Exploring the Use of Three-Dimensional Dispersion to Damp Building Vibrations

This paper explores the use of mass/stiffness eccentricity in simple buildings to damp the response to excitation due to base motion. Examples include one- and two-story buildings when discussing low-rise structures and shear beams when discussing taller structures. Base motions include a simple step function and earthquake input. A broad range of efficiencies is achieved depending upon the system eccentricity and the available viscous damping. Asymptotic efficiencies of 50% are indicated in some cases. Optimal parameters are discussed.     

Blast Limits for Transmission Structures. I: Response Spectra Development

To develop a defense strategy to protect power transmission lines against blast-induced ground motions, an understanding of the dynamic responses of these structures must be first established. This paper presents the results from ground motion monitoring at two blast sites in southern United States. These studies are being conducted as part of a research effort to establish strong ground motion characteristics necessary for developing blast limits for power transmission systems. Ground movements caused by the surface mining blast and quarry blasting were recorded using geophones and wireless triaxial sensing units. The process of establishing the ground motion response spectra via analyzing actual ground motion measurements, including noise filtration and signal processing, is then described. These ground motion response spectra are the necessary inputs for spectrum analysis of structural responses that can be used to establish ground vibration limits.     

Optimal Control of Earthquake Response Using Semiactive Isolation

The responses of two, low-rise, 2-degree-of-freedom base isolated structures with different isolation periods to a set of near-field earthquake ground motions are investigated under passive linear and nonlinear viscous damping, two pseudoskyhook semiactive control methods, and optimal semiactive control. The structures are isolated with a low damping elastic isolation system in parallel with a controllable damper. The optimal semiactive control strategy minimizes an integral norm of superstructure absolute accelerations subject to the constraint that the nonlinear equations of motion are satisfied and is determined through a numerical solution to the Euler–Lagrange equations. The optimal closed-loop performance is evaluated for a controllable damper and is compared to passive viscous damping and causal pseudoskyhook control rules. Results obtained from eight different earthquake records illustrate the type of ground motions and structures for which semiactive damping is most promising.     

Damping in Shear Beam Structures and Estimation of Drift Response

Under pulse-type ground motions modal analysis is not quite efficient for estimating the elastic response of multi-degree-of-freedom systems, in particular when the effects of higher modes are significant. This paper first shows that the assumption of nondispersive damped waves for shear beams leads to inconsistent response estimation. Subsequently, a closed form time domain dispersive damped wave solution to the partial differential equation of motion is presented and it is verified with frequency domain solutions. Finally, using the solutions to the differential equation of motion, the response of frame structures with energy dissipating devices is studied.     

Liquefaction and Soil Failure During 1994 Northridge Earthquake

The 1994 Northridge, Calif., earthquake caused widespread permanent ground deformation on the gently sloping alluvial fan surface of the San Fernando Valley. The ground cracks and distributed deformation damaged both pipelines and surface structures. To evaluate the mechanism of soil failure, detailed subsurface investigations were conducted at four sites. Three sites are underlain by saturated sandy silts with low standard penetration test and cone penetration test values. These soils are similar to those that liquefied during the 1971 San Fernando earthquake, and are shown by widely used empirical relationships to be susceptible to liquefaction. The remaining site is underlain by saturated clay whose undrained shear strength is approximately half the value of the earthquake-induced shear stress at this location. This study demonstrates that the heterogeneous nature of alluvial fan sediments in combination with variations in the ground-water table can be responsible for complex patterns of permanent ground deformation. It may also help to explain some of the spatial variability of strong ground motion observed during the 1994 earthquake.     

