Deterministic and probabilistic analysis of great-depth braced excavations:A 32 m excavation case study in Paris

The Fort d’Issy-Vanves-Clamart(FIVC)braced excavation in France is analyzed to provide insights into the geotechnical serviceability assessment of excavations at great depth within deterministic and probabilistic frameworks.The FIVC excavation is excavated at 32 m below the ground surface in Parisian sedimentary basin and a plane-strain finite element analysis is implemented to examine the wall deflections and ground surface settlements.A stochastic finite element method based on the polynomial chaos Kriging metamodel(MSFEM)is then proposed for the probabilistic analyses.Comparisons with field measurements and former studies are carried out.Several academic cases are then conducted to investigate the great-depth excavation stability regarding the maximum horizontal wall deflection and maximum ground surface settlement.The results indicate that the proposed MSFEM is effective for probabilistic analyses and can provide useful insights for the excavation design and construction.A sensitivity analysis for seven considered random parameters is then implemented.The soil friction angle at the excavation bottom layer is the most significant one for design.The soil-wall interaction effects on the excavation stability are also given.

Experimental and numerical study of buckling-restrained braces configured with out-of-plane eccentricity under cyclic loading

This study focuses on variations in the hysteretic behavior of buckling-restrained braces(BRBs)configured with or without out-of-plane eccentricity under cyclic loading.Quasi-static experiments and numerical simulations were carried out on concentrically and eccentrically loaded BRB specimens to investigate the mechanical properties,energy dissipation performance,stress distribution,and high-order deformation pattern.The experimental and numerical results showed that compared to the concentrically loaded BRBs,the stiffness,yield force,cumulated plastic ductility(CPD)coefficient,equivalent viscous damping coefficient and energy dissipation decreased,and the yield displacement and compression strength adjustment factor increased for the eccentrically loaded BRBs.With the existence of the out-of-plane eccentricity,the initial yield position changes from the yield segment to the junction between the yield segment and transition segment under a tensile load,while the initial high-order buckling pattern changes from a first-order C-shape to a secondorder S-shape under a compressive load.

Ductility demands on buckling-restrained braced frames under earthquake loading

Accurate estimates of ductility demands on buckling-restrained braced frames(BRBFs)are crucial to performance-based design of BRBFs.An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center,Lehigh University to prepare for an upcoming experimental program.The analysis program DRAIN-2DX was used to model a one-bay,four-story prototype BRBF including material and geometric nonlinearities.The buckling- restrained brace(BRB)model incorporates both isotropic and kinematic hardening.Nonlinear static pushover and time- history analyses were performed on the prototype BRBF.Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results.Particular emphasis was placed on global ductility demands and ductility demands on the BRBs.These demands were compared with anticipated ductility capacities.The analysis results,along with results from similar previous studies,are used to evaluate the BRBF design provisions that have been recommended for codification in the United States.The results show that BRB maximum ductility demands can be as high as 20 to 25.These demands significantly exceed those anticipated by the BRBF recommended provisions.Results from the static pushover and time- history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5.Modifications to the testing protocol are recommended.

Damping characteristics of friction damped braced frame and its effectiveness in the mega-sub controlled structure system

Based on energy dissipation and structural control principle, a new structural configuration, called the megasub controlled structure （MSCS） with friction damped braces （FDBs）, is first presented. Meanwhile, to calculate the damping coefficient in the slipping state a new analytical method is proposed. The damping characteristics of one-storey friction damped braced frame （FDBF） are investigated, and the influence of the structural parameters on the energy dissipation and the practical engineering design are discussed. The nonlinear dynamic equations and the analytical model of the MSCS with FDBs are established. Three building structures with different structural configurations, which were designed with reference to the conventional mega-sub structures such as used in Tokyo City Hall, are comparatively investigated. The results illustrate that the structure presented in the paper has excellent dynamic properties and satisfactory control effectiveness.

Shaking table test and numerical analysis of a 1:12 scale model of a special concentrically braced steel frame with pinned connections

This paper describes shaking table tests of a 1：12 scale model of a special concentrically braced steel frame with pinned connections, which was fabricated according to a one-bay braced frame selected from a typical main factory building of a large thermal power plant. In order to investigate the seismic performance of this type of structure, several ground motion accelerations with different levels for seismic intensity Ⅷ, based on the Chinese Code for Seismic Design of Buildings, were selected to excite the model. The results show that the design methods of the members and the connections are adequate and that the structural system will perform well in regions of high seismicity. In addition to the tests, numerical simulations were also conducted and the results showed good agreement with the test results. Thus, the numerical model is shown to be accurate and the beam element can be used to model this structural system.

