Application of BCP-2007 and UBC-97 in seismic vulnerability assessment of gravity designed RC buildings in Pakistan

Abstract

Recent earthquakes in Pakistan (Kashmir 2005, Balochistan 2008, and Balochistan 2013) revealed the vulnerability of existing building stock and the deficiencies in the then prevalent Pakistan Seismic Code (PSC-86 (1986)). This study investigates, through an analytical framework, the seismic vulnerability of these and other such buildings, in accordance with the newly developed Building Code of Pakistan – Seismic Provisions 2007 (BCP-SP 07). Detailed failure mode is presented for buildings designed as per the new code. Collapse of structures is predicted for only 8% increase in PGA after moderate damage. A previously developed method, based on Eurocode-8 (2004), is used as baseline. A deficient reinforced concrete frame, typical to local building practices, is analyzed and assessed for vulnerability using the BCP- SP 07 (2007) framework. A comparison is drawn for the same building, based on Eurocode-8 (2004). Derived vulnerability curves show that the previous framework overestimated the damage and hence the vulnerability. Comparison of vulnerability parameters with previous studies show slight difference in performance of buildings.

Keywords

Building Code of Pakistan / earthquake engineering / seismic effects / vulnerability assessment of buildings / vulnerability framework

Introduction

Geographically, Pakistan is at immense risk of being affected by the strong earthquake events [1–3]. Most recent major earthquakes hitting Pakistan include Kashmir earthquake in 2005, Balochistan earthquakes in 2008 & 2013. These events were disastrous in terms of the loss of life and property due to failure of infrastructure hit by the mentioned earthquakes [4]. Earthquake resistant design requires the development and implementation of proper seismic codes that accurately incorporates the design practices prevalent in the subject area. In Pakistan, a seismic code, Pakistan Seismic Code PSC-86 was developed in 1986 [5]. Besides being very raw, it was not implemented properly. Most of the buildings constructed before Kashmir earthquake were designed for gravity load only and others were designed with PSC-86. A better compression resistance is shown by these buildings but their resistance to shear forces was not good [6].

Kashmir earthquake of 2005 not only exposed the prevailing resistance of existing reinforced concrete (RC) buildings [7] but also highlighted the deficiencies of PSC-86. This enforced a hasty formulation of new code for this area i.e. Building Code of Pakistan BCP-SP 07 [8]. It is, thus, necessary to effectively relate the seismic risk with the infrastructure for a better earthquake disaster planning, emergency preparedness, policy decision making, risk mitigation and most importantly for calibration of the new code itself.

For this reason, vulnerability assessment of structures designed as per seismic demand parameters of BCP-SP 07 is required. Multiple studies have been conducted, which provide guidelines for vulnerability assessment of buildings e.g. ATC-40 and FEMA-440 [9,10], and these guidelines have led to development of different analytical frameworks. This study focuses on an existing methodology which may be used to assess the vulnerability of the building stock of Pakistan after incorporating the parameters of BCP-SP 07. For this purpose, previously built framework by Kyriakides et al. [11] is used and the parameters of BCP-SP 07 are incorporated for the present study.

Methodology

Major steps of the frame work developed by Kyriakides et al. [11] for vulnerability assessment of buildings are structural modeling, prediction of structural response to a certain seismic hazard level and evaluation of damage index of the subject structures. These steps, for the framework, are detailed below.

1)‚A typical (or representative) building of Pakistan designed with the PSC-86 Code is modeled through FEA analysis. Static cyclic analysis for the representative building is performed. Output of this analysis is a backbone curve of a multiple degree of freedom system (base shear vs top storey displacement).

2)‚After plotting the backbone curve, the mentioned capacity curve of multi degree of freedom (MDOF) system, is simplified to an equivalent single degree of freedom (SDOF) system following the procedures of ATC-40.

3)‚Each point on the capacity curve is treated as a performance point and is resultantly idealized into an equivalent elastic-perfectly-plastic system for substandard construction [11]. The corresponding ductility levels and secant periods for these systems are then evaluated using the following relations, given in FEMA 440.