Dynamic Stiffness and Damping of a Shallow Foundation from Forced Vibration of a Field Test Structure

Foundation impedance ordinates are identified from forced vibration tests conducted on a large-scale model test structure in Garner Valley, California. The structure is a steel moment frame with removable cross-bracing, a reinforced concrete roof, and a nonembedded square slab resting on Holocene silty sands. Low-amplitude vibration is applied across the frequency range of 5–15?Hz with a uniaxial shaker mounted on the roof slab. We describe procedures for calculating frequency-dependent foundation stiffness and damping for horizontal translational and rotational vibration modes. We apply the procedures to test data obtained with the structure in its braced and unbraced configurations. Experimental stiffness ordinates exhibit negligible frequency dependence in translation but significant reductions with frequency in rotation. Damping increases strongly with frequency, is stronger in translation than in rocking, and demonstrates contributions from both radiation and hysteretic sources. The impedance ordinates are generally consistent with numerical models for a surface foundation on a half-space, providing that soil moduli are modestly increased from free-field values to account for structural weight, and hysteretic soil damping is considered.     

Kinematic Pile Response to Vertical P-wave Seismic Excitation

An analytical solution based on a rod-on-dynamic-Winkler-foundation model is developed for the response of piles in a soil layer subjected to vertical seismic excitation consisting of harmonic compressional waves. Closed-form solutions are derived for: (1) the motion of the pile head; (2) the peak normal strain in the pile, and (3) the group effect between neighboring piles. The solutions are expressed in terms of a dimensionless kinematic response factor Iv, relating pile-head motion and free-field soil surface motion, a dimensionless strain transmissibility factor Iε, relating pile and soil peak normal strains, and a pile-to-pile interaction factor α measuring group effects. It is shown that a pile foundation may significantly reduce the vertical seismic excitation transmitted to the base of a structure.     

Base Isolation by a Soft First Story with Inclined Columns

An idea of passive base isolation of buildings is explored, using inclined rubber base isolators or inclined “soft” first-story columns. Such a system behaves as a physical pendulum, “pivoted” above center of mass, and is more stable than the standard system. Another advantage of the inclination is that the inertia forces of the structure due to rotation about the pivot point cancel to some degree the inertia forces due to the base translation. This is expected to result in smaller relative deformations of the building and smaller internal forces. In this paper, the consequences of this concept are illustrated on a simple model (base isolated single-degree-of-freedom oscillator), but also considering the soil flexibility and the wave nature of strong earthquake shaking (these are associated with additional rotations of the system and also affect the system period). A frequency domain solution is presented for small deformations, rigid foundations embedded in a homogeneous elastic half-space, and horizontal in-plane and Rayleigh wave foundation driving motion.     

Seismic Site Response for Near-Fault Forward Directivity Ground Motions

Forward directivity effects in the near-fault region produce pulse-type motions that differ significantly from ordinary ground motions that occur at greater distances from the causative fault. Current code site factors are based on empirical observations and analyses involving less intense nonpulse ordinary ground motions. Nonlinear site response analyses with bidirectional shaking are performed using representative site profiles to quantify seismic site response effects for intense near-fault motions resulting from forward directivity. Input rock motions are represented with simplified velocity pulses that characterize the amplitude and period of forward directivity motions. Results indicate that site response affects both the amplitude and period of forward directivity pulses, and hence, local site conditions should be considered when evaluating seismic designs in the near-fault region. Stiff soil sites tend to amplify the peak ground velocity and increase the period of pulse-type motions, particularly, when the period of the rock motion coincides with the degraded period of the site. Amplification is limited at soft soil sites by the dynamic strength of the weak soil, so attenuation occurs for intense input motions. This nonlinearity is not reflected in the site factors in current building codes. Guidance is provided for estimating the amplitude and pulse period for velocity pulses at soil sites.     

