Seismic Analysis of Caisson Foundation

Seismic Analysis of Caisson Foundation

Aswathy M.G.1

1P.G. Student

Department of Civil Engineering Mar Athanasius College of Engineering

Kothamangalam, Kerala, India.

Boby Jacob2 2Asst. Professor

Department of Civil Engineering Mar Athanasius Col lege of Engineering

Kothamangalam, Kerala, India.

Abstract Caisson foundations are extensively used as supports and anchors for major structures especially bridges in soft soils. This study involves seismic analysis of caisson foundations in cohesive soil under lateral load and overturning moment. A simplified model of caisson is developed in ANSYS software and nonlinear static pushover analysis is performed. A caisson with pier column is modeled and a mass is attached to the top of pier column. Rotational springs are attached to both caisson and deck mass. This arrangement constitutes a simplified model. Different simplified models are prepared with changes in spring stiffness, and a most effective model is selected. For this effective model, the pier height is varied and analysed.

KeywordsCaisson Foundation; Nonlinear Static Analysis; Cohesive Soil; Lateral Load; Overturning Moment.

1. INTRODUCTION

   Caisson foundations are widely used as supports and anchors for major structures in soft soils. Mainly caissons are used for supporting bridges, transmission towers etc. In cases where the span of the bridge is very much greater and the structure becomes very heavy, in such situations a massive foundation called caisson is provided. But this massive dimension of caisson does not guarantee seismic resistance. As a result of their geometry and stiffness characteristics, the mechanisms of load transfer from the superstructure to the surrounding soil become complex. A study of the behavior of caisson when subjected to horizontal load is essential to understand the foundation behavior. For analysis, the caisson- soil- pier system is simplified. Finite element simplified model is developed which will allow for realistic representation of complex soil-structure interaction effects associated with these foundation elements. The main advantages of using simplified model for analysis include: (a) simplicity, (b) computational cost effectiveness and (c) versatility to describe the observed response. Caissons are highly versatile in constructability for a wide variety of soil formations, and can be installed in virtually any soil type including residual soils, soft soils and marine sites. Even further, since no dewatering is necessary during construction, caissons are particularly advantageous at soft sites or sites where excessive groundwater is considered to be critical for the selection of the excavation and support method. Large diameter caisson foundations are used for the most part as bridge foundation elements, as well as deep-water wharves, and overpasses.

   In this thesis work a simplified model of caisson-pier system is developed. The major components of model are soil (cohesive), caisson, pier column and mass. Soil is modeled as

   spring, and the stiffness of soil is given to rotational spring. The pier column is modeled as a beam element and the mass of deck is attached to the pier column. A horizontal load and overturning moment is applied at the top of the pier. For deck stiffness rotational spring is attached with the mass. In 2014, Athanasios Zafeirakos and Nikos Gerolymos conducted an analytical study involving nonlinear static analysis of caissons and they proposed a methodology for seismic capacity design [1]. Gazetas. G and Varun Assimaki D (2009) developed an analytical model that accounts for the multitude of soil resistance mechanisms mobilized at their base and circumference, while retaining the advantages of simplified methodologies for the design of non-critical facilities [6].

2. SELECTION OF IDEALISED MODEL

   1. Finite Element Modeling

      The nonlinear response under lateral monotonic and slow- cyclic loading of caisson foundations supporting bridge piers in cohesive soils is investigated. The caisson under study is supporting a reinforced concrete arch bridge; the bridge has a total length of 200m and a central span of 90m. The bridge deck was constructed by the cantilever method and is rigidly connected to the piers. The caisson is surrounded by soil and the load transfer from the deck is through the pier column. Here the caisson is a concrete square structure having a size of 10m x 10mx 10m. The caisson material is modeled as isotropic linear elastic, with a unit weight of =25 kN/m3, a Young's modulus of Ec=3 x 108 kPa and a Poisson's ratio of c=0.15. The concentrated mass on pier column is 2700 kg. Two layers of soil are modeled, assuming homogeneous elastic soil conditions. Top layer has a depth of 6m and for bottom layer 14m. The size of the finite element mesh is 5Bx5Bx5B where B is the width of caisson. The element chosen is SOLID 187 for both caisson and soil and BEAM 188 for pier column.

      TABLE I. PROPERTIES OF MATERIALS

      Property	Concrete	Top Soil	Bottom Soil
      Density	2548 kg/m3	1723.65 kg/m3	1814.37
      Modulus of elasticity	3 x 1011 Pa	97.5 MPa	195 MPa
      Poissons ratio	0.15	0.25	0.25
      Bulk modulus	1.4286 x 1011 Pa	65 MPa	130 MPa
      Shear modulus	1.3043 x 1011 Pa	39 MPa	78 MPa

      In this study a simplified model of caisson- soil- pier system is modeled and four idealized versions of actual system are considered with respect to the top (pier- bridge- deck support connection) and bottom (foundation compliance) boundary conditions.