Experimental study on the seismic response of braced reinforced concrete frame with irregular columns

A 15-storey K-braced reinforced concrete model frame with irregular columns, i.e., T-shaped, L-shaped, as well as ＋-shaped columns, was constructed and tested on the six-degree-of-freedom shaking table at the State Key Laboratory for Disaster Reduction in Civil Engineering in Tongji, China. Two types of earthquake records, El-Centro wave （south-north direction） and Shanghai artificial wave （SHAW） with various peak accelerations and principal-secondary sequences, were input and experimentally studied. Based on the shaking table tests and theoretical analysis, several observations can be made. The failure sequence of the model structure is brace→beam→column→joints, so that the design philosophy for several lines of defense has been achieved. Earthquake waves with different spectrums not only influence the magnitude and distribution of the earthquake force and the storey shear force, but also obviously affect the magnitude of the displacement response. The aftershock seismic response of previously damaged reinforced concrete braced frames with irregular columns possesses the equivalent elastic performance characteristic. Generally speaking, from the aspects of failure features and drift ratio, this type of reinforced concrete structure provides adequate earthquake resistance and can be promoted for use in China.

Behavior of braced excavation in sand under a seismic condition: experimental and numerical studies

The behavior of braced excavation in dry sand under a seismic condition is investigated in this paper.A series of shake table tests on a reduced scale model of a retaining wall with one level of bracing were conducted to study the effect of different design parameters such as excavation depth,acceleration amplitude and wall stiffness.Numerical analyses using FLAC 2D were also performed considering one level of bracing.The strut forces,lateral displacements and bending moments in the wall at the end of earthquake motion were compared with experimental results.The study showed that in a post-seismic condition,when other factors were constant,lateral displacement,bending moment,strut forces and maximum ground surface displacement increased with excavation depth and the amplitude of base acceleration.The study also showed that as wall stiffness decreased,the lateral displacement of the wall and ground surface displacement increased,but the bending moment of the wall and strut forces decreased.The net earth pressure behind the walls was influenced by excavation depth and the peak acceleration amplitude,but did not change significantly with wall stiffness.Strut force was the least affected parameter when compared with others under a seismic condition.

An intelligent procedure for updating deformation prediction of braced excavation in clay using gated recurrent unit neural networks

This paper aims to establish an intelligent procedure that combines the observational method with the existing deep learning technique for updating deformation of braced excavation in clay.The gated recurrent unit(GRU) neural network is adopted to formulate the forecast model and learn the potential rules in the field observations using the Nesterov-accelerated Adam(Nadam) algorithm.In the proposed procedure,the GRU-based forecast model is first trained based on the field data of previous and current stages.Then,the field data of the current stage are used as input to predict the deformation response of the next stage via the previously trained GRU-based forecast model.This updating process will loop up till the end of the excavation.This procedure has the advantage of directly predicting the deformation response of unexcavated stages based on the monitoring data.The proposed intelligent procedure is verified on two well-documented cases in terms of accuracy and reliability.The results indicate that both wall deflection and ground settlement are accurately predicted as the excavation proceeds.Furthermore,the advantages of the proposed intelligent procedure compared with the Bayesian/o ptimization updating are illustrated.

Peak displacement patterns for the performance-based seismic design of steel eccentrically braced frames

Performance-based seismic design(PBSD) aims to assess structures at different damage states. Since damage can be directly associated to displacements, seismic design with consideration of displacement seems to be logical. In this study, simple formulae to estimate the peak floor displacement patterns of eccentrically braced frames(EBFs) at different performance levels subjected to earthquake ground motions are proposed. These formulae are applicable in a PBSD and especially in direct displacement-based design(DDBD). Parametric study is conducted on a group of 30 EBFs under a set of 15 far field and near field accelerograms which they scaled to different amplitudes to adapt various performance levels. The results of thousands of nonlinear dynamic analyses of EBFs have been post-processed by nonlinear regression analysis in order to recognize the major parameters that influence the peak displacement pattern of these frames. Results show that suggested displacement patterns have relatively good agreement with those acquired by an exact nonlinear dynamic analysis.