Exact Solution of Nonlinear Hysteretic Responses Using Complex Mode Superposition Method and its Application to Base-Isolated Structures

In this paper, the responses of the structures subjected to arbitrary ground motions are evaluated. With the problem formulated in a state-space form, an exact solution scheme capable of dealing with a variety of material cases is proposed, including cases when postyield stiffness exhibits strain-hardening, strain-softening, and elastic-perfectly plastic properties, respectively. The proposed method can provide much higher accuracy, and requires less computational effort than the traditional step-by-step integration solution technique. The reason for these advantages is discussed and the related formulas are provided. In addition, a new efficient approach is provided for evaluating dynamic response of nonlinear base-isolated structures by taking advantage of their characteristics. Two buildings excited by real earthquake and harmonic ground motions are considered in numerical examples to demonstrate the efficiency of the proposed method.     

Response of an Earth Dam to Spatially Varying Earthquake Ground Motion

The stochastic response of the Santa Felicia earth dam, in southern California, to spatially varying earthquake ground motion (SVEGM) is analyzed. An SVEGM model that accounts for both incoherence and propagation of seismic waves is used, the results are compared with those for various simplified excitations, and the sensitivity of the responses to coherency models proposed by different researchers is investigated. A 3D inhomogeneous finite-element model is used to represent the dam. Finite element-based random vibration analysis is performed and the statistical moments of Cartesian displacement, stress, and strain responses are computed. Statistical moments of the maximum shear stress are computed using Monte Carlo simulation that utilizes results from the random vibration analysis. The results indicate that the stress response of stiff material near the base of the dam can be significantly increased due to SVEGM, and that the increase is sensitive to the low-frequency variation of ground motion coherency.     

Reinforced Concrete Walls with Vulnerable Foundations

Moment capacities of shallow foundations are compared with those of reinforced concrete walls in order to determine the likelihood of exceeding the bearing capacity of the supporting soil in buildings subjected to strong ground motions. Recommendations are made regarding the appropriate modeling at the base of first-story walls in compliance with the moment-capacity axial load interaction of the supporting foundations.     

Response Spectrum Analysis of Suspension Bridges for Random Ground Motion

The response spectrum method of analysis for suspension bridges subjected to multicomponent, partially correlated stationary ground motion is presented. The analysis is based on the relationship between the power spectral density function and the response spectrum of the input ground motion and fundamentals of the frequency domain spectral analysis. The analysis duly takes into account the spatial correlation of ground motions between the supports, the quasi-static component of the response, and the modal correlation between different modes of vibration. A suspension bridge is analyzed under a set of important parametric variations in order to (1) compare between the responses obtained by the response spectrum method of analysis and the frequency domain spectral analysis; and (2) investigate the behavior of suspension bridges under seismic excitation. The parameters include the spatial correlation of ground motion, the angle of incidence of the earthquake, the ratio between the three components of ground motion, the number and nature of modes considered in the analysis, and the nature of the power spectral density function of ground motion. It is shown that the response spectrum method of analysis provides a fair estimate of responses under parametric variations considered in the study.     

Estimation of Maximum Roof Displacement Demands in Regular Multistory Buildings

For approximate estimation of the maximum inelastic roof displacement demand for existing multistory buildings, the current displacement coefficient method uses the maximum linear elastic displacement of the first-mode single-degree-of-freedom (SDOF) system corresponding to the buildings. The statistics of the SDOF system estimate of the roof displacement on the following topics are presented by three SAC steel buildings subjected to 72 earthquake ground motions recorded on firm sites. (a) How uncertain is the first-mode SDOF system estimation of the roof displacement? (b) What are the main sources of uncertainty in the estimation of the roof displacement? (c) How can the uncertainty be reduced? It is shown from the study that the maximum inelastic roof displacement demand of multistory buildings can be more accurately and more directly estimated by the maximum inelastic displacement of the first-mode elastoplastic SDOF system. This is especially true for low-rise buildings.     