(1)\mu ={\displaystyle \frac{{{\displaystyle \mathrm{S}\mathrm{D}}}_{\mathrm{p}\mathrm{i}}}{{{\displaystyle \mathrm{S}\mathrm{D}}}_{\mathrm{y}}}}

(2){{\displaystyle T}}_{\sec }=\mathrm{2}\mathrm{\pi }\sqrt{{\displaystyle \frac{{{\displaystyle \mathrm{S}\mathrm{D}}}_{\mathrm{i}}}{{{\displaystyle \mathrm{S}\mathrm{A}}}_{\mathrm{i}}}}}

where, SD is spectral displacement of selected point; SA is spectral acceleration of selected point

4)‚ Following the provisions of FEMA 440, the parameters β_eff and T_eff are evaluated for each ductility level, where, β_eff is Effective damping, T_eff is Effective period.

5)‚ Reduction factors B and M are calculated as per recommendations of FEMA-440. The elastic spectrum is reduced by dividing acceleration ordinate with reduction factor B. Then non-linearity of the structure is incorporated into the framework by generating Modified Acceleration Displacement Response Spectrum (MADRS) format, which is obtained by multiplying acceleration ordinate with reduction factor M.

6) Each point on the capacity curve is assumed to be a performance point and is intersected with MADRS. The corresponding acceleration ordinate in ADRS format is calculated by employing the following equation.

(3)\mathrm{S}\mathrm{A}(\mathrm{A}\mathrm{D}\mathrm{R}\mathrm{S})={\displaystyle \frac{\mathrm{S}\mathrm{A}(\mathrm{M}\mathrm{A}\mathrm{D}\mathrm{R}\mathrm{S})\times B}{M}}

7) Once the SA ordinate is calculated, combined with the already known SD of that point, the seismic coefficient C_v can be computed. For C_v, Eq. (4), as taken from the BCP-SP 07, is used.

(4){{\displaystyle C}}_{\mathrm{V}}=\mathrm{S}\mathrm{A}(\mathrm{A}\mathrm{D}\mathrm{R}\mathrm{S},{{\displaystyle \beta }}_o)\times T

where, {{\displaystyle \beta }}_o = viscous damping.

8) Once the C_v, is known the corresponding hazard level is calculated with the procedure and equations given in Section 2.1. Where, C_v is seismic coefficient.

9) Damage index is quantified after finding out necessary parameters T_ini (initial period of vibration) and T₁₀₀ (Period at collapse) using Eqs. (5), (6) respectively [11].

(5){{\displaystyle T}}_{\mathrm{100}}=\mathrm{2}\mathrm{\pi }\sqrt{{\displaystyle \frac{{{\displaystyle \mathrm{S}\mathrm{D}}}_{\lim \mathrm{i}\mathrm{t}}}{\mathrm{S}\mathrm{A}}}}

where, SD_limit is limit value of spectral displacement (100% damage).

(6)\mathrm{D}\mathrm{I}=\mathrm{100}\left({\displaystyle \frac{{{\displaystyle T}}_{\sec }-{{\displaystyle T}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}}{{{\displaystyle T}}_{\mathrm{100}}-{{\displaystyle T}}_{\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{t}\mathrm{i}\mathrm{a}\mathrm{l}}}}\right)

10) DI is then correlated with mean damaging ratio (MDR) to employ in the vulnerability plot. The following Eq. (7) relates the DI with MDR [11].

(7)\mathrm{M}\mathrm{D}\mathrm{R}=\mathrm{f}(\mathrm{D}\mathrm{I})

11) The last step provides with the plot between MDR and PGA to give vulnerability curve.

Calculation of PGA

Peak Ground Acceleration (PGA) corresponding to each displacement step on capacity curve is required for derivation of vulnerability curve for a building. In order to use MADRS procedure of FEMA440 (2005), a reverse engineering procedure is used in this framework formulation [11] instead of varying performance point (PP) to match with the hazard level, the hazard level is tuned to relate with PP. Assuming each point on the capacity curve to be a performance point, their corresponding parameters are found out according to aforementioned step 3 to step 7. Fig. 1 represents the Bi-linear idealized curve for a performance point on MADRS (β_eff, M) spectrum plot. The corresponding ADRS (β₀) for this curve gives the hazard level (PGA) which brought the subject building to