Cumulative Absolute Velocity as a Local Damage Indicator of Instrumented Structures

Abstract

This paper addresses the critical issue of localized damage detection in structural health monitoring. It evaluates the application of cumulative absolute velocity (CAV) as a local damage indicator for analyzing the acceleration response of a shaking table test specimen as well as real instrumented buildings. A bridge column test specimen instrumented with 18 accelerometers is subjected to increasing six levels of shaking corresponding to different damage states. The CAV analysis of the horizontal response of the accelerometers identified the elevation where damage is located. The vertical CAV analysis not only identified the existence of damage but also located the damage with high precision. This method is subsequently applied to two instrumented buildings damaged during earthquakes. The results show that for the seven-story Van Nuys hotel, the CAV can correctly locate the damage that occurred during the 1994 Northridge earthquake. For the Imperial county services building, the CAV is also able to correctly identify the location of damage. Thus, the presented CAV method enables identifying the onset and location of damage to evaluate the structural integrity.

Introduction

Civil infrastructures undergo a gradual loss of structural integrity due to aging. This structural deterioration is accelerated when the infrastructure resists sudden large forces caused by natural disasters such as earthquakes. Progressively, internal and concealed damages may accumulate, making the structures substantially vulnerable to imminent aftershocks and future earthquakes. If such damages are detected at an early stage, complete collapse and subsequent loss of life and property can be prevented. Therefore, immediate damage detection is essential for maintaining the structural safety and tracking the structural integrity. Moreover, this damage detection facilitates the decision-making process regarding emergency response, retrofit projects, and future use of the structure following an earthquake event.

Different techniques such as visual, non-destructive evaluation (NDE), and vibration-based methods are currently used for damage detection (Doebling et al. 1998). Among them, visual assessment and NDE such as ultrasonic or eddy-current methods can detect damage on or near the surface of the structure (Maierhofer 2003). However, these methods require some prior knowledge about the approximate damage location and access to this location (Doebling 1996). Besides, these methods are often time consuming and expensive. On the other hand, vibration-based methods can identify damage remotely and immediately after an extreme event.

Most of the vibration-based damage detection methods are founded on detecting changes in modal frequencies, mode shapes, curvature of mode shapes, and power spectrum densities of the structure (Arici and Mosalam 2003, 2005a, 2005b; Pandey et al. 1991; Zou et al. 2000). Most of these methods can only determine whether or not damage is present in the entire structure and hence, referred to as “global health monitoring” methods (Chang et al. 2003, Johnson et al. 2004). Besides, modal characteristics are sensitive to environmental influences (e.g., temperature) and changes in the boundary conditions (e.g., soil–foundation system), which are difficult to separate and may produce similar effects as damage on the recorded response (Todorovska and Trifunac 2007). Moreover, localized damage detection using modal characteristics require extensive measurement grid making these methods expensive.

To overcome these issues, researchers focused on finding local damage indicators. Behnia et al. (2014) used acoustic emission and travel time tomography to detect development of fractures with embedded sensors. Memmolo et al. (2015) used ultrasonic-guided wave tomography technique focused on impact damage detection in composite plate-like structures to detect damage through a distributed network of embedded sensors. Gallo and Thostenson (2015) used embedded carbon nanotubes and generated conductivity maps using electrical impedance tomography (EIT) to detect localized and site-specific damage. However, embedding a network of sensors inside a structure increases cost of construction and manufacturing making these methods less feasible for full scale implementation.

Several studies have been carried out to identify local damages by analyzing recorded signals (Park et al. 2006, Sohn et al. 2000, Yang et al. 2013, 2016). Statistical time series (TS) modeling is one of the earliest and the most common vibration-based method used for localized damage detection (Sohn and Farrar 2001, Fan and Yao 2003, Nair 2006, Carden and Brownjohn 2008, Loh et al. 2016). However, most of these techniques are model-based approaches and depend on several modeling parameters. In recent years, Hilbert–Huang transform (HHT) has emerged as an important signal processing tool for system identification and damage detection of civil structures. Shi et al. (2012) used HHT to identify the modal frequencies and damping ratios of the Shanghai World Financial Center subjected to both ambient dynamic and forced excitations. However, a major drawback of HHT method is the so-called mode mixing effect encountered in the equivalent mode decomposition (EMD) method which means waves with the same frequency are assigned to different intrinsic mode functions. Recently, Dorvash et al. (2015) used influence-based damage detection algorithm (IDDA) to detect damage using correlation functions between the structural responses at different locations. In this paper, a simple response-based damage detection technique is presented using the cumulative absolute velocity (CAV) computed from recorded accelerations that utilizes trends determined from the structural responses at different locations.