Potential for Structural Failure in the Seismic Near Field

This study analyzes the possibility that large distortions and distortion rates due to wave-propagation phenomena within structures were responsible for unexpected cracking at connections of steel-frame buildings in the seismic near-field region during the Northridge (1994) and Kobe (1995) earthquakes. Since such internal wave propagation is characteristic of a structure with a continuous distribution of mass, the problem is studied by numerically simulating the structural response for both discrete and continuous models of a 20-story building, using ground motion time histories from the Northridge earthquake. The time histories are chosen from the far-field and near-field regions of the earthquake to determine if wave-propagation effects within the structure are especially significant in the near field. A truncated modal analysis is also performed using only the first vibrational mode to see if significantly lower response levels result. It is found that the continuous model gives higher response levels—indicating that wave propagation may have been a factor—but the discrepancy is not limited to the near field. Strain rates are higher from the continuous model than from the discrete model and much higher than from the truncated modal analysis, but the magnitudes are too low to be a significant factor in the observed damage. The explanation for the connection cracking may simply be high-intensity ground motion in the near field.     

Dynamic Testing of a Masonry Structure on a Passive Isolation System

Lightly reinforced and unreinforced masonry buildings have not performed well in earthquakes. Evaluation of past performance of masonry structures has led to more stringent design and construction requirements in the current building codes, and has raised concerns about the performance of existing lightly reinforced and unreinforced masonry buildings in future earthquakes. Base isolation has been shown to be effective in reducing damage to large building structures, and appears to be particularly effective in protecting stiff masonry structures. Using the base isolation principle, Kansas State University’s stiffness decoupler for the base isolation of structures (SDBIS) was designed to effectively reduce the acceleration and force transferred into a building superstructure during a seismic event. The sliding system uses a passive method to provide damping and to dissipate some of the kinetic energy to reduce relative displacements. In addition, the SDBIS system includes a self-centering element that will recover the majority of the induced displacement and provide resistance to overturning. In order to apply the SDBIS system to the masonry building industry, dynamic testes were performed to evaluate the structural response of a full-size one-story masonry model that was supported by the SDBIS system. Acceleration time-history results are presented for dynamic tests using the July 21, 1952 Kern County earthquake, Station 1095 Taft Lincoln School record, the May 19, 1940 Imperial Valley earthquake, Station 117 El Centro Array #9 record, the February 9, 1971 San Fernando earthquake, Station 279 Pacoima Dam record, and the January 17, 1994 Northridge earthquake, Station 24436 Tarzana Cedar Hill record ground motions. Test results show the system is effective when used with a masonry structure.     

Static Pushover Analyses of Pile Groups in Liquefied and Laterally Spreading Ground in Centrifuge Tests

Monotonic, static beam on nonlinear Winkler foundation (BNWF) methods are used to analyze a suite of dynamic centrifuge model tests involving pile group foundations embedded in a mildly sloping soil profile that develops liquefaction-induced lateral spreading during earthquake shaking. A single set of recommended design guidelines was used for a baseline set of analyses. When lateral spreading demands were modeled by imposing free-field soil displacements to the free ends of the soil springs (BNWF_SD), bending moments were predicted within ?8% to +69 (16th to 84th percentile values) and pile cap displacements were predicted within ?6 to +38%, with the accuracy being similar for small, medium, and large motions. When lateral spreading demands were modeled by imposing limit pressures directly to the pile nodes (BNWF_LP), bending moments and cap displacements were greatly overpredicted for small and medium motions where the lateral spreading displacements were not large enough to mobilize limit pressures, and pile cap displacements were greatly underpredicted for large motions. The effects of various parameter relations and alternative design guidelines on the accuracy of the BNWF analyses were evaluated. Sources of bias and dispersion in the BNWF predictions and the issues of greatest importance to foundation performance are discussed. The results of these comparisons indicate that certain guidelines and assumptions that are common in engineering design can produce significantly conservative or unconservative BNWF predictions, whereas the guidelines recommended herein can produce reasonably accurate predictions.     

