INFLUENCE OF PILE HEAD RESTRAIN LEVEL ON LATERAL RESPONSE OF PILES SUBJECTED TO GROUND MOTION

Transcription

1 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska INFLUENCE OF PILE HEAD RESTRAIN LEVEL ON LATERAL RESPONSE OF PILES SUBJECTED TO GROUND MOTION L. R. Fernandez-Sola 1 and G. Martínez-Galindo 2 ABSTRACT In this work, a parametric study of the bending moment distribution in concrete piles produced by kinematic interaction due to seismic excitation is presented. A finite layer method is used, that considers partially or fully constrains against rotation of pile ends (head and tip). In addition, different levels of pile head rotational restriction are considered. First, a parametric analysis of the rotational stiffness needed to produce a fixed head condition in the pile is developed. An equation to define this stiffness is proposed. Then, the distribution and magnitude of bending moments with partial rotation at pile head is studied. Finally, a comparison between numerical transient pile response and the proposed equations is presented. 1 Professor, Dept. de Materiales, Universidad Autonoma Metropolitana-Azcapotzalco, Av. San Pablo No. 180 Col. Reynosa Tamaulipas, C.P , Distrito Federal,Mexico 2 Graduate Student, Dept. de Materiales, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo No. 180 Col. Reynosa Tamaulipas, C.P , Distrito Federal,Mexico Fernandez-Sola LR, Martinez-Galindo G. Influence of pile head restrain level on lateral response of piles subjected to ground motion. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

2 10NCEE Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska Influence of Pile Head Restrain Level on Lateral Response of Piles Subjected to Ground Motion L. R. Fernandez-Sola 1 and G. Martinez-Galindo 2 ABSTRACT In this work, a parametric study of bending moment distribution in concrete piles produced by kinematic interaction due to seismic excitation is presented. A finite layer method is used, that considers partially or fully constrains against rotation of pile ends (head and tip). In addition, different levels of pile head rotational restriction are considered. First, a parametric analysis of the rotational stiffness needed to produce a fixed head condition in the pile is developed. An equation to define this stiffness is proposed. Then, the distribution and magnitude of bending moments with partial rotation at pile head is studied. Finally, a comparison between numerical transient pile response and the proposed equations is presented. Introduction Structural design of foundation elements requires understanding of both: structural and geotechnical engineering. Structure and soil response, and soil properties influence the magnitude and characteristics of the force elements on the foundation. Generally, these effects are considered separately. This consideration neglects the influence of the foundation in the response of either structure or soil. Since the 50 s the influence of soil-foundation flexibility on structural behavior is recognized [1] by introducing Soil Structure Interaction (SSI) on dynamic analysis of buildings. Several codes around the world acknowledge the importance of consider the variation that SSI produces on structural dynamic properties (period lengthening and damping modification). These modifications (known as inertial interaction) may produce changes on loads introduced on the foundation due to structural response. Designers in general consider exclusively these loads on structural design of the elements, sometimes even neglecting SSI influence. 1 Professor, Dept. de Materiales, Universidad Autonoma Metropolitana-Azcapotzalco, Av. San Pablo No. 180 Col. Reynosa Tamaulipas, C.P , Distrito Federal,Mexico 2 Graduate Student, Dept. de Materiales, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo No. 180 Col. Reynosa Tamaulipas, C.P , Distrito Federal,Mexico Fernandez-Sola LR, Martinez-Galindo G. Influence of pile head restrain level on lateral response of piles subjected to ground motion. Proceedings of the 10 th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