Cumulative Absolute Velocity

The CAV was first introduced as a potential damage-related ground motion intensity measure in a study sponsored by the Electric Power Research Institute (EPRI; Reed and Kassawara 1990). This study concluded that ground motion CAV can be considered as a second optional exceedance criterion of the operating-basis earthquake (OBE) in nuclear power plants correlating CAV value of 0.3 g-sec with damage. The method of calculating the CAV was modified by removing low amplitude non-damaging records and referred to as the standardized CAV (Campbell and Bozorgnia 2010). Several studies have looked into the global damage potential of ground motion CAV (Benito and Cabanas 1997, Campbell and Bozorgnia 2012). Most of these studies have successfully correlated the CAV from ground motion instruments to the qualitative levels of structural damage. However, to the best of the authors’ knowledge, the CAV as a damage detection technique and its application in structural health monitoring have not been explored. Only the CAV of ground motion has been studied thoroughly but CAV of response data from instrumented structures, for example, at different floor levels of buildings, has not been applied yet. The objective of this paper is to investigate the potential of CAV as a damage indicator. The results from a previous experimental study (Lee and Mosalam 2014a, 2014b) have been utilized for this purpose. Moreover, several case studies on real building structures damaged during past earthquakes have been presented to investigate the capability of the proposed CAV to detect the observed and measured localized damages.

Physical Interpretation of Cav

The CAV is mathematically defined as follows:

A V = \int_{0}^{T} | \ddot{u} (t) | d t

(1)

where |ü(t)| is the absolute value of acceleration at time t and T is the total duration of the recorded acceleration. Unlike the peak intensity measures such as peak ground acceleration (PGA) or peak ground velocity (PGV), the CAV takes into account contributions from both the amplitude and duration. The CAV is comparable to the widely used intensity measure Arias intensity (AI) that corresponds to the energy content of the earthquake excitation quantitatively. The CAV performs better than AI in damage detection as the AI discounts smaller amplitude waves. Besides, AI has larger standard deviations than CAV (Campbell and Bozorgnia 2010).

According to the mean value theorem for integrals, Equation 1 may be written as follows:

C A V = E [| \ddot{u} (t) |] \times T

(2)

where E[|ü(t)|] is the expected value of the absolute acceleration. According to Equation 2, the CAV can be considered as the product of two random variables. Let us consider ü(t) to be a stationary Gaussian process with zero mean. Then, the expected absolute value of a normal random variable with mean, μ = 0, and variance, σ², is expressed as follows:

E [| \ddot{u} (t) |] = \sqrt{\frac{2}{π} \times σ^{2}}

(3)

If S(f) is the power spectral density (PSD) function of ü(t), then, according to Wiener-Khinchin theorem (Wiener 1949), we have:

σ^{2} = 2 \int_{0}^{\infty} S (f) d f

(4)

Moreover, the total power of the signal, P_ü, becomes the area under the PSD curve, that is:

P_{\ddot{u}} = σ^{2} = \int_{- \infty}^{\infty} S (f) d f = 2 \int_{0}^{\infty} S (f) d f = 2 \times S_{f_{c}} \times Δ f

(5)

where S_{f
_c} is the spectral ordinate around the median frequency, f_c, within the bandwidth, Δf.

Let us assume the total number of load cycles to be N, then Equation 2 can be written as:

C A V = T \sqrt{\frac{2}{π} \times P_{\ddot{u}}} = \frac{N}{f_{c}} \sqrt{\frac{2}{π} \times P_{\ddot{u}}}

(6)

From Equation 6, it is evident that the CAV is correlated to the power of the earthquake motion as well as the number of load cycles. It is to be noted that the acceleration is considered as a stationary Gaussian process for simplicity in this derivation. However, earthquakes are non-stationary Gaussian processes with a changing variance σ² (t) where:

σ^{2} (t) = q^{2} (t) P_{\ddot{u}} (t)

(7)

where q²(t) is the envelope function which takes into account the non-uniform modulation of earthquake motion. The simplest form of an envelope function is a piecewise separable function which breaks the ground motion down to initial build-up portion, relatively high-intensity portion, and gradual decaying tail. Substituting Equation 7 into Equation 2 making use of Equation 3, we have CAV at time t expressed as follows:

C A V (t) = t \times \sqrt{\frac{2}{π} \times q^{2} (t) \times P_{\ddot{u}} (t)}

(8)

This can be expressed in an incremental form as follows:

Δ C A V = Δ t \times \sqrt{\frac{2}{π} \times q^{2} \times Δ P_{\ddot{u}}}

(9)

Equation 9 shows, for a certain time step Δt, that the incremental change in CAV (i.e., ΔCAV) is proportional to the change in the input power, ΔP_ü, which is true for stationary as well as non-stationary case. This is helpful to understand the correlation of damage to the CAV of the structural response.

Cav Analysis

For a multi degree of freedom (MDOF) system, the equations of motion are expressed as:

m {\ddot{u}}^{t} + f_{d} + f_{s} = 0

(10)

where m is the mass matrix, f_d and f_s are damping and restoring force vectors and ü^t is the total acceleration vector corresponding to the total displacement vector u^t = u + i u_g with u is the relative displacement vector with respect to the ground, i is a unit vector and u_g is the ground displacement.