      1. A top free to rotate column (appropriate for modeling the lateral response of relatively long- spanned bridges, or when the bridge columns and beams are connected through a hinge) fixed at its base.

      2. A beam column fixed at its base, the motion of which is hampered at its top against rotation via a rotational spring kR representing the pier-to- deck connection rigidity.

      3. Similar to model 2, additionally four rotational springs on the four surfaces of caisson (kH) and a rotational spring at the bottom (kM).

      4. Similar to model 3, but with consideration of linear

         stiffness matrix for foundation compliance, i.e., k H, kM, k MH (on bottom edges of caisson).

         Out of which the best model is chosen and analysis

         is carried out for that model for different pier heights 6m, 17m, and 55m. The value of KH, KM, and KMH are found by equations (2),(3) and (4).

   2. Properties of Pier Column

   Model	Load carrying capacity (%)	ltotal (m)	o on caisson (Pa)	l on pier (m)	Axial force on pier (kN)	M (Nm)	(rad)
   	(1)	(2)	(3)	(4)	(5)	(6)	(7)
   I	54%	11.2	1.6×107	11.2	2.11 x10-8	1.4 x108	0
   II	71%	1.14	3.5×107	0.06/p>	82.06	2.4 x106	0
   III	98%	0.24	2.56 x107	98 x10- 5	61.07	3 x105	0.033
   IV	100%	0.14	2.49 x107	19 x10- 5	1.547	5 x107	0.019

   The pier columns are modeled with 3-D beam elements, with elasticity modulus E =3 x108 kPa and =0.15. The geometric

   Fig. 1. Simplified model 4 (For 6m pier height and Kratio= 0.1) TABLE IV ANALYSIS RESULTS

   c c

   properties of the piers, namely the cross-sectional areas (A: m2) and moments of inertia (I: m4), are given in Table2. To investigate the effect of pier-to deck stiffness on the response of the foundation, the stiffness of the rotational spring, KR, was appropriately modified so that the stiffness ratio,

   Kratio = KR/(4EcI/H) (1)

   where, (4EIc/H) is the flexural stiffness of the column, yields the following values: Kratio=0.1,0.25,0.5,1 for every case examined. The shear modulus of rock at very small deformations is estimated to G0 =1 GPa.

   KH = 9.4G0B; (2)

   KM = 10.8G0B3; (3)

   KMH = -6.3G0B2 (4)

   where, B is the width of square caisson, B=10m. On substituting this in above equations we get,

   KH = 9.4 x 1010 N/m

   KM = 10.8 x 1012 N/m

   KMH =-6.3 x 1011 N/m

   TABLE II GEOMETRIC PROPERTIES OF PIER COLUMN

   H (m)	A (m2)	I (m4)
   6	13.85	3.98
   17	22.90	15.27
   55	40.72	41.74

   TABLE III VALUES OF KR FOR DIFFERENT KRATIO AND PIER HEIGHT

   H (m)	Kratio= 0.1	Kratio =0.25	Kratio =0.5	Kratio =1
   6	7.96 x 1010	1.99 x 1011	3.98 x 1011	7.96 x 1011
   17	1.078 x 1011	2.7 x 1011	5.4 x 1011	10.8 x 1011
   55	9.12 x 1010	2.28 x 1011	4.56 x 1011	9.12 x 1011

   The table IV shows the results of different models for 6m pier height and Kratio= 0.1, representing (column1) load carrying capacity, (2) total deformation, (3) stress on caisson, (4) deformation on pier, (5) axial force on pier, (6) total moment,

   (7) rotation angle in radians. On comparing the results, the load carrying capacity of model 4 is more than model 1. For second model only kR contribute the stiffness, so the load carrying capacity for model 2 is less. Model 4 is transferring the load into the soil through spring, so the load on the pier is less and thus the deformation will be less. The model 4 is the best model which is selected as the idealized simplified model.

   Rui Zhong and Maosong Huang (2014) introduced a simplified method with a dynamic Winkler model to study the seismic response of composite caisson piles foundations [2]. Juan M.Mayoral and Miguel P.Romo (2014) conducted numerical study to evaluate the seismic performance of massive foundations [3].

3. NONLINEAR STATIC ANALYSIS

   The whole soilfoundationsuperstructure system is then subjected to lateral loading at the deck level. Nonlinear static analysis is carried out using idealized simplified model. The values of ultimate lateral load is Qu= 44 x 106 N and overturning moment is Mu= 430 x 106 Nm. These load and moment were applied at the mass on top of the pier column. The structure is analyzed for this slow cyclic loading and overturning moment. The analysis results of model with 6m pier height and Kratio= 0.1 are as follows,

   Fig. 2. Applying moment and horizontal load on the mass

   Fig. 3. Stress on caisson

   Table V Total Bending Moment With Respect To Time

   The results of simplified model with different pier heights are analysed and compared. As the height of the column varies, the cross-sectional area and moment of inertia of pier column also changes. The short columns can carry more load and it is safe on comparing the results. If the structure is over designed it can carry more load, if it is under designed it is not sufficient to carry load.