3 In case of deep foundations such as piles, there is experimental [2-4] and analytical [5-11] evidence that they are also subject to forces produced by wave passage. These forces arises from the incompatibility of soil and pile strains (kinematic interaction), and are considered on the design of underground structures [12-16]. Distribution and magnitude of element forces produced by kinematic and inertial interaction are completely different [17]. In general design codes does not consider kinematic forces on foundation structural design. Pile toe and head boundary conditions control the magnitude and distribution of kinematic forces [5,10 y 11]. Many authors have used Beam-on-Winkler-Foundation models to study these forces [5,9 y 10]. In such models, piles are modeled as Euler-Bernoulli beams considering either fixed or stress free conditions for head and toe. In fact, fixity conditions are neither completely fixed nor stress free. Pile tip fixity depends on soil stiffness and pile diameter. For the case of head, fixity depends on the relation between flexural stiffness of the shallow foundation element that is supported by the pile (e.g. footing, foundation slab or beam, etc.) and flexural stiffness of the pile (Fig.1). Figure 1. Scheme of kinematic soil-structure interaction problem. On steel structures, the type of beam-to-column connection depend on the rotation restrain developed by the connection. AISC [18] classify connections on three types: Fully restrained, semi-rigid and simple framing or shear connections (Fig. 2). Connection-to-beam relative flexural stiffness (Krel=Kconnection/Kbeam) is the governing parameter of the restrain level. For piles, there are not recommendations about which values of Krel produce fully restrained connections between pile head and the shallow foundation element. Definition of this parameter is fundamental to consider appropriate boundary conditions. A model based on the finite layer method for seismic analysis of piles embedded in layered soil deposits is used. This model has been proposed by Fernadez-Sola et al. [17]. The pile-soil system is discretized vertically in thin layers. Response to vertically propagating shear

4 waves is directly expressed as wave mode expansions (Fig.1). The expansion factors are obtained by satisfying rigorously the soil-pile boundary conditions. The wave modes fulfilling the freesurface and rigid bedrock conditions are obtained by the thin-layer method [20]. The pile head is elastically constrained against rotation by vertical springs. Details of numerical model formulation and validation can be consulted on [20]. With this model an analysis of the influence of head restrain level on bending moments distribution along the pile is performed in the present paper. Connection stiffness required to consider fully fixed condition is computed. Figure 2. Connection types on steel structures (adapted from Cruz-Mendoza 2011[20]). Computation of fully fixed stiffness To determine the values of Krel that ensure a fully restrained pile-shallow foundation connection, a parametrical analysis is performed. The parameters that control lateral pile behavior subjected to ground motion are [11]: Pile slenderness ratio (L/r) Soil-pile shear wave velocity ratio (Vs/V0) Soil-pile Poisson coefficient ratio (νs/ν0) Soil-pile density ratio (ρs/ρ0) Soil and pile damping ratio (ζs, ζ0) Circular concrete piles with radius r are considered with the following properties V0=2,000.0 m/s, ν0=0.3, ρ0=2,000.0 kg/m 3 and ζ0=0.05. Homogeneous soil profiles with values of ρs/ρ0 =0.75, νs=0.5 and ζs =0.05 are used. Taking in to account common practical dimensions of piles, five slenderness ratios (L/r =10, 20, 30, 60 y 90) are considered. To cover a wide range of soil types, eight soil-pile shear wave velocity ratios (Vs/V0 =0.025, 0.035, 0.045, 0.050, 0.100, 0.150, 0.200, 0.250) are used, producing 40 different models.

5 Connection stiffness needed to ensure head full fixity (K0) is computed by iterative analysis of piles with increasing values of Kconnection. The threshold value at which the moment at pile head remains almost constant (variation less than 10%) is established. As mentioned above, for steel beams values, fully restrained connection condition is fulfilled with values of Krel 25. Once K0 is computed for each model, Krel considering Kconnection = K0 is defined (K rel). Since actual pile flexural stiffness depends on boundary conditions, a stiffness factor EI/L is used to represent pile stiffness. So K rel is expressed as (Eq. 1) K ' rel = K 0 EI L (1) Variation of K rel with Vs/V0 for different slenderness ratios is shown in Fig. 3. Unlike steel beams, K rel value for piles is not constant. In fact, a nearly linear dependence with Vs/V0 is observed. In addition, it can be seen that this dependence is sensitive to slenderness ratio. As pile becomes more slender, K rel values are larger. On the other hand, as Vs/V0 increases (which means that soil is stiffer) an increment on K rel values can be observed. Figure 3. K rel variation with respect of Vs/V0 for L/r =10, 20, 30, 60 and 90. These effects may be associated to active pile length. Active pile length is defined as the upper portion of the pile that bends when a force (or moment) is applied at pile head. It can be expressed with L/r as a fraction of total length (Eq. 2 [11]). L 3.0 E 0 L a E s L r (2)