Let us assume a two-degree-of-freedom (2DOF) system as shown in Figure 1 with $u^{t} = (\begin{array}{l} u_{1}^{t} \\ u_{2}^{t} \end{array})$ such that, $u_{2}^{t} = φ \times u_{1}^{t}$ where ϕ is a real number and for first mode, ϕ > 1. Differentiating $u_{2}^{t}$ twice with respect to time, t, we obtain:

{\ddot{u}}_{2}^{t} = φ \times {\ddot{u}}_{1}^{t}

(11)

Assuming the simplest case where the structure vibrates in its first mode with the displacement u^t back and forth, then we can write:

\begin{array}{l} C A V_{1} = \int_{0}^{T} | {\ddot{u}}_{1}^{t} (t) | d t \\ C A V_{2} = \int_{0}^{T} | {\ddot{u}}_{0}^{t} (t) | d t = φ \int_{0}^{T} | {\ddot{u}}_{0}^{t} (t) | d t = φ \times C A V_{1} \end{array}

(12)

Therefore, the CAV plot will show a trend of higher CAV values for higher floors for the first mode-dominant structural response. By normalizing the CAV values at all times with the maximum CAV value we obtain the normalized CAV (NCAV). For the case described earlier, the NCAV for the first and second floors are expressed as follows:

\begin{matrix} N C A V_{1} (t) = \frac{\int_{0}^{t} | {\ddot{u}}_{1} (t) | d t}{C A V_{1}}, & N C A V_{2} (t) = \frac{\int_{0}^{t} | {\ddot{u}}_{2} (t) | d t}{C A V_{2}} = \frac{φ \int_{0}^{t} | {\ddot{u}}_{1} (t) | d t}{φ \times C A V_{1}} = N C A V_{1} (t) \end{matrix}

(13)

Equation 13 shows that the NCAV plots will overlap each other for all the floors when the structure is excited by an undamaging earthquake. In other words, the incremental change ΔNCAV _j = NCAV _j(t_i+1)-NCAV _j(t_i) for the j^th floor during the time history is the same for all floors, that is, for floors 2 and 1 in the above 2DOF system we have:

N C A V_{2} = Δ N C A V_{1} = Δ N C A V_{g}

(14)

where ΔNCAV _g is the corresponding NCAV incremental change of the input ground motion.

Figure 1.

Sketches of deviations in the CAV trends due to damage for a 2DOF system.

In order to understand the change in the trends of the above incremental changes due to damage, we consider the power balance equation of the 2DOF system in Figure 1. Rewriting Equation 10 for individual floors and integrating it with respect to $d \dot{u}$ from the time of the start of the ground motion excitation, we obtain:

\int m_{j} {\ddot{u}}_{j} d {\dot{u}}_{j} + \int f_{d} j d {\dot{u}}_{j} + \int f_{s_{j}} d {\dot{u}}_{j} = - \int m_{j} {\ddot{u}}_{g} d {\dot{u}}_{j}, P_{k_{j}} + P_{ξ_{j}} + P_{a_{j}} = P_{g_{j}}, P_{D_{j}} = P_{I_{j}}

(15)

where j takes the values 1or 2. Equation 15 represents the power balance equation of the system with the left-hand side showing dissipated power, P_{D
_j}, and the right-hand side is the input power, P_{I
_j}. Here, P_k is the relative kinetic power, P_ξ is the damping power, P_a is the absorbed power which comes from recoverable strain and irrecoverable hysteresis powers, and P_g is the kinetic power corresponding to the input ground motion. This power balance is maintained for each time step, that is:

\begin{array}{l} \int m_{j} {\ddot{u}}_{j} d {\dot{u}}_{j} + \int f_{d} j d {\dot{u}}_{j} + \int f_{s_{j}} d {\dot{u}}_{j} = - \int m_{j} {\ddot{u}}_{g} d {\dot{u}}_{j}, P_{k_{j}} + P_{ξ_{j}} + P_{a_{j}} = P_{g_{j}}, P_{D_{j}} = P_{I_{j}} \\ \begin{matrix} Δ P_{D_{j}} = Δ P_{I_{j}} & f o r a l l & Δ t = t_{i + 1} - t_{i} \end{matrix} \end{array}

(16)

Before damage, ΔP_{I
_j} is equal to the change in power due to ground excitation ΔP_{g
_j}. However, at the onset of damage at a certain level (e.g., floor in a building), additional power is dissipated, P_damage, lowering the input power above the damaged level. Assuming damage occurs at first floor, at the time step when damage occurs, we can state that ΔP_{I
₁} = Δ P_{g
₁} and ΔP_{I
₂} = ΔP_{g
₂} − P_damage.

From Equation 9, we see that the incremental change in CAV (i.e., ΔCAV) is correlated to the change in the input power. As a result, with decrease in the input power, the ΔCAV value is lowered at the second floor compared to the first floor which can be observed in the CAV plots when compared to the undamaged state plots. Due to damage, for the subsequent time steps after damage is ceased, mass and/or stiffness of the system will be reduced leading to an increase of the acceleration and consequently increasing the ΔCAV for both floors which will be manifested in the form of a steeper slope of the CAV plot. Therefore, the final CAV value will be higher at the damaged floor compared to undamaged state. The increased final CAV value causes the NCAV plots of the two floors to deviate compared to the ground level NCAV.

