil should not be prone to liquefaction or lateral spreading(c) The shafts are assumed to be embedded deep enough to avoid rigid body

rotation.(d) The spacing between shafts is sufficient to avoid shadowing effects(e) P- effects are not accounted for design.(f) Assuming fixed head or pinned head is acceptable.

If these conditions are not met, it is recommended that the proposed procedure be appliedwith a pushover analysis of a proper model of the structure to determine the yielddisplacement and if needed, the relation between curvature and displacement ductility.This would of course require an initial assumption of the amount of reinforcement in thecolumns.

It is strongly recommended that the design be verified by: 1) IDA, if severalperformance levels are to be checked. 2) NTHA with compatible records if only oneperformance level is to be checked. 3) Capacity spectrum method (Freeman, 1998) withthe equivalent damping relations proposed here, if methods 1 or 2 can not beimplemented. A flow chart that summarizes the procedure is presented in Fig. 13.

Conclusions

Soil structure-interaction results in added flexibility and damping but it can not beconcluded that the soil-structure interaction reduces the strength demand in the structure.If compared to the yield displacement of a column on rigid foundation, the increase of yield displacement can be as much as four times for pinned head columns and three timesfor fixed head columns in sand and it could be more than ten times for pinned head andsix times for fixed head columns in soft clay. The equivalent damping is alsoconsiderably increased as a function of the deformation of the soil. However, theincrement of damping and flexibility has opposite effects on the response of the bent. If the yield displacement increases, the ductility demand will decrease and this tends toincrease the force demand in the system. Opposite to that, the increase in equivalentdamping and flexibility causes the period to increase and this is likely to cause areduction of seismic forces.

The yield displacement depends mainly on the boundary conditions at the top of thecolumn and on the soil properties. Increasing the diameter of the column in an attempt to


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increase the ductility demand has the contrary effect since even though the yieldcurvature will decrease, the location of the plastic hinge will be shifted to a deeper pointtherefore increasing the equivalent length L e .

The second design example showed that it is not rational to use a fixed value of R asis done in the current practice. The ductility capacity of the system depends on thegeometry and soil properties and might be limited by allowable displacement limits andP- effects.

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Engineers Association of California,Suarez, V. 2005. Implementation of Direct Displacement Based Design for Pile and Drilled Shaft

Bents. Masters Thesis, North Carolina State University.Takeda T., Sozen M. and Nielsen N. Reinforced concrete response to simulated earthquakes.

Journal of the Structural Division, ASCE 1970; 96(12): 2557-2573.Veletsos, A, Newmark, N. M., 1960. Effect of inelastic behavior on the response of simple systemsto earthquake motions. Proceedings of 2nd World Conference on Earthquake Engineering, Vol. 2,pp. 895912.Vamvatsikos, D, and Cornell, C. 2002. Incremental dynamic analysis. Earthquake Eng. Struct.

Dyn., 31-3, 491514.


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Fig. 1. General configuration of drilled shaft bents

CAP BEAM

DRILLED SHAFTS

SOIL

OUT-OF-PLANEDISPLACEMENT

IN-PLANEDISPLACEMENT

DRILLED SHAFTS


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Table 1. Parametric matrix for dynamic and staticanalyses

HEAD D (m) La /D SoilsPINNED 0.3 2 Clay-20FIXED 0.6 4 Clay-40

0.9 6 Sand-301.2 8 Sand-371.5 101.82.4

Number of combinations: 280


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Table 2. Definition of soil parameters

CLAYS Su (Kpa) e 50 w (kN/m3) P-y model

Clay-20 20 0.02 16 MatlockClay-40 40 0.015 17 Matlock

SANDS k (kN/m3) w (kN/m3) P-y modelSand-30 30 5500 16.7 APISand-34 34 16600 17.6 APISand-37 37 33200 18.5 API


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p-y Springs

BendingMoment

V

Mmax

Mmax

V

MomentBending

p-y Springs

Le

y p

Fixed Base Fixed Base

py

Le

PH PH

PH

PINNED HEAD COLUMN FIXED HEAD COLUMN

Fig. 2 Equivalent models for pinned and fixed head columns


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Fig. 3. L e, for definition of equivalent model.