6 First, it can be seen from Eq. 2 that the fraction of pile that may bend is inversely proportional to L/r. Taking this fact in to account, it is to be expected that as the pile is more slender, the actual pile flexural stiffness is greater than the one computed with the total length L instead of active length La. On the other hand, the dependence of pile active length with Vs/V0 ratio is similar. Given that shear wave velocity (Vs and V0) is directly proportional to elastic modulus (Es and E0), as Vs/V0 is larger, E0/Es is reduced, and therefore active pile length is reduced too. The use of a value of pile flexural stiffness smaller than the actual one, produces an increment of K rel value. In addition, as mentioned above, boundary conditions of the pile ends (head and toe) influence its flexure stiffness. The stiffness of fixed-fixed beam is larger than the stiffness of the case fixed-pinned. Piles toes are neither pinned nor fixed. Actual toe restrain level depends on soil stiffness and pile diameter. This fact produces pile flexure stiffness to be dependent on soil stiffness and pile dimensions due to boundary conditions too. A linear trendline of K re-vs/v0 relation can be established for each slenderness ratio. General equation of these trendlines is (Eq. 3): K ' rel = m V s + b V 0 (3) Different values of m and b parameters are needed to match trendlines for each slenderness ratio. Variation of these parameters with slenderness ratio are plotted in Fig. 4. Figure 4. Trendline parameters m and b variation with L/r. It can be seen from Fig. 4 that variation of parameters m and b with L/r follow a steady trend. Nearly quadratic and linear trend can be stablished for m and b respectively. Equations that match these trends are (Eq. 4): m = 0.3 L 2 r L r b = 1.4 L r 10.0 (4)

7 With Eqs. 3 and 4 connection stiffness needed to ensure full fixity of the head of a pile with specific L/r and Vs/V0 can be computed. Knowledge of this parameter is useful to define shallow foundation elements properties or for evaluation of actual restrain level of pile head. Piles with partially restrained head As mentioned before, the connection stiffness, given by the shallow foundation element, required to achieve a fully restrained condition (K0) is function of soil stiffness, and pile flexural rigidity. In some cases this condition is not achieved. One example is when shallow foundation elements supported by the pile are not stiff enough to provide an appropriate restrain level. Additionally, if there is some damage on the connection zone, pile head restrain level may decrease. To study the influence of partially restrain condition at pile head, the variation of normalized bending moment (M 0) distribution of piles with different restrain level is presented. The moment is normalized with respect to πρ0rügl 3, where üg corresponds to the soil acceleration at the base of the model. Five different connection stiffness are used (Kconnection=K0, 0.75K0, 0.5K0, 0.25K0 and 0 (free head)) for each slenderness ratio considered on previous section. It has been shown that moment distribution is very similar for pseudo-static and transient excitation [11], so in this work pseudo-static excitation is considered. Results are presented with M 0 distribution along normalized pile depth (z/l). Just with demonstrative objectives, in Fig. 5 these distributions are shown for models with L/r=30 and Vs/ V0=0.025 and Results for other models are similar, and not shown here due to lack of space. They can be consulted on [21]. It can be seen that head boundary condition effect is limited to active pile length, as proved on early studies [11], so M 0 on the bottom portion of piles is the same independently on head restrain level. Moment distribution curves for different restrain levels come closer for deeper zones along the pile, getting almost equal at pile active length depth. Besides in pile head moment, no significant differences are noted. At pile head, M 0 values increase as restrain level gets bigger, as expected. For free head case M 0 is zero. For the pile with Kconnection=K0 moment is maximum. Moments at pile head, expressed as a fraction of the moment developed for a fully restrain condition (M0),(Eq. 5), for each Kconnection are computed for all models. M rel = M ' 0 M 0 (5)