To quantify the above-mentioned deviations in the CAV trends, an index for inter-story CAV ratio, R_CAV, is used. The R_CAV of a certain floor/elevation is defined as the ratio of the CAV at that elevation to the CAV at a consecutive lower elevation as given by Equation 17. Under different scales of the input motions, R_CAV values should remain the same at each elevation if no damage occurs. However, when damage occurs, R_CAV of the damaged elevation will increase since the final CAV value at the damaged elevation will be higher than the undamaged state whereas CAV at the lower undamaged elevation will remain the same. Moreover, R_CAV of the consecutive upper level will decrease since the damage initially reduces the CAV at the upper levels which is divided by the increased CAV of the damaged lower elevation. Thus, damage at a certain floor/elevation is indicated by an increase in the R_CAV at that elevation and a decrease in the R_CAV at the upper elevation compared to the previous event. However, if successive elevations are damaged, the trend is less obvious. Thus, the trend of R_CAV changes for different elevations is also compared (refer to Equation 18). The R_CAV and Trend for the n^th floor/elevation and j^th earthquake level are defined as follows:

\begin{matrix} R_{C A V_{n, j}} = C A V_{n, j} / C A V_{n - 1, j}, & n \geq 1, j \geq 1 \end{matrix}

(17)

\begin{matrix} T r e n d_{n, j} = [(R_{C A V_{n . j}} - R_{C A V_{n, j - 1}}) / R_{C A V_{n, j - 1}}] \times 100 %, & n \geq 1, j \geq 2 \end{matrix}

(18)

where n = 1, …, number of floors/elevations and j = 1, …, number of recorded events. In this way, changes in consecutive events as well as in consecutive floors/elevations are quantified. Damage is identified at the n^th elevation when the two conditions of Equation 19 are fulfilled.

{\begin{cases} R_{C A V_{n + 1, j}} < R_{C A V_{n + 1, j - 1}} \\ T r e n d_{n + 1, j} < T r e n d_{n, j} \end{cases}, \begin{matrix} n \geq 1, j \geq 2 \end{matrix}

(19)

Another matric, S_CAV, in Equation 20 is introduced to examine the spreading or slope of the CAV observed in the NCAV plots. The S_CAV,n highlights the relative wave travel times between the n^th elevation and the base (ground) level (n = 0) providing insight into the change in the wave propagation behavior caused by damage where higher S_CAV means a slower rate of change due to damage. The parameter D_5–75 in journalEquation 20 is the effective duration of an earthquake (Bommer and Martinez-Pereira 1999) defined by the time to achieve 75% of the final CAV value starting from the 5% of that value:

S_{C A V, n} = [(D_{5 - 75, n} - D_{5 - 75, 0}) / D_{5 - 75, 0}] \times 100 %

(20)

Experimental Evaluation

Experimental Test Setup

The performance of the CAV as a damage indicator is evaluated by a series of tests conducted at the University of California, Berkeley, shaking table on a bridge column test specimen. These tests were conducted for two purposes: (1) to simulate shear strength reduction of bridge columns under vertical acceleration (Lee and Mosalam 2014a) and (2) to document progressive damage in a column in order to correlate the response parameters to localized damage. In this paper, the analysis performed to verify the hypothesis of the CAV as a localized damage indicator is presented.

The reinforced concrete (RC) column specimen considered in this study had 20 in. (508 mm) diameter, 70 in. (1,778 mm) height and 1.563% longitudinal reinforcement ratio (Figure 2a). For the transverse reinforcement, #2 (∼6 mm diameter) hoops were used with 3 in. (76 mm) uniform spacing over the entire column height. An 8 ft × 8 ft × 3.35 in. (2.44 m × 2.44 m × 85 mm) base steel plate was designed to place the test specimen at the center of the shaking table. To fix the column to the shaking table, 5 ft × 5 ft × 18 in. (1.524 m × 1.524 m × 457 mm) RC footing was designed and reinforced with a grid of #6 (∼19 mm diameter) deformed bars top and bottom both ways and #3 (∼10 mm diameter) ties in the transverse direction. Top steel beams were designed to resist the prestressing forces and to support the inertia forces of the mass blocks, namely two large concrete blocks and 72 small lead blocks (Figure 2b). The four beam cross sections, HSS 20 × 12, were designed to have small deflection and sufficient flexural capacity to resist the bending moment produced in the tests. A detailed description of the test specimen and the similitude requirements can be found in (Lee and Mosalam 2014a).

Figure 2.

Bridge column shaking table test (Lee and Mosalam 2014a): (a) Column cross section, (b) set up, (c) locations of accelerometers.

A total of 18 accelerometers [9 three-dimensional (3-D) and 9 one-dimensional (1-D)] were installed to measure the acceleration during the test (Figure 2c). The 3-D ones measured the responses at different levels, where four were located at the corners of the base plate, one at the top of column, and four at the corners of the top of the mass blocks. The 1-D ones measured the vertical acceleration with eight attached along the column height on the north side and one at the center of the top mass block. Moreover, 38 strain gages were installed on the column reinforcement with 18 and 20 gages on the longitudinal and transverse bars, respectively.