Optimized functional linked neural network for predicting diaphragm wall deflection induced by braced excavations in clays

Deep excavation during the construction of underground systems can cause movement on the ground,especially in soft clay layers.At high levels,excessive ground movements can lead to severe damage to adjacent structures.In this study,finite element analyses(FEM)and the hardening small strain(HSS)model were performed to investigate the deflection of the diaphragm wall in the soft clay layer induced by braced excavations.Different geometric and mechanical properties of the wall were investigated to study the deflection behavior of the wall in soft clays.Accordingly,1090 hypothetical cases were surveyed and simulated based on the HSS model and FEM to evaluate the wall deflection behavior.The results were then used to develop an intelligent model for predicting wall deflection using the functional linked neural network(FLNN)with different functional expansions and activation functions.Although the FLNN is a novel approach to predict wall deflection;however,in order to improve the accuracy of the FLNN model in predicting wall deflection,three swarm-based optimization algorithms,such as artificial bee colony(ABC),Harris’s hawk’s optimization(HHO),and hunger games search(HGS),were hybridized to the FLNN model to generate three novel intelligent models,namely ABC-FLNN,HHO-FLNN,HGS-FLNN.The results of the hybrid models were then compared with the basic FLNN and MLP models.They revealed that FLNN is a good solution for predicting wall deflection,and the application of different functional expansions and activation functions has a significant effect on the outcome predictions of the wall deflection.It is remarkably interesting that the performance of the FLNN model was better than the MLP model with a mean absolute error(MAE)of 19.971,root-mean-squared error(RMSE)of 24.574,and determination coefficient(R^(2))of 0.878.Meanwhile,the performance of the MLP model only obtained an MAE of 20.321,RMSE of 27.091,and R^(2)of 0.851.Furthermore,the results also indicated that the proposed hybrid models,i.e.,ABC-FLNN,HHO-FLNN,HGS-FLNN,yielded more superior performances than those of the FLNN and MLP models in terms of the prediction of deflection behavior of diaphragm walls with an MAE in the range of 11.877 to 12.239,RMSE in the range of 15.821 to 16.045,and R^(2)in the range of 0.949 to 0.951.They can be used as an alternative tool to simulate diaphragm wall deflections under different conditions with a high degree of accuracy.

Assessment of buckling-restrained braced frame reliability using an experimental limit-state model and stochastic dynamic analysis

Buckling-restrained braces （BRBs） have recently become popular in the United States for use as primary members of seismic lateral-force-resisting systems. A BRB is a steel brace that does not buckle in compression but instead yields in both tension and compression. Although design guidelines for BRB applications have been developed, systematic procedures for assessing performance and quantifying reliability are still needed. This paper presents an analytical framework for assessing buckling-restrained braced frame （BRBF） reliability when subjected to seismic loads. This framework efficiently quantifies the risk of BRB failure due to low-cycle fatigue fracture of the BRB core. The procedure includes a series of components that： （1） quantify BRB demand in terms of BRB core deformation histories generated through stochastic dynamic analyses; （2） quantify the limit-state of a BRB in terms of its remaining cumulative plastic ductility capacity based on an experimental database; and （3） evaluate the probability of BRB failure, given the quantified demand and capacity, through structural reliability analyses. Parametric studies were conducted to investigate the effects of the seismic load, and characteristics of the BRB and BRBF on the probability of brace failure. In addition, fragility curves （i.e., conditional probabilities of brace failure given ground shaking intensity parameters） were created by the proposed framework. While the framework presented in this paper is applied to the assessment of BRBFs, the modular nature of the framework components allows for application to other structural components and systems.

Steel rings as seismic fuses for enhancing ductility of cross braced frames

A new remedy is proposed in this study to increase the ductility of cross-braced frames to a level comparable with ductile moment frames.The suggested system consists of one or two concentric steel rings installed in the cross-braced bay vertically.The steel rings are designed such that they fail in bending sooner than failure of the braces in compression.Then the rings act as seismic fuses with multiple bending plastic hinges.Using nonlinear static analysis,it is shown that the proposed system can be designed to behave like cross-braced frames with regard to stiffness and strength,and like special moment frames with regard to ductility.Seismic design factors for the proposed system are recommended based on nonlinear pushover and cyclic analysis studies.

