Rigid Foundation Research Articles

Progressive collapse analysis of experimental building skeleton based on stress-strain state of columns and joints

Purpose: The aim of this work is to compare three methods of the progressive collapse analysis of the experimental building skeleton based on the stress-strain state of the columns and joints. Design technique: The stress-strain state modeling of the columns is performed for the building with the removed intermediate column in the basement. The building includes a basement and represents a reinforced concrete composite frame without collar beams. The MicroFe software is used for three modeling methods, which include quasi-static, dynamic, and kinematic method of limit equilibrium. The MicroFe analysis is combined with the development of the three-dimensional model on a rigid foundation. Findings: The progressive collapse is proven to be impossible for the building skeleton after the removal of the intermediate column in its basement. Originality/value: Based on the three analytical methods, the limit load reproducibility is 15 %. The dynamic analysis gives higher values of the limit load as compared to the quasi-static and kinematic methods. Practical implications: The proposed procedure of three methods for the progressive collapse analysis can be used for the seismic vulnerability analysis.

Vertical vibration of a rigid strip footing on a half-space of unsaturated porous soil

This study presents an analytical solution to the compliance coefficient of rigid strip footings lying on an unsaturated porous soil half-space when subjected to vertical vibration. Using the Fourier transform techniques, the complex interaction between unsaturated soils and rigid strip foundations is transformed into a mixed boundary-value problem based on the developed framework of Biot’s model. The wavenumber domain auxiliary function and boundary conditions are used to convert the governing equations to a pair of dual integral equations. To yield the compliance function, the integral equations are transformed into a system of inhomogeneous linear equations by utilizing hypergeometric polynomials and Bessel functions. The proposed analytical solution is verified against existing solutions to interactions between foundations and saturated soil or single-phase soil by adjusting the parameters in the unsaturated soil model. Additionally, the impacts of soil skeleton saturation, intrinsic permeability, and Poisson’s ratio of unsaturated soil on the dynamic compliance coefficient of rigid strip footings are examined. It is shown that the Poisson’s ratio of the soil skeleton and the soil saturation at critical saturation have a significant effect on the dynamic compliance coefficient, but have a negligible effect on the intrinsic permeability.

ДОСЛІДЖЕННЯ ДЕФОРМУВАННЯ БАГАТОШАРОВОЇ ТРАНСВЕРСАЛЬНО-ІЗОТРОПНОЇ ПЛИТИ НА ЖОРСТКІЙ ОСНОВІ ЗА БЕЗЗГИНОВОЮ УТОЧНЕНОЮ КОНТИНУАЛЬНОЮ МОДЕЛЛЮ

The high-precision estimation of the stress-strain state (SSS) of multilayered plates on a rigid foundation under the action of stationary transverse loading is an urgent task. As its includes the calculations of strength and deformability of various homogeneous and multilayer coatings. This is the calculation of road surface on relatively rigid bridge structures, or on a non-deformable underlying layer or calculation protective multilayer coatings of flat structural elements of greater rigidity than coatings, etc. The combining of materials with isotropic and transversal-isotropic physical characteristics into a multilayer package allows creating of the multifunctional designs. The SSS of such structures due to their structural heterogeneity and the relatively low transverse stiffness of the individual layers is significantly associated with the effect of transverse shear deformations and transverse compression deformations. Therefore, the problem of refined modelling of SSS of plates, which takes into account these types of deformations, is an urgent one. Based on the decomposition the SSS of plate into the flexural and unflexural components, it is proposed to optimize the design diagram of deformation a rectangular multilayer plate on a rigid foundation. The essence of optimization is to consider such a design diagram of the plate, in which the SSS of plate would be fully described by only one component, namely the unflexural component of SSS. To do this, instead of the actual design of the multilayer plate, which is deformed without separation from the foundation, it is suggested to consider the design diagram of the plate, which is formed by supplementing it with a symmetric one about the contact surface of the foundation. In this case, the plate will be symmetrically loaded with respect to the middle surface of the plate, and the thickness of the plate will double. The SSS of plate will be unflexural, which greatly simplifies its modeling. For unflexural SSS, a twodimensional and high-degree iterative approximation but three-dimensional by the nature reflection of SSS, model of deformation of multilayer rectangular plates on a rigid foundation with isotropic and transverse-isotropic layers is constructed in an elastic formulation. This model takes full account deformations of transverse shear and of transverse compression at transverse loading of a plate. Calculations of homogeneous and two-layer transverse-isotropic plates on a rigid foundation under the action evenly distributed and localized transverse loads on the surface of a plate are performed by the finite difference method.