The ground motion recorded at Pacoima Dam station of the 1994 Northridge earthquake was used in the test based on an extensive study as documented in (Lee and Mosalam 2014b). One horizontal component and the vertical component have been used as input motions. The ground motion was applied in increasing intensity levels with seven different scale factors where a total of 11 shaking table runs were conducted. In this study, only results from 6 of these runs with noticeably damaged states are considered.

Result of the Cav Analysis

Horizontal Acceleration

The CAV is calculated from the horizontal acceleration response captured by the 3D accelerometers located on the base plate (BP), column top (CT), and mass block (MB) with data shown in Figure 3 for identified four runs. It is noted that data were also available from accelerometers installed under the shaking table.

Figure 3.

Acceleration time history for different scales in the horizontal direction of the column test.

Figures 4a and 4b respectively show the CAV and NCAV for the horizontal response from 25%, 50%, 95%, and 125% scales. At the 12.5% (not shown) and 25% scales, the CAV from the MB has the highest value when compared to the BP and CT. This is due to increased flexibility in the horizontal response with this cantilever-type specimen height. The CAV from the 50% scale shows a shift in behavior where the MB CAV values are lower than those of the CT. At the 95% scale, the CAV from the CT drops below that of the 70% scale (not shown) and the NCAV plots show more spreading for both CT and MB when compared to that of the BP. For the 125% scale, the CAV plots show that the MB values drop below the BP and CT CAV and the NCAV plots show large spreading indicating a major change in the power flow.

Figure 4.

CAV and NCAV from column horizontal response for 25%, 50%, 95%, and 125% scales.

Table 1 lists the R_CAV from the CT, MB and BP together with the trends of the R_CAV variations. Reductions in R_CAV from the previous scale and in the trend from the lower level are highlighted by underlined values. The trends are calculated by finding the relative change of the R_CAV from the previous scale. Note that a negative trend value represents energy dissipation. From Table 1, at 12.5%, R_CAV for CT is 2.76 and for MB is 2.77 while at 25%, R_CAV values from both CT and MB drop by about 18%. At 50% scale, CT R_CAV does not practically change whereas MB R_CAV decreases to 1.71 with trend value showing 24% drop indicating energy dissipation at CT. R_CAV increased for CT and decreased for MB at 70% scale, where increase in the CT level and decrease in the upper level indicate further damage at CT. At 95% scale, the trend value at CT drops by about 35% indicating a major energy dissipation between BP and CT. As the scale is increased to 125%, the energy transfer mechanism in the bridge column specimen completely changed. This is evident from the R_CAV values of 1.03 and 0.82 and trend values of almost −36% and −60% for CT and MB, respectively, detecting some damage at the bottom and heavy damage at the top of the column.

Table 1

R_CAV and Trend values for 12.5% to 125% scales of the horizontal response (a dashed box indicates a damaged zone)

Scale	12.5%		25%		50%		70%		95%		125%
Quantity	R _CAV	Trend	R _CAV	Trend	R _CAV	Trend	R _CAV	Trend	R _CAV	Trend	R _CAV
MB	2.77	-18.2	2.26	-24.0	1.71	-2.99	1.66	23.4	2.05	-60.0	0.82
CT	2.76	-18.0	2.26	0.47	2.27	8.49	2.47	-34.7	1.61	-36.2	1.03
BP	1.0	0.0	1.0	0.0	1.0	0.0	1.0	0.0	1.0	0.0	1.0

Figure 5 shows that S_CAV values obtained using Equation 20 consistently increase from the 12.5% scale to the 70% scale. At the 95% scale, spreading suddenly decreases. The S_CAV jumps to 300% for the MB in the 125% scale indicating that the wave is traveling very slowly at that location compared to that of the BP. The fact that the excitation is barely reaching that elevation is indicative of heavy damage below the mass block.

Figure 5.

S_CAV values of the column horizontal response for different scales.

Vertical Acceleration

Vertical CAV response is calculated from the eight 1D accelerometers placed along the column height, h = 0, 5, 15, 25, 45, 55, 65, and 70 in. (0, 127, 381, 635, 1143, 1397, 1651, and 1778 mm). With a dense array of sensors, better damage detection has been observed. Since the column is stiff in the vertical direction, no amplification is expected with height. Any change in the vertical CAV value is assumed to be caused by a change in vertical stiffness only.

Figure 6 shows that for the 12.5% (not shown) and 25% scales, the CAV values are higher for the 55 to 70 in. (1,397 to 1,778 mm) zone than those for other locations. Thus, damage is anticipated in this zone [within the anticipated plastic hinge zone, i.e., a distance equals the column diameter from the top, where the large mass moment of inertia at the top leads to large bending moment at the column top sections as discussed by Lee and Mosalam (2014b)] before other locations. Figure 6 shows that for the 50% scale, the vertical CAV values at 15 in. (381 mm) and for the 55 to 65 in. (1,397 to 1,651 mm) zones are high. This indicates two damaged zones in the range of one column diameter distance from the top and bottom of the column, confirming the possibility of double curvature in the column (Lee and Mosalam 2014a, 2014b).