Behavior of braced wall embedded in saturated liquefiable sand under seismic loading

It is well known that the generation of excess pore water pressure and/or liquefaction in foundation soils during an earthquake often cause structural failures.This paper describes the behavior of a small-scale braced wall embedded in saturated liquefiable sand under dynamic condition.Shake table tests are performed in the laboratory on embedded retaining walls with single bracing.The tests are conducted for different excavation depths and base motions.The influences of the peak magnitude of the ground motions and the excavation depth on the axial forces in the bracing,the lateral displacement and the bending moments in the braced walls are studied.The shake table tests are simulated numerically using FLAC 2D and the results are compared with the corresponding experimental results.The pore water pressures developed in the soil are found to influence the behavior of the braced wall structures during a dynamic event.It is found that the excess pore water pressure development in the soil below the excavation is higher compared to the soil beside the walls.Thus,the soil below the excavation level is more susceptible to the liquefaction compared to the soil beside the walls.

Simulating the Seismic Response of Concentrically Braced Frames Using Physical Theory Brace Models

The aim of this paper is to assess the accuracy of brace models formulated in Drain 2DX and OpenSees by comparing the simulated results with those obtained from experimental tests. Both, Drain 2DX and OpenSees rely on the physical theory brace model. In this study, experimental tests conducted on the behaviour of structural hollow section braces subjected to symmetric and asymmetric quasi-static cyclic loading were selected for calibrating the numerical model. In addition, the predicted failure strain parameter resulted from a proposed empirical equation as a function of slenderness ratio, width-to-thickness ratio and steel properties was used to define the low-cycle fatigue material that was assigned to model braces in OpenSees. It is concluded that both Drain 2DX and OpenSees brace models give a good prediction in terms of maximum tensile and buckling force, as well as interstorey drift. However, in Drain 2DX, the brace model is not able to replicate the out-of-plan buckling and the braced frame model cannot provide an accurate response when the system experiences highly nonlinear demand. To emphasise the differences in performance between Drain 2DX and OpenSees, the behaviour of a 4-storey concentrically braced frame with zipper bracing configuration, located in Victoria, BC, was investigated.

Parametric Study on Cable-Stayed and Knee-Braced Steel Portal Frames

To improve wind resistance capacity of cable-braced steel portal frames,a double-braced portal frame was proposed by adding two pre-stressed knee braces to a cable-braced portal frame. To study the reasonable range of application and method of cable parameter determination for this novel structure,the influences of load condition, span, base constraint, and cable parameters on structural performance were investigated by using the finite element code SAP2000. The results show that pre-stressed knee braces can effectively resist both uplifted and lateral wind loads,so this cablestayed and knee-braced steel portal frame is suitable for large wind.When the vertical load is comparable with the wind load,this novel type of portal frames is suitable for a medium span( 21-48 m). The cables in the cable brace can be determined by structural vertical stiffness,and the cables in the knee brace can be designed as the same as those in the cable-stayed part for the reason that their cross sectional area has only a weak effect on the structure. If no cable fails,the pretension variation of the cable does not affect the stiffness of the portal frame. The cable in the cable brace,working together with the cables in the knee braces,can ease uneven distribution of internal force,and their pretensions can be determined according to actual engineering projects.

Behavior of ductile steel X-braced RC frames in seismic zones

A satisfactory ductile performance of moment-resisting reinforced concrete concentric braced frame structures (RC-MRCBFs) is not warranted by only following the provisions proposed in Mexico’s Federal District Code (MFDC-04). The nonlinear behavior of low to medium rise ductile RC-MRCBFs using steel X-bracing susceptible to buckling is evaluated in this study. The height of the studied structures ranges from 4 to 20 stories and they were located for design in the lakebed zone of Mexico City. The design of RC-MRCBFs was carried out considering variable contribution of the two main lines of defense of the dual system (RC columns and steel braces). In order to observe the principal elements responsible for dissipating the earthquake input energy, yielding mappings for diff erent load-steps were obtained using both nonlinear static and dynamic analyses. Some design parameters currently proposed in MFDC-04 as global ductility capacities, overstrength reduction factors and story drifts corresponding to diff erent limit states were assessed as a function of both the considered shear strength and slenderness ratios for the studied RC-MRCBFs using pushover analyses. Additionally, envelopes of response maxima of dynamic parameters were obtained from the story and global hysteresis curves. Finally, a brief discussion regarding residual drifts, residual drift ratios, mappings of residual deformations in steel braces and residual rotations in RC beams and columns is presented. From the analysis of the obtained results, it is concluded that when a suitable design criterion is considered, good structural behavior of RC-MRCBFs with steel-X bracing can be obtained. It is also observed that the shear strength balance has an impact in the height-wise distribution of residual drifts, and an important “shake-down” eff ect is obtained for all cases. There is a need to improve design parameters currently proposed in MFDC to promote an adequate seismic performance of RC-MRCBFs.