8 Relation between restrain level reduction and the decrease of moment developed at pile head is the same regardless soil-pile stiffness contrast. On figure 6, variation of Mrel is plotted as function of relative restrain level (Kconnection/K0). Moment decrease at pile head does not keep a linear relation with restrain reduction. This relation can be approximated by Eq. 6: ( ) if K connection > ln(K connection K 0 ) (1 K connection K 0 M rel 0 if K connection = 0 (6) Vs/V0=0.025 Vs/V0=0.050 K K 0 0.5K K 0 Freehead Figure 5. Normalized bending moment (M 0) for piles with different head restrain level, for Vs/V0=0.025 (left) and Vs/V0=0.050 (right) for L/r=30. Figure 6. Fraction of fully restrain moment (Mrel) variation with restrain level (Kconnection/K0)

9 With Eq. 6, the moment developed at pile head partially restrained can be defined as a fraction of moment developed when the pile is fully fixed. This equation is useful to compute the moment at pile head when either shallow footing element is not stiff enough to fully fix pile head or some damage is expected at the connection. Numerical example To show the applicability of the described procedure, a demonstrative example is presented. A frictional concrete pile with V0=2,000.0 m/s, ν0=0.3, ρ0=2, kg/m 3 and ζ0=0.03 is considered. Pile geometrical properties are L=20.0 m and r=0.50 m, so pile slenderness ratio yields to L/r=40. A very soft clay layer is used with Vs =70.0 m/s, νs=0.5, ρs=1, kg/m 3 and ζ0=0.05. These soil properties are representative of clay in Mexico City [22]. With these properties of soil and pile materials, values of Vs /V0 =0.035 and ρs/ρ0=0.75 are established. Transient response of soil-pile model to time-history acceleration recorded on deep rock deposits of Mexico City is computed. The time-history acceleration used as excitation is shown on Fig. 7. Substituting L/r=40 on Eq. 4 values for m=796 and b=46 are computed. With these values and using Vs/V0=0.035 on Eq. 4 yields to K rel= From Eq. 1 with flexural pile stiffness factor EI/L, connection rigidity to ensure fully fixation K0 is defined. Response of three models were computed. One model with Kconnection =K0, other with Kconnection =1000K0 and a third one with Kconnection =0.3K0. The first two models are considered to confirm that a connection with K0 is indeed enough to consider fully fixation. Third model is used to demonstrate usage and validation of Eq. 6. Figure 7. Time-history acceleration recorded on deep rock deposits in Mexico City. On Fig. 8, envelopes of maximum bending moments of three models are presented. Pile head moment of models with Kconnection=K0 and 1000K0 are very close, the difference is less than 10%. This result confirms that increments of Kconnection above K0 value yields in a very small increment on pile head moment, so it can be said that K0 ensures a fully fixed condition.

10 Pile head moment for fully fixed condition is M0 = kn-m. Third model considers a connection stiffness reduction of 70% (Kconnection/K0=0.3). Using Eq. 6, a value of Mrel=0.816 is computed, so reduced pile head moment will be M0=(58.01)(0.816)=47.37 kn-m. Moment computed from time-history analysis of third model is equal to the one calculated with Eq. 6. (Fig. 7). K K 0 0.3K 0 Figure 8. Envelopes of maximum bending moment of piles with different restrain level (Kconnection={K0, 1000K0 and 0.3K0}). Conclusions Analysis of partially restrained head piles is presented. First, the stiffness to ensure fully fixed condition on pile head is computed (K0). This stiffness is defined in terms of relative connection-pile flexural rigidity (K rel=k0/(ei/l)). It is found that, besides pile flexural stiffness, soil-pile stiffness contrast affects this parameter. An equation to compute K rel in terms of pile slenderness ratio and soil-pile shear wave ratio is proposed. It is found that partially restrain head condition affects only above pile active length. The main difference is magnitude of the moment at pile head. Moment variation for piles with different restrain levels is independent of soil-pile shear wave velocity ratio. An equation to compute moment reduction in terms of restrain level reduction is also proposed. Comparative analysis between proposed equations and numerical transient pile response shows that computations with proposed equations agrees with numerical results. All computations showed in this work are for elastic and homogeneous materials and single piles. Soil heterogeneity, material no-linear behavior and group effects must be studied.

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