Figure 6.

CAV vs. time plots of test column vertical response for different scales.

At the 70% scale (not shown), a significant rise occurred in the CAV at 70 in. (1,778 mm) indicating major damage at column top. For the scale of 95%, the CAV at 55 in. (1,397 mm) is found to be the highest followed by that at 65 in. (1,651 mm), 70 in. (1,778 mm), 45 in. (1,143 mm), and 15 in. (381 mm) in this order. For the 125% scale, high CAV occurred between heights 55 and 70 in. (1,397 and 1,778 mm). Since travel time of the wave does not significantly change in the vertical direction, NCAV does not provide important insight in that direction.

Figure 7 shows the trend of the R_CAV variations along the column height. Based on the idea that damage at a level is indicated by an increase of the R_CAV at that level and decrease in the upper level, damage is identified at 10 to 20 in. (254 to 508 mm) and 55 to 65 in. (1,397 to 1,651 mm) regions for the 25% scale (positive peaks in Figure 7). For the 50% scale, damage is identified at the 0 to 20 in. (0 to 508 mm) and 45 to 60 in. (1,143 to 1,524 mm) regions. The 70% scale indicates damage between 20 to 50 in. (508 to 1,270 mm) region and at 70 in. (1,778 mm). Further damage is predicted at 10 to 20 in. (254 to 508 mm) and 50 to 60 in. (1,270 to 1,524 mm) regions and at 70 in. (1,778 mm) for the 95% scale. For the 125% scale, damage is identified along almost the entire column height. The S_CAV does not provide important insight for the vertical CAV, which is expected due to similar wave travel time.

Figure 7.

Trend of the R_CAV variations of the test column in the vertical response.

Damage Progression and Detection

In this section, actual damage progression and damage detection by CAV analysis are compared to evaluate the hypothesis that the CAV being a localized damage indicator. As documented in (Lee and Mosalam 2014a, 2014b), damage states of the test column were recorded in detail by visual observation, sketches and photographs of the surface cracks in addition to use of strain gage measurements to detect local damage and its severity. Figure 8 shows the crack propagation with thicker cracks showing the newest ones and darker zones indicating the damaged regions detected by the CAV.

Figure 8.

Crack propagation and damage detection for the 25% to 125% scales for the test column.

No damage was detected up to the 12.5% scale both visually and instrumentally. Strain gage measurements showed that the column reached half the yield level at the 25% scale. Although no visual cracks were observed following this 25% scale run, vertical CAV plots and the corresponding R_CAV indicated damage at 55 to 65 in. (1,397 to 1,651 mm) and 10 to 20 in. (254 to 508 mm) regions. Interestingly, flexural cracks emerged first at these regions during the 50% scale confirming the prediction by the CAV. Vertical CAV analysis showed for the 50% scale that the damage is at 45 to 60 in. (1,143 to 1,524 mm) and 0 to 20 in. (0 to 508 mm) regions. Horizontal CAV analysis indicates damage near the column top at this 50% scale. From the experimental observations, the cracks at this scale accumulated in the top zone of the column defined by its diameter, that is, 20 in. (508 mm), which agrees with the CAV analysis. Strain measurements also confirmed this damage detection where column longitudinal reinforcing bars reached their yield strain values.

Shear cracks appeared in the top part of the east and west sides of the column during the 70% scale run. These cracks propagated toward the mid-height of column. In addition, a significant number of vertical cracks, above h = 20 in: (508 mm) on the north side, became visible following this run. On the other hand, vertical CAV detects damage between 20 and 50 in. (508 and 1,270 mm). Moreover, the CAV value at the column top increases at this scale indicating possible spalling which occurs in the following scale of 95%. Horizontal CAV also shows damage between the MB and the CT elevations.

At the 95% scale, concrete spalling occurred at the top of the north and south sides of the column with shear cracks spreading along the height of the column. There were no shear cracks between 20 to 30 in. (508 to 762 mm) height. However, several vertical cracks appeared in this region. Strain gages recorded first residual curvature at 60 in. (1,524 mm) for the 95% scale run and confirmed the double curvature of the column response. On the other hand, the vertical CAV indicates damage at the top and bottom plastic hinge zones. Moreover, the horizontal CAV shows damage between the CT and BP elevations.

As the earthquake intensity level increased, cracks extended over the column height. Spalling continued to occur on the top of column at the north and south sides with spalling height greater than 5 in. (127 mm) during the 125% scale run. Additional shear and vertical cracks appeared toward the bottom of the column at the east and west sides. Moreover, some wide cracks started to emerge within the 50 to 60 in. (1,270 to 1,542 mm) zone in the east and west sides and at 45 in. (1,143 mm) in the east side only. Horizontal CAV captures this damage pattern by observed decrease in the MB CAV and jump in the S_CAV. Finally, vertical CAV successfully detects the damage locations including damage near the column base.