Conceptual study of X-braced frames with different steel grades using cyclic half-scale tests

In this paper, an experimental and analytical study of two half-scale steel X-braced flames with equal nominal shear strength under cyclic loading is described. In these tests, all members except the braces are similar. The braces are made of various steel grades to monitor the effects of seismic excitation. Internal stiffeners are employed to limit the local buckling and increase the fracture life of the steel bracing. A heavy central core is introduced at the intersection of the braces to decrease their effective length. Recent seismic specifications are considered in the design of the X-braced frame members to verify their efficiency. The failure modes of the X-braced frames are also illustrated. It is observed that the energy dissipation capacity, ultimate load capacity and ductility of the system increase considerably by using lower grade steel and proposed detailing. Analytical modeling of the specimens using nonlinear finite element software supports the experimental findings.

Seismic response of high-rise steel framed buildings with Chevron-braced designed according to Venezuelan codes

The object of this study is to determine the seismic response of regular high-rise steel buildings with chevron-braced frames. Mechanics models of three buildings of 14, 18 and 20 stories are studied, all of them with similar geometric characteristics in plant and elevation. These models are realized using prescriptions and parameters from venezuelan design codes. The seismic action is carry on through varius synthetic design spectrum compatible accelerograms defined by the seismic codes in this study, with three levels of intensity corresponding to three specific Limit States. Dynamic analysis is used to compute parameters of ductility, over strength and maximum displacements. From these results it can be concluded that chevron-braced frames presented a good overall performance and non V-braced frames show greater damage due to dynamic actions, validating non linear dynamic analysis as a very powerful tool to seismic-resistance design and chevron-braced frames as a very useful choice in improving the response of tall steel structures. since this lateral bracing system is absent from Venezuelan seismic codes.

Optimization of design parameters for controlled rocking steel braced dual-frames

A controlled rocking concentrically steel braced frame(CR-CSBF)is introduced as an alternative to conventional methods to prevent major structural damage during large earthquakes.It is equipped with elastic post-tensioned(PT)cables and replaceable devices or fuses to provide overturning resistance and dissipate energy,respectively.Although CR-CSBFs are not officially legalized in globally valid codes for new buildings,it is expected to be presented in them in the near future.The main goal of this study is to determine the optimal design parameters consist of the yield strength and modulus of elasticity of the fuse,the initial force of the PT cable,and the gravity load on the rocking column,considering different heights of the frame,spanning ratios and ground motion types for dual-configuration CR-CSBF.Nonlinear time-history analyses are performed in OpenSees.This study aims to define the optimal input variables as effective design parameters of CR-CSBFs by comparing four seismic responses consisting of story drift,roof displacement,roof acceleration and base shear,and also using the Euclidean metric optimization method.Despite the previous research,this study is innovative and first of its kind.The results demonstrate that the optimal design parameters are variable for various conditions.

Nonlinear Seismic Response of Steel Concentrically Braced Frames Using Endurance Time Analysis Method

In present paper application of Endurance Time Analysis （ETA） method in nonlinear seismic assessment of steel concentrically braced frames is studied. In this method structure is subjected to a set of predesigned increasing acceleration functions and various responses of the structure are recorded during synthetic seismic excitation. The averages of maximum values for various responses in Nonlinear Time-History Analyses （NTHA） extracted from real ground motions are expected to be close to those obtained from ETA up to equivalent target time. For this purpose a set of 9, 11, 13 and 15 stories steel frames were designed and plastic hinge method was selected as source of nonlinearity in all cases. Responses were compared based on interstory drift ratio and story shear in two methods and results show satisfactory consistency between two methods. Finally, it was concluded that the ETA method can be used as alternative method in nonlinear seismic analysis of concentrically braced steel frames.