   Fig. 4. Bending moment diagram

   We can plot graphs based on the results obtained from analysis. From the graphs, 6m pier column is giving good results when compared to other two pier heights. So it is concluded that short columns behaves effectively when load coming on it.

   Ht. of the pier	Kratio	ltotal (m)	l on pier (m)	o on caisson (Pa)	Axial force on pier (N)	M (Nm)	()
   6m	0.1	0.00935	5.39 x10-4	2.7 x107	352.6	2.1 x107	0.079
   	0.25	0.00928	2.77 x10-4	2.5 x107	130.5	1.3 x107	0.079
   	0.5	0.00925	2.62 x10-4	2.5 x107	76.96	1.04 x107	0.079
   	1	0.00924	2.59 x10-4	2.5 x107	54.48	8.94 x106	0.079
   17m	0.1	0.0092	4.1 x10-4	2.538 x107	19.75	6.6 x106	0.079
   	0.25	0.00918	3.05 x10-4	2.544 x107	1.96	4.5 x106	0.079
   	0.5	0.00918	3.08 x10-4	2.546 x107	-3.051	3.8 x106	0.079
   	1	0.00918	3.1 x10-4	2.547 x107	-5.349	3.4 x106	0.079
   55m	0.1	0.009	1.11 x10-3	6.596 x106	-21.7	1.254 x106	0.074
   	0.25	0.00933	1.03 x10-3	6.595 x106	-22.97	9.606 x105	0.077
   	0.5	0.00933	1.01 x10-3	6.595 x106	-23.29	8.674 x105	0.077
   	1	0.00932	1.02 x10-3	6.595 x106	-22.96	9.606 x105	0.071

   TABLE VI RESULTS OF STATIC ANALYSIS

   Time [s]	Minimum [N·m]	Maximum [N·m]
   0.2	1588	4.2467e+006
   0.4	6351.2	8.4927e+006
   0.7	19448	1.4861e+007
   1.	39685	2.1227e+007

   Fig. 5. Axial force diagram for different Kratio

   Fig. 6. Bending moment diagram for different Kratio

4. CONCLUSIONS

A simplified model is analysed using ANSYS software. The pier hight (H), the embedment ratio of the caisson (D/B) and the pier-to-deck joint rigidity (KR) varied parametrically, with the latter being modeled by a rotational spring at the deck level. The soil is also modeled as rotational springs. The foundationsuperstructure systems were then subjected to lateral monotonic and slow-cyclic loading at the deck level. The load transfer is from pier to the caisson then to the spring. The spring stiffness value affects the pier height. In the case of pier column, the axial force on the pier is more at the top. The load carrying capacity is more for pier height=6m. The deformation on the pier increases with increase in pier height. The stiffness value of spring is changed and analysed. The response of structure is different for different stiffness ratio. The rotational stiffness on the deck mass is different for different stiffness ratios. It is concluded that the model 4 is proved as an idealized simplified model where the pier should not be too long or too short.

REFERENCES

1. Athanasios Zafeirakos and Nikos Gerolymos, Towards a seismic capacity design of caisson foundations supporting bridge piers, Soil Dynamics and Earthquake Engineering, vol. 67, 2014, pp.179197.

2. Rui Zhong and Maosong Huang, Winkler model for dynamic response of composite caissonpiles foundations, Soil Dynamics and Earthquake Engineering, vol.66, 2014, pp. 241251.

3. Juan M.Mayoral and Miguel P.Romo, Seismic response of bridges with massive foundations, Soil Dynamics and Earthquake Engineering, vol.71, 2014, pp. 8899.

4. Konstantinos Karapiperis and Nikos Gerolymos, Combined loading of caisson foundations in cohesive soil: finite element versus winkler modeling, Computers and Geotechnics, vol.56, 2013, pp. 100120

5. Zafeirakos A, Gerolymos N, Drosos V, Incremental dynamic analysis of caissonpier interaction, Soil Dynamics Earthquake Engg, vol.48, 2013, pp.7188.

6. Gazetas. G and Varun Assimaki D., A simplified model for lateral response of large diameter caisson foundations-linear elastic formulation, Soil Dynamics Earthquake Engg , 2009, vol.29(2):268 91.

7. Ignatius Po Lam, Hubert Law and Geoffrey R. Martin, bridge foundations:modeling large pile groups and caissons for seismic design, Earthquake Engineering to Extreme Events, MCEER-07-0018, 2007.

8. Varun, A simplified model for lateral response of caisson foundations, Georgia, 2006.

.