Settlements and Subgrade Reactions of Surface Raft Foundations Subjected to Vertically Uniform Load

The settlements and corresponding soil reactions of a surface raft foundation subjected to vertically uniform load at the sites of granular or cohesive soils have been qualitatively introduced to engineers in the past. This study intends to verify the foundation load-response mechanism using three-dimensional finite-element analyses. The Mohr–Coulomb soil model was used to simulate the nonlinear effects of the granular and cohesive soils. The coefficients of subgrade reactions of the soil were back-calculated and compared to those obtained from the rigid foundation model. For all the square surface rafts studied, non-uniform settlements with the largest value at the center can be found. For the smallest rafts located in clay, the soil reactions were found to be rather consistent. For larger rafts in clay, the soil reactions would be changed according to the soil stiffness and raft dimensions. For surface rafts in sand, the effects of soil stiffness on soil reactions appeared to be insignificant. The soil reactions were generally higher at the center and varied with raft dimensions. For the smallest raft in sand, large soil reactions can be found at the edge. The coefficients of subgrade reactions were found to be more consistent with the smallest values occurring at the center. The results of this study indicate that the load-response mechanism of the raft foundation is rather complicated. Such load-response mechanisms are strongly affected by the relative rigidity of the foundation depending on soil stiffness and foundation dimensions.

Partitioned analysis of soil‐structure interaction for Nuclear Island Buildings

AbstractThe present methods for three‐dimensional time‐domain soil‐structure interaction (SSI) analysis are often uneconomical because they are performed with a single time integration scheme and a single time step, which prohibits their application to large‐scale SSI problems. In this study, a partitioned analysis of SSI (PASSI) is proposed for enhancing SSI computational efficiency. This is accomplished by partitioning the soil‐foundation‐structure system into the soil (foundation) and structure subsystems and implementing the continuity conditions of the displacements and reaction forces at the soil (foundation)‐structure interface in a primal way. A lumped‐mass explicit finite element method and a transmitting artificial boundary are used to model the unbounded soil, the structure is analyzed via the implicit finite element method, and the response of the rigid foundation is calculated through an explicit time integration scheme. The solution is separately advanced over time for each subsystem. Different time steps can be chosen for the explicit and implicit integration schemes, which can greatly improve efficiency. Interaction effects are accounted for by the transmission and synchronization of the coupled state variables. In addition, intrafield and interfield parallel procedures for PASSI are developed, and their theoretical efficiencies are analyzed. A simple example is provided to verify the performance of the partitioned approach with an explicit‐implicit co‐computation and to compare it to the fully explicit approach. Finally, the seismic response analysis of a nuclear power plant is presented to validate the feasibility and efficiency of the intrafield and interfield parallel procedures.

Vibration of Semi Rigid Foundation Locating on Elastic Half Space

Vibration of Semi Rigid Foundation Locating on Elastic Half Space

Dynamic analysis of eccentrically loaded rigid strip foundation on layered transversely isotropic poroelastic media

This paper presents an analytical method for analyzing vertical and rocking motions of a rigid strip foundation on layered transversely isotropic poroelastic media. The extended precise integration method is employed to obtain the plain strain dynamic responses of layered poroelastic media due to the reaction force from the rigid strip. Then, the contact stresses for dynamic soil-structure interactions (SSI) are modelled by the Bessel series expansions, and a set of linear equations can be developed from the dual integral equations of mixed boundary value problems. The explicit expressions for the contact stresses are further obtained by solving these linear equations. Finally, the presented method is verified, and numerical examples are provided to demonstrate the effects of stratifications, transverse isotropy and permeability of media on the dynamic responses of eccentrically loaded rigid strip foundation.

