_{1}

^{*}

A three dimensional finite element of nonlinear pushover analysis for short span Reinforced Concrete (RC) bridge with circular piers cross section is modeling to present effects of soil structural interaction (SSI). Structural elements model s are including linear foundation springs modeling, and nonlinear RC piers modeling. The paper succeeded to present the SSI effects of nonlinear pushover analysis of short spans RC bridges to determine the significant effects on dynamic characteristics and displacement capacity of short span RC bridges performance; that is increasing within range 11% to 20% compared to baseline pushover analysis of bridge without SSI effects. Results show the bridge stiffness decreases due to SSI effects on the bridge support for more flexible soils types that generates large displacement, with corresponding less base shear in bridge piers and footings by average percentage 12% and 18%, which is important for structural evaluation for new bridge construction and also, for strengthening and repair works evaluation of existing bridges.

The modeling and seismic analysis of bridge structures have been a major evolution over recent decades linked directly to the rapid development of digital computing. Both static and dynamic analysis of bridge systems experienced major breakthroughs when finite-element techniques were developed. In past, elastic analysis procedures used for bridge structural assessment which is not sufficient for inelastic action occurred. Nonlinear dynamic analysis become essential for bridges structural assessment however, it’s costly consuming. For that, nonlinear static analysis (pushover) becomes preferable inelastic seismic behavior tool in structural evaluation of bridges because of its low costs and time consuming.

In damage surveying of bridge rezones by recent earthquakes, the main basic structural rezones can be classified as the following: underestimated of pier section capacity of seismic shear value; large seismic movement of bridge deck that can add additional moment and share to bridge pier, in case of bridge base isolation was under design estimated; inelastic structural actions and associated concepts of ductility were not considered. All the structural deficiencies lead to inelastic failure modes of bridges due to plastic hinge that was created in bridge pier in different locations and levels based on the seismic force value and overall bridge stiffness elements, which was almost uniformly adopted for seismic design of bridges prior to 1970 [

In many of previous studies on bridges that included SSI as well as inelasticity in bridge pier resulted in conflicting opinion on the role of structural inelasticity on seismic demand.

In conventional bridges analysis, their bases are considered fixed bases; very limited investigations have focused on identifying SSI in bridges supporting on shallow foundation. Flexibility levels of the supporting soil will be depended on the soil types and soil parameters from medium to soft soils. This decreases the overall stiffness of the bridge resulting in a subsequent increase in the natural periods of the system and the overall response is altered. The soil structure interaction will have significant effect on the overall capacity curve of bridge under pushover analysis, which is reflected on the failure mode of superstructure of bridge, [

In previous study, [

The study focused on simple finite element modeling of multi-spans of short span RC bridge without curve or skew in plan or elevation as it is shown in the following parts. SAP2000 is the finite element that is used in simulation of nonlinear super structure and soil structure interaction by linear springs. Soil springs stiffness properties are not degradation with pushover load curve; as linear simulation of shallow foundation system of bridge footing. Bridge deck for this types of existing bridges in study case area is defined as no seismic forces in the Gulf zone; for that base isolation between bridge deck and its pier is missing and neglected in simulation.

The paper focus to present simple representation of a soil-bridge pier system, yet one able to capture the effects of the most significant physical parameters. It has been found that SSI greatly affects the dynamic behavior of bridge piers leading to more flexible systems, decrease damping and larger total bridge pier displacements. Besides a thorough investigation of the relative significance of various physical parameters of the system response, an easy-to-use approach that can be incorporated for a preliminary design of bridges and helpful for structural assessment, strengthening and/or rehabilitation of existing short span RC bridges.

The paper has select one of the famous and repeated bridge module in Middle zone of Kingdom of Saudi Arabia (KSA) using in the main road intersection, on of this bridge that used as study case Al-Fahs Bridge located in North-East of Riyadh, KSA. The bridge is a continuous, two-span, cast-in-place concrete girder structure. The two intermediate bents consist of three columns with a cross beam on top as shown in

The bridge consists of multi-spans continuous deck supported by a row of isolation bearings as shown in

Bridge Properties | Al-Fahs Bridge, RUH, KSA |
---|---|

Span length (ft) | 2@15 and (2@4.5 abutment) |

Pier height (m) | 7.5 |

Main girder cross section area (m^{2}) | 0.5 |

Pier cross section area (m^{2}) | 3.8 |

Moment of inertia of bridge pier transverse direction (m^{4}) | 33.7 |

Moment of inertia of bridge pier in longitudinal direction (m^{4}) | 33.7 |

Natural time period of bridge in longitudinal direction (sec) | 0.59 |

Natural time period of bridge in transverse direction (sec) | 0.43 |

rigid abutments and reinforced concrete piers. The isolation bearings are provided instead of conventional bearings between superstructure and substructure at abutment and pier locations. This system is idealized in the accurate finite element mode using professional seismic isolation computer code and nonlinear static analysis using SAP2000 [

Mathematical model of transversal section of bridge model presents in

The 3D finite element of Al-Fahs Bridge presented in

The soil surrounding the foundation of the pier is modeled by springs which has frequency independent stiffness in space. The complete dynamic analysis is carried out in the time domain using Newmark β-method [

In order to measure the effect of SSI on the push over analysis of existing Piers Bridge, base shear force and top displacement are compared with the response of the corresponding bridge ignoring SSI effects. A parametric study is also conducted to investigate the effects of soil flexibility of soft soil, medium soil properties and hard soil report as base line of comparisons.