DRILLED SHAFTS IN SAND

456789

1011

121314

2 4 6 8 10

L e / D

FIXED&PINNED =30 o

FIXED&PINNED =37 o

00.5

11.5

22.5

33.5

44.5

55.5

2 4 6 8 10

PINNED =30 o

PINNED =37 o

FIXED SHAFTS

00.5

11.5

22.5

33.5

44.5

55.5

2 4 6 8 10

PINNED su=40kPA

PINNED su=20kPA

FIXED SHAFTS

DRILLED SHAFTS IN CLAY

456789

1011

121314

2 4 6 8 10

FIXED&PINNED su=20kPA

FIXED&PINNED su=40kPA

La /D La /D


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Fig. 4. a) Location of soil reaction resultant b) Location of inflection point

0.40 (L e-La) (Clay)0.32 (L e-La) (Sand)

0.57 L e (Clay)0.52 L e (Sand)


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1

3

5

7

9

11

13

1 1.5 2 2.5 3 3.5 4

Displacement Ductility

C u r v a

t u r e

D u c

t i l i t y

Load test

Proposed Model

Fig. 5. Comparison of predicted ductility and experimental data.


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0

50

100

150

200

250

300

350

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

LATERAL DISPLACEMENT (m)

L A T E R A L F O R C E

1%

2%

3%

4%YIELD DISPLACEMENT FROM

NONLINEAR ANALYSIS

YIELD DISPLACEMENT FROMEQUIVALENT MODEL

Fig 6. Force-Displacement response of single shafts with different reinforcement ratios


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0

2

4

6

8

10

12

14

16

18

20

0 1 2 3 4 5 6 7

DISPLACEMENT DUCTILITY

C U R V A T U R E D U C T I L I T

1%

2%3%

4%

1%

2%

3%

4%

MODEL

UNDERGROUND HINGE

HINGE AT COLUMN HEAD

Figure 7. Ductility in single shafts with different reinforcement ratios


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0

5

10

15

20

25

1 2 3 4 5 6 7


H y s

t e r e

t i c D a m p i n g

Sand =37

Sand =30

Sand =37 Sand =30

Clay su =20 kPAClay su =40 kPA

Clay su =20 kPAClay su =40 kPA

PINNED-HEAD ROTATION

FIXED-HEAD ROTATION

Fig. 8. Hysteretic equivalent viscous damping


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Fig. 9 Design example drilled shaft bent

P = 7500 kN

Clay su=40kPA

EARTHQUAKEACTION

1.2m

5.4 m


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Fig. 11. Spectral acceleration vs. top displacement

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Top displacement (m)

S a

( g )

y

Capacity Curve

Design Spectral Acc.

Intended Performance D , S aD

Avg. simulated performance

Force Reduction @ =3

16 th 50 th 84 th


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Fig. 12. First-mode 5% damping spectral acceleration vs. displacement ductility.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5


S a

( g )

Design Spectral Acc.

Intended Performance, D=3

Avg. simulated performance16 th 50 th 84 th


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Start

End

end

Define equivalent model: using D,La , (s u or ') find L e , (Fig,3)

Define equivalent SDOF structure: find equivalent viscousdamping, effective period and design base shear

Determine curvature ductility, yielddisplacement and then displacementductility Eq. 3.6

Calculate yield displacementand displacement ductility

Estimate the location of inflection pointand calculate required momentcapacity (Fig. 5) at top of column

Estimate soil reaction and determinerequired moment capacty underground(Fig.5)

Design long. Reinforcement for the highest moment demand.Design shear reinforcement in columns and cap beamreinforcement following capacity principles.

Target perfomance given interms of top displacement?

Is it i n-plane bent design?

yes

yes

no

no

Does the structure meet the limitations of theequivalent model? (Section 4)

Build proper model and performPushover analysis

yesno

Perform verification analysis

Fig. 13. Flow chart of DDBD of drilled shaft bents.

drilled shafts paper jee suarez kowalsky

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