Site-Specific Validation of Random Vibration Theory-Based Seismic Site Response Analysis

Seismic site response analysis is typically performed using a suite of rock acceleration-time histories prescribed at the base of a soil column and propagated to the ground surface. To develop statistically stable estimates of the site response, a large number of input motions are required. Alternatively, random vibration theory (RVT) can be used to predict statistically stable estimates of the surface response spectrum in one analysis without the need to prescribe the input rock motion in the time domain. Thus, the critical and time consuming activity of choosing appropriate input ground motions and fitting them to a target spectrum is avoided. This paper describes the RVT approach, its analytical background and input requirements, and provides a site-specific validation of the procedure against traditional site response predictions. The single-corner frequency Brune source spectrum is used in the RVT procedure to describe the input motion in the frequency domain. RVT site response predictions using the Brune spectrum as input are compared with those from traditional site response analyses that incorporate different suites of input rock motions. Results indicate that RVT site response analysis can provide a response spectrum that is similar to the median response spectrum from analyses performed using a suite of input rock motions. However, the favorable comparison is obtained only when the seismological parameters used to describe the RVT input motion are carefully chosen to be consistent with the suite of input rock motions.     

Use of Exact Solutions of Wave Propagation Problems to Guide Implementation of Nonlinear Seismic Ground Response Analysis Procedures

One-dimensional nonlinear ground response analyses provide a more accurate characterization of the true nonlinear soil behavior than equivalent-linear procedures, but the application of nonlinear codes in practice has been limited, which results in part from poorly documented and unclear parameter selection and code usage protocols. In this article, exact (linear frequency-domain) solutions for body wave propagation through an elastic medium are used to establish guidelines for two issues that have long been a source of confusion for users of nonlinear codes. The first issue concerns the specification of input motion as “outcropping” (i.e., equivalent free-surface motions) versus “within” (i.e., motions occurring at depth within a site profile). When the input motion is recorded at the ground surface (e.g., at a rock site), the full outcropping (rock) motion should be used along with an elastic base having a stiffness appropriate for the underlying rock. The second issue concerns the specification of viscous damping (used in most nonlinear codes) or small-strain hysteretic damping (used by one code considered herein), either of which is needed for a stable solution at small strains. For a viscous damping formulation, critical issues include the target value of the viscous damping ratio and the frequencies for which the viscous damping produced by the model matches the target. For codes that allow the use of “full” Rayleigh damping (which has two target frequencies), the target damping ratio should be the small-strain material damping, and the target frequencies should be established through a process by which linear time domain and frequency domain solutions are matched. As a first approximation, the first-mode site frequency and five times that frequency can be used. For codes with different damping models, alternative recommendations are developed.     

Cyclic Softening of Low-Plasticity Clay and Its Effect on Seismic Foundation Performance

During the 1999 Chi-Chi Earthquake (Mw = 7.6), significant incidents of ground failure occurred in Wufeng, Taiwan, which experienced peak accelerations ～ 0.7?g. This paper describes the results of field investigations and analyses of a small region within Wufeng along an E–W trending line 350?m long. The east end of the line has single-story structures for which there was no evidence of ground failure. The west end of the line had three to six-story reinforced concrete structures that underwent differential settlement and foundation bearing failures. No ground failure was observed in the free field. Surficial soils consist of low-plasticity silty clays that extend to 8–12?m depth in the damaged area (west side), and 3–10?m depth in the undamaged area (east side). A significant fraction of the foundation soils at the site are liquefaction susceptible based on several recently proposed criteria, but the site performance cannot be explained by analysis in existing liquefaction frameworks. Accordingly, an alternative approach is used that accounts for the clayey nature of the foundation soils. Field and laboratory tests are used to evaluate the monotonic and cyclic shear resistance of the soil, which is compared to the cyclic demand placed on the soil by ground response and soil–structure interaction. Results of the analysis indicate a potential for cyclic softening and associated strength loss in foundation soils below the six-story buildings, which contributes to bearing capacity failures at the edges of the foundation. Similar analyses indicate high factors of safety in foundation soils below one-story buildings as well in the free field, which is consistent with the observed field performance.