Consider the typical two-span continuous deck bridge shown in

piers. The structure is assumed to consist of a series of line column-beam elements. The following assumptions are made for pushover analysis of existing bridges taking soil-structure interaction effect into consideration:

1) The soil supporting the foundation of the pier is modeled as springs acting in the vertical, horizontal, and rotational directions.

2) The foundation is represented using rigid elements connected to the soil springs that has frequency-independent coefficients.

The above assumptions lead to the mathematical model of the bridge system shown in

The main parameter to classify the clay soil properties are mentioned in

Comprehensive research has been carried out to evaluate the stiffness of such springs. Closed form expressions for stiffness of equivalent soil springs as depicted in

Soil Types | N value | C (kN/m^{2}) | φ (degree) | γ_{sat} (kN/m^{3}) | C_{c} | e_{0} |
---|---|---|---|---|---|---|

Soft | 10 | 18.5 | 0.0 | 17.0 | 0.189 | 0.90 |

Medium | 20 | 36.8 | 0.0 | 18.5 | 0.135 | 0.72 |

Hard (Baseline) | 45 | 220.0 | 0.0 | 21.0 | 0.093 | 0.58 |

where: N (SPT test), C (cohesion value), φ (Angle of soil internal friction), γ_{sat} (Soil density), Cc (compression index of soil) and e_{0} (initial void ratio of soil).

Degrees of freedom | Stiffness of equivalent soil spring |
---|---|

Vertical | |

Horizontal (transversal direction) | |

Horizontal (longitudinal direction) | |

Rocking (about the longitudinal axis) | |

Rocking (about the transversal axis) | |

Torsion |

A_{b} area of the foundation; B and L, half-width and half-length of a rectangular foundation, respectively; I_{bx}, I_{by}, and I_{bz}, moment of inertia of the foundation area with respect to longitudinal, lateral and vertical axes, respectively [

have been evaluated using the empirical relationship G = 120 N 0.8 t/ft^{2} i.e. G = 12,916,692.48 N 0.8 MPa [

Finite element method was adopted to formulate the mass and stiffness matrices for the bridge model. Responses due to real ground motions were obtained using Newmark step by step direct integration method.

A numerical study is conducted to evaluate the effect of SSI on the pushover results of bridge with different soil types; It is obviously, that elastic analysis procedures used in the past for structural assessment of short span bridge behavior are insufficient and inadequate due to the inability to define the modification of bridge response during inelastic action, which is reflecting on the displacement capacity curve of bridge. However, real seismic analysis is still as the most accurate method to predict structure seismic characteristic; the Pushover analysis is as nonlinear static analysis techniques, which can be used to determine the dynamic characteristics and peak ground footing base shear corresponding to top pier displacement that called displacement curve of structures, to estimate available plastic rotational capacities to ensure satisfactory seismic performance. Estimation of plastic hinge creation will be helpful for structural assessment and expectation of real and more applicable failures modes of bridge. In additional to the above varieties of results and seismic data can be getting more easier than time history analysis that need more time and effort in simulation and modeling compared to pushover analysis that has accepted level of accuracy as it was verified in [

Stiffness of equivalent soil spring | Type of soils | ||
---|---|---|---|

Soft | Medium | Hard | |

Footing dim. 30 * 30 ft | Footing dim. 25 * 25 ft | Footing dim. 15 * 15 ft | |

Vertical (kip/ft) | 42,897 | 130,586 | 1,089,276 |

Horizontal (transversal direction) (kip/ft) | 32,335 | 93,119 | 905,725 |

Horizontal (longitudinal direction) (kip/ft) | 32,335 | 93,119 | 905,725 |

Rocking (about the longitudinal) (kip.ft) | 7,689,516 | 12,130,288 | 17,914,003 |

Rocking (about the transversal) (kip.ft) | 8,361,189 | 13,548,574 | 19,255,865 |

Torsion (kip.ft) | 396,725 | 835,256 | 1,697,930 |

The damping of the bridges is taken as 5% of the critical in all modes of the vibration. The soil surrounding the pier is considered as hard, medium, and soft soil, respectively. The properties of these soils were given in

The pushover loading was not the simple lateral force but related to structure mode shapes. The equivalent lateral seismic load was proportional to a specified mode shape, its angular frequency and the mass tributary to a node where the force is applied. It can be calculated as in Equation (1) [

where: i is (number of node), and j is (number of mode).