Static Parametric Stress-Strain Analysis for Asphaltic Concrete Core of Rockfill Dams

Abstract This study was conducted to investigate the effect of variations in the asphaltic concrete core Rockfill dam geometric parameters on the core behavior at different upper, middle, and lower points under two-dimensional static stress-strain analysis. The mentioned analysis was performed using SIGMA/W software. In the modeling and analysis process, the geometry of a large number of dams constructed around the world was studied and many numerical models with variations in eight classes of height, three dams upstream/downstream slope modes, and three different asphaltic core positions and thicknesses on a rigid foundation were created and analyzed. In addition, for each of the above models, four dam operation stages including “End of Construction”, “Full Reservoir”, “Half-Full Reservoir”, and “Rapid Drawdown” were considered. The results show, in four different stages of construction and impounding and three different slope modes, the maximum stress as well as horizontal and vertical displacements at the upper, middle, and lower points of the core increase with increasing height. In all models, increasing upstream and downstream slopes results in an increase in the amount of vertical displacement for all construction and impounding stages at the upper, middle, and lower points of the core. In the middle and lower points of the core, with increasing height, the amount of deviatoric stress increases for all construction and impounding conditions. In addition, for all operation cases, the maximum strain increases in all points of the vertical and tilted cores as the core thickness increases. Additional results are presented in the next sections.

Rheological Consolidation of Partially Penetrated Deep Mixed Column-Reinforced Soft Soil under Rigid Foundation

Rheological Consolidation of Partially Penetrated Deep Mixed Column-Reinforced Soft Soil under Rigid Foundation

Comparative Study of S2-Alar-Iliac Screw Trajectories between Males and Females Using Three-Dimensional Computed Tomography Analysis: The True Lateral Angulation of the S2-Alar-Iliac Screw in the Axial Plane.

The S2 alar-iliac screw (S2AIS) is commonly used for long spinal fusion as a rigid distal foundation in spinal deformity surgeries, and it is also used in percutaneous sacropelvic fixation for providing an in-line connection to the proximal spinal constructs without using offset connectors. Although the pelvic shape is different between males and females, reports on S2AIS trajectories according to gender have been scarce in the literature. In this paper, S2AIS trajectories are compared between males and females using pelvic three-dimensional computed tomography (3D-CT) in a normal Japanese population. After resetting the caudal angulation in CT-imaging plane manipulation, the angulation of S2AIS was more lateral in the axial plane and more horizontal in the coronal plane in females. Mean distances from the midline to starting points of S2AIS tended to be shorter in females, whereas mean distances from the midline to the posterior superior iliac spine was significantly longer in females. We also found that there were positive correlations between the patients’ height and the maximal lengths of S2AISs, and the patients’ height and minimal areas of S2AIS pathways. Our results are useful not only for conventional open spinal surgery, but also for minimally invasive spine surgery.

Updated Lagrangian for Compressible Hyperelastic Material with Frictionless Contact

The Updated Lagrangian method for nonlinear elasticity with contact is presented. First, we describe the Total Lagrangian for a compressible Neo-Hookean material. Next, we introduce the Updated Lagrangian formulation for Neo-Hookean and Ogden compressible materials with contact. An advantage of this approach is that at each iteration only a linear system is solved. The linear problem to be solved is written in the updated domain. Numerical results are presented: compression of a Hertz half ball and of a hyperelastic ring against a flat rigid foundation, and contact of an elastic cube and a ball.

Evaluation of the contact problem of functionally graded layer resting on rigid foundation pressed via rigid punch by analytical and numerical (FEM and MLP) methods

Evaluation of the contact problem of functionally graded layer resting on rigid foundation pressed via rigid punch by analytical and numerical (FEM and MLP) methods

Mechanical regulation of tissues that reproduces wrinkle patterns of gastrointestinal tracts

Gastrointestinal tracts exhibit a number of surface morphologies including zigzags, labyrinths, protrusions, and invaginations that are associated with digestive functions and are suggested to be formed by mechanical mechanisms. In this study, we investigate loading conditions and mechanical properties of tissues that reproduce different wrinkle patterning of gastrointestinal tracts on cell culture platforms. Numerical simulations of wrinkling dynamics are performed for a layered model consisting of an anisotropic epithelial layer resting on a bimodular soft substrate, which in turn adheres to a rigid foundation. Motivated by the patterning of intestinal villi of chicks and mice, we examine two-step compression, where the epithelial layer is subjected to uniaxial compression followed by biaxial compression, and one-step compression, where the epithelial layer is compressed in biaxial directions. Under different mechanical conditions of tissues, a wide variety of surface patterns are displayed that reproduce luminal patterns of digestive tracts. These results suggest possible conditions for mechanical regulation of tissues to duplicate gastrointestinal surface patterns in vitro and provide insight into mechanistic understandings of biological tissues.

Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering

Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and tunnel. This paper introduces the solution principle of DDA motion equations in detail, as well as the development status of the 2D open-source program. Numerical simulation of shaking table test of rock mass engineering using 2D DDA program is highlighted, and investigations of seismic wave pre-processing and seismic input method are carried out. First, based on the Newmark integration scheme, the integration algorithms of synthetic or measured seismic wave time history, correction function of seismic wave, and DDA simulation are unified. Then, three seismic input methods are implanted in the DDA program, and the applicability of various seismic input methods is discussed. On this basis, using the improved seismic 2D DDA program, a shaking table test of typical rock mass engineering is simulated. Through the comparison between the theoretical/test data and simulation results, the reliability of the improved DDA program in seismic response analysis is verified; the large mass method and the large stiffness method are more suitable for rigid foundation, such as shaking table test; the propagation of the seismic wave presents a significant amplification effect due to the reflection, refraction, and diffraction in the tunnel. The research results provide DDA theory and an open-source program for analyzing the seismic response of rock mass engineering.

Seismic displacement ratios for soil-pile-structure systems allowed to uplift

In this paper, the soil-pile-structure interaction effects on seismic displacement demands are investigated using various dimensionless parameters. The code prescribed procedures for estimating seismic displacement demands are built upon fixed-base structure assumption and neglect the effect of foundation uplift. Tensile index, the ratio of the summation of the tensile strength of all piles to the weight of the structure, is introduced as a novel dimensionless ratio for the seismic assessments. The seismic behavior of the structures with a small tensile index is close to the structures with uplift-allowed shallow foundations. Structures with a large tensile index behave like tied foundation structures. The tensile index paves the path to cover the interaction effects from the soil-structure to soil-pile-structure interaction. The considered simplified structure in this study is a single degree of freedom model with a rigid foundation mounted on a group of piles simulated using the Winkler springs. The piles are simulated using nonlinear uniaxial springs with asymmetrical behavior under tensile and compressive forces. The accuracy of the model is verified by calculating the displacement ratios for four cases; The first three cases representing high tensile index (tied foundation), are verified with the code results, and Case 4, which represents low tensile index (uplift-allowed foundation), is compared to the literature. More than 150,000 nonlinear response history dynamic analyses are conducted for several dimensionless parameters and 20 ground motion records with various intensities and for each analysis, the displacement of the structure, linear and nonlinear hinge plastic rotation, and the foundation rotation and uplift are collected. The results, including elastic and inelastic displacement ratios, are finally compared with those of ASCE41 for shallow fixed-base foundations. It is concluded that for the cases with no pile slippage, the code prediction is accurate enough. However, in cases with high soil-pile-structure interaction effects and low tensile index, the displacement ratios are up to twice the code predictions. • Tensile index is developed to assess the soil-pile-structure interaction effects. • Simplified uplift-allowed SDOF model with piles simulated using Winkler springs. • Elastic and inelastic displacement ratios are compared with the code predictions. • Foundation uplift, tensile index and aspect and periodic ratios are investigated.

Effects of poling direction and imperfection of interfaces on a pre-stressed system with a piezoelectric core bonded to elastic faces

This paper models the resonance behavior of an initially stressed sandwich plate-strip consisting of a piezoelectric core and elastic faces, based on a rigid foundation, exposed to a time-harmonic force. Our research is conducted according to the linearized theory of electro-elasticity for solids under initial stress. This model assumes that there is a spring-type imperfectness at interfaces between the piezoelectric core and the face materials, both in the normal and tangential directions, and the core layer is poling in various directions. A mathematical model is created for the current problem, and then the finite element method (FEM) is used to solve it. Further, attention is focused on the influence of the mentioned imperfectness and the poling directions on the frequency response of plate-strip, in addition to the effects of the most important parameters on this response. The results show that as the imperfectness at the interface planes has the greatest effect on the horizontal polarization of the piezoelectric core, the mentioned polling direction inhibits the resonance mode of the system.