Building Case Studies

The experimental study of the previous section showed the CAV analysis detecting damage with good accuracy. In this section, the CAV is applied to actual instrumented building structures, which experienced damage during earthquakes. A seven-story hotel at Van Nuys and Imperial County Services (ICS) building at El Centro have been selected as representative of damaged buildings since their performances are well documented in the literature. Acceleration data of these buildings are obtained from the database of the Center for Engineering Strong Motion Data (CESMD 2014) operated by California Strong Motion Instrumentation Program (CSMIP) to set up a statewide network of strong motion instruments in selected structures.

Van Nuys Seven-Story Hotel

Van Nuys hotel is located in central San Fernando Valley northwest of downtown Los Angeles. It was severely damaged during the 1994 Northridge earthquake. Major structural damage occurred in the exterior north and south frames (broken lines in Figure 9 marked on the E/W elevation). The east-west running frames were the primary lateral force resisting system. South exterior column experienced severe shear cracks near the top of fourth-floor columns (Todorovska and Trifunac 2008b). Shear cracks also occurred in the north exterior frame on the second and fourth floors. No major damage to the interior longitudinal frames and the slabs was observed. However, significant nonstructural damage was observed.

Figure 9.

Van Nuys hotel instrumentation and damage locations during 1994 Northridge earthquake.

The building had 16 acceleration sensors on five different floors. Figure 9 shows the sensor locations and direction of the response captured by each sensor. The building responses due to several other earthquakes have been recorded with these sensors. In this study, the responses to two previous earthquakes, namely 1992 Landers and 1992 Big Bear, before Northridge, are presented as representative of undamaged cases. These two events are low intensity ones with PGA of 0.04 g and 0.03 g, respectively, compared to the much larger PGA of Northridge of 0.47 g. Figure 10a shows the acceleration response of these earthquakes. The building had one vertical sensor at the ground floor only. Thus, only horizontal CAV analysis is conducted.

Figure 10.

East-west direction response of Van Nuys hotel for three earthquakes.

The CAV calculated from the E-W sensors response show consistent behavior for Landers and Big Bear earthquakes with higher floors gradually reaching higher CAV values (Figure 10b). However, for Northridge, this trend differed. The second-floor CAV value is lower (reaching 1.47 g-sec) than that at the ground floor (reaching 1.63 g-sec). Initially, the third-floor CAV value is also lower than that at the ground floor for Northridge earthquake and only exceeds it near the end of the earthquake duration (after 30 sec). The sixth-floor CAV also shows decrease in the trend. These deviations are caused by two damaged zones below the second and fifth floors.

The NCAV plots (Figure 10c) from the Landers and Big Bear earthquakes wave propagation behavior are similar for all the floors. However, during Northridge earthquake, wave propagation behavior changes significantly for the upper floors. The second-floor NCAV plot shows deviation due to damage below this floor. The third-floor plot deviates slightly more because of the damage at a single column as reported in (Todorovska and Trifunac 2008b). The sixth floor NCAV shows significant deviation from that of the third floor due to damage at the fourth and fifth floors. On the other hand, the NCAV for the roof overlaps that of the sixth floor indicating no damage in between the sixth floor and the roof.

The R_CAV values and its trend in Table 2 indicate heavy damage below the second floor during the Northridge earthquake with 30% lower R_CAV value compared to the Landers and Big Bear earthquakes. Moreover, further damage is located between the third and sixth floors where the CAV trend values decrease more at the sixth floor than at the third floor indicating energy dissipation between these floors. Interestingly, the R_CAV values between the third and sixth floors vary significantly even in the Landers and Big Bear earthquakes indicating possible weaknesses between these floors.

Table 2

R_CAV values and trends for the EW direction of Van Nuys hotel (a dashed box indicates a damaged zone and as in Table 1, comparative reductions of values are underlined)

EQ	Landers	Big Bear		Northridge
Quantity	R _CAV	Trend	R _CAV	Trend	R _CAV
Roof	0.56	0.24	0.56	2.97	0.58
6^th floor	0.55	6.74	0.59	-21.11	0.46
3^rd floor	1.34	1.89	1.37	-15.61	1.16
2^nd floor	1.83	8.13	1.98	-29.39	1.40
Ground	1.0	0.0	1.0	0.0	1.0

Figure 11 shows that the S_CAV is more than 5 times higher during Northridge than those of the previous events and exceeds the threshold value of 50% which is found as the lower limit of the undamaged state during the experimental study in the previous section. Moreover, the highest S_CAV is observed in the sixth floor indicating a damaged zone between the sensors of the third and sixth floors. The S_CAV values of the sixth floor are also higher for the Landers and Big Bear earthquakes due to possible structural weaknesses. Overall, it is observed that the horizontal CAV response is able to detect the damaged zones for this case study of the Van Nuys hotel.

Figure 11.

S_CAV values in EW direction of Van Nuys hotel for three earthquakes.