F_{ij} is the force at node (i) in the (j) mode of vibration;

d_{ij} is The displacement of node (i) in the (j) vibration mode at the angular circular frequency of ω_{j}; m_{i} is the mass tributary to the node (i).

SAP2000 generates the equivalent static loads at each time step of pushover analysis corresponding to structures modes are defined, the pushover procedure is cleared in manual of software tutorial as explained in details and verification in [

During the numerical analysis procedure of pushover analysis, Seismic demands are estimated by lateral loads that monotonically increase at each time step. The load modes remain the same, until a prescribed displacement is rea- ched or the structure collapses which one achieved firstly in analysis. The equivalent

seismic loads can be forces as well as displacements, and the associated control methods are force and displacement control methods. There are main two disadvantages points of the force control method compared to displacement control method; the first disadvantage point in force control method is the difficulty to refine the force vector increment at each step of the increment analysis after inelasticity develops in the structure. The Second disadvantage point, possibility of reaching to the maximum lateral force and stop the analysis iteration prior to developing the ultimate displacement, [

For that, the displacement control method is more suitable and is adopted in this research. SAP2000 is a nonlinear finite element program software analysis tools, that was used to monitor a target displacement is prescribed at a monitored point, which is usually the mass center of a bridge.

After the pushover analysis has been performed, a static pushover curve and a capacity spectrum of the structure could be generated for each load case. The pushover curve was in the form of the displacement at the monitored point verses the base shear, which is the total force reaction on all the supports in each global direction.

A Capacity Spectrum curve in longitudinal direction is shown in

Capacity spectrum curve of a static Pushover curve and capacity spectrum of the pier bridge presents in

In this study pushover analysis done under three soil structures interaction circumstances; the first one was the datum of comparison which is as per original design that was neglect SSI and called as Hard Soil as shown in

It is obvious due to different flexibility levels of the bridge piers, the compari-

son of the response of these types of soils will be useful in studying the effect of pier flexibility on the response of pushover bridge analysis. The soil surrounding the pier is considered as hard, medium, and soft soil, respectively.

In the bridge transversal direction the pushover displacement capacity curve has the same behaviour with lesser percentage of base shear decreasing and displacement increasing compared to the longitudinal direction of bridge, which is can be explained by the stiffness difference of bridge in both directions, as presented in

This paper succeeds to present numerical analysis of Soil Structure Interaction (SSI) effects on the pushover analysis of short span reinforced concrete bridge pier of multi-spans without curve or skew in plan or elevation. The results from this study indicate the finite element modeling strategies of SSI modeling for three different cases, one is hard soil as datum of comparison with others two soils cases medium, and soft soils; to be more realistic of SSI modeling. In this study the footing size was taken into consideration due to the soil bearing capacity changes as important parameters during calculating SSI equivalent stiffness as it is presented in

The paper succeeds to investigate the SSI effects of nonlinear pushover analysis of short spans RC bridges to evaluate the effects and sensitivity of global performance on dynamic characteristics and displacement capacity curve of study case bridge (Al-Fahs bridge); which is short span RC bridge existing in Riyadh, KSA, simulated SSI effects on the pushover analysis as nonlinear static analysis techniques to present the displacement and base shear capacity of study case for three different soils cases, hard (baseline), Medium, and soft soil.

The numerical finite element analysis and its results succeed to present simple representation of a soil-bridge pier system, yet one able to capture the effects of the most significant physical parameters. It has been found that SSI greatly affects the dynamic behavior of bridge piers leading to more flexible systems, decrease damping and larger total bridge pier displacements. Besides a thorough investigation of the relative significance of various physical parameters of the system response, an easy-to-use approach that can be incorporated for a preliminary design of bridges and helpful for structural assessment, streng- thening and/or rehabilitation of existing short span RC bridges.

The main conclusion and technical explanation of the SSI effects can be summarized in the following points:

1) Both peak displacement and base shear are reduced due to the further flexibility introduced to the system when SSI is accounted for. Thus considerations of the SSI effects will result in substantial reduction in the construction cost and/ or strengthening and repairs of new or existing bridges.

2) The effects of SSI are more pronounced for stiff bridges in comparison to flexible bridges, where the overall stiffness of stiff bridge will be decreased with high percentage compared to the stiff one,

3) Bearing damping does not influence the effects of SSI. This is due to fact that the soil damping is more dominating the bridge response in comparison to bearing damping.

El-Arab, I.M.E. (2017) Soil Structure Interaction Effects on Pushover Analysis of Short Span RC Bridges. Open Journal of Civil Engineering, 7, 348-361. https://doi.org/10.4236/ojce.2017.73024