Theoretical models for T-stubs in contact with intermediate layer

During the last decade, simple solutions of thermal breaks have been developed for steel structures that consist in inserting an intermediate insulating layer (composed of PVC, plywood, elastomer, FRP…) between a bolted end-plate and a steel/concrete support. Experimental tests highlighted that failure modes under bending moment are similar to that of conventional bolted connections particularly in the tensile area, whereas the ultimate resistance decreases. For standard bolted connections loaded by a bending moment, the T-stub concept is used to model the tensile area. This model, extensively used in Eurocode 3, assumes that the end-plate is in contact with a rigid foundation or concrete/grout. T-stub can potentially be used to model the tensile area of bolted connections in presence of intermediate insulating layer. However the current model cannot be directly applied as the end-plate rests on a flexible support.In the present paper, a mechanical model is proposed to firstly model the elastic behaviour of T-stubs in contact with a flexible intermediate layer. The model relies on the Timoshenko beam theory in contact with a Winkler foundation modelling respectively the end-plate and the intermediate layer. The contact pressure distribution being almost linear, simplifications are proposed in this sense. It is demonstrated that simplifications can be considered for standard material used as intermediate layer such as PVC or FRP. An analytical model is also given to calculate the ultimate resistance of T-stubs considering yielding of the intermediate layer. These results are validated by comparison to finite element analysis results performed with ANSYS code using solid and contact elements. This FE analysis highlights a clear distinction between the elastic and elasto-plastic behaviors of these T-stubs particularly concerning prying effects.

Study on the efficiency and energy consumption of electric and diesel pumping stations

Restricted water and energy resources of the planet, as well as an increasing demand for water and energy owing to population growth and an ever-increasing development of human societies, require an optimal utilisation of such resources. This study was conducted to investigate the consumption, dissipation and efficiency of energy in electric and diesel fuel pumping stations in the fields of Hamedan city, located in the west of Iran. The Nebraska pumping plant performance criteria were used to compare the performance of irrigation pumping stations. The input power, output power and total energy efficiency were calculated for the pumping stations. The results revealed that the total efficiency ranged between 3.2 and 24.4% in the diesel pumping stations and from 15.7 to 100% in the electric pumping stations. The mean of total efficiency and mean wasted energy in the diesel pumping stations were 14.1% and 51.8 kWh/h, respectively. The mean total efficiency and wasted energy in the electric pumping stations were 58.3% and 9.0 kWh/h, respectively. Factors such as pump and engine selection proportionate to the system's capacity and pressure, proper upkeep and maintenance of pumps and engines, and implementation of an optimum, rigid foundation could improve energy efficiency.

Impedance functions of rigid rectangular foundations bonded on layered transversely isotropic elastic/poroelastic half-space

This paper explores a complete set of impedance functions including vertical, torsional, horizontal, rocking, and coupling impedances for a surface rigid rectangular foundation bonded on a multilayered transversely isotropic half-space composed of alternatively elastic and poroelastic layers with the use of boundary element method. The slow convergence issue of Green's functions in numerical evaluation is remedied by a simple asymptotic approach presented in this paper. To evaluate the impedances accurately and efficiently, new finite elements namely exponentially-gradient elements are employed to consider the singular behavior of tractions that happens at the edges and corners of the foundation. The validity and accuracy of the solutions are verified by comparing the results with some simpler existing cases. The impedance functions are presented for different aspect ratios of the foundation to be applicable for a variety of structures. The effects of anisotropy, inhomogeneity, layer thickness, underground water level, and soil damping are assessed.

Experimental investigation and numerical modeling of rocking cross laminated timber walls on a flexible foundation

AbstractWith recent developments of engineered wood products such as cross laminated timber, mass timber buildings in areas of high seismicity are becoming feasible and offer benefits such as faster construction and unique architectural features. It has also opened the door to creating seismically resilient lateral systems that sustain minor and reparable damage during large earthquakes. This paper presents a numerical modeling procedure for mass timber rocking wall lateral system with distributed spring elements to model base rocking. This modeling technique was validated by comparing the behavior with results from the full‐scale two‐story shake table test on a mass timber building with coupled CLT rocking walls completed as part of the NHERI TallWood Project. Although the lateral system performed better than expected during testing, it was determined that the flexibility of the foundation actually limited damage to the rocking wall panels. By adjusting the numerical model to represent a rigid foundation boundary condition, it was determined that the wall system would have experienced more damage, but would have still met design performance objectives had it been tested on a rigid foundation.