Imperial County Service Building

The six-story ICS building was located in the city of El Centro, near southern California border region. This RC building had four moment frames as lateral force resisting system in the longitudinal (EW) direction. In the transverse (NS) direction, lateral resistance was provided in a discontinuous manner with four short interior shear walls on the ground floor and two exterior shear walls from the second floor to the roof. The building was instrumented by 13 sensors on four different levels. On the ground floor, second floor and roof, the responses of the longitudinal and transverse directions are recorded. However, on the fourth floor, only the longitudinal response is recorded. Figure 12 shows the location and direction of these sensors. A detailed description of the structure and its instrumentation is provided in (Kojic et al. 1984).

Figure 12.

Imperial County Service building instrumentation.

The building was severely damaged by the 1979 Imperial Valley earthquake with major failure sustained by the ground floor column line at the east end. The columns experienced bursting of the reinforcing bar cages and crushing of the concrete at the base resulting in significant shortening (Todorovska and Trifunac 2008a). This, in turn, caused an incipient vertical fall of the eastern end of the building, producing cracking of the floor beams and slabs on the second, third and higher floors. For this earthquake, both EW and NS components of the response were available, which were respectively recorded at the center of the structure and near the east and west exterior frame lines. Records of only this earthquake are available for the structure. Thus, unlike the Van Nuys hotel discussed in the previous section, it is not possible to study changes in the dynamic properties with prior earthquakes in the ICS building.

Due to its distributed array of NS aligned sensors, the CAV is not only able to detect existence of damage but also to identify the location of this damage. Figure 13 shows the CAV response in the NS direction for sensors located near the east and west ends. The CAV plots show values significantly higher on the east side for both the second floor and roof. Ground floor CAV for the west and east sides are 1.04 g-sec and 1.01 g-sec, respectively. For the second floor, the west side CAV value reaches 1.1 g-sec but the east side CAV value is 31% higher, that is, 1.45 g-sec. The roof CAV value on the east side is also higher by 31% than the west side reaching 2.51 g-sec and accordingly identifying that damage occurred on the east side of the building.

Figure 13.

(a) CAV and (b) NCAV of the NS components of the ICS building.

NCAV in Figure 13 shows no deviation in response for the west end sensors but some deviation in the second-floor east-end sensors and significant deviation in the east end roof response. These deviations correspond to slower wave propagation due to east side damages.

For the EW direction, sensors were located only at the center of the floors. Therefore, it is not possible to identify precise locations of damage. However, the NCAV plots show clear deviations for the fourth floor and roof in the EW component (Figure 14). It is to be noted that the ground floor shear walls were not damaged and hence the wave travel mechanism did not significantly change for the second floor. Thus, its response does not show major deviations even though damage occurred right below that floor. However, the wave travel mechanism changed for the other floors since the east end shear wall was situated right above the damaged columns.

Figure 14.

(a) CAV and (b) NCAV of the EW components of the ICS building.

From the above results for the ICS building, the CAV is able to identify the existence of damage as well as to locate the damaged side even for this single event case. This shows that the CAV can be applied to any newly constructed or instrumented structures for which no previous earthquake records are available to develop baselines of the structural response.

Conclusions

This paper presented the prospect of the CAV to be used as a local damage indicator and possible metric. Damage causes changes in the input power and subsequently deviations in the CAV and NCAV trends from sensors used at different elevations to identify the location of damage. Moreover, event-to-event trends are observed. Results from the experimental study showed that the CAV analysis on both horizontal and vertical acceleration responses can detect damage. Horizontal CAV vs time plots are able to indicate observed damaged levels. The R_CAV and S_CAV values quantitatively detected damaged zones for horizontal response. However, the vertical CAV showed more precision to detect damage with the used closely distributed sensors. Vertical CAV vs time plots and R_CAV values accurately located and, in some cases, predicted the location of damage in the experimental study.

Only horizontal CAV is applied to analyze data of the real damaged structures since vertical components of the responses were either not available or very limited. For the Van Nuys hotel, comparison between a current event and prior ones was essential to identify damaged floor levels with CAV plots showing clear deviations. In the case of the ICS building, lack of data prevented to establish a baseline for the undamaged case. However, the NCAV plots identified the existence of damage. Moreover, comparison of CAV plots of east and west sides accurately identified the location of damage on the east side of the building.

The application of the CAV as a structural damage indicator is promising. Although, more studies are required to further assess and quantify the reliability of the damage detection by CAV, results of this study show that the CAV can be applied to instrumented structures which have recorded response. With only ground and roof instrumentation, CAV can be used as a global damage indicator. However, more importantly, with multiple sensors including ones for the vertical accelerations, CAV can be applied as a local damage indicator. This provides an opportunity to effectively and practically identify the onset, location and severity of local structural deterioration which are critical issues in the field of structural health monitoring.

Footnotes

Acknowledgments

The authors acknowledge the financial support from the Taisei Chair in Civil Engineering, University of California, Berkeley, and the Pacific Earthquake Engineering Research Center. They also thank Dr. S. Günay and Dr. H. Lee for providing the data for the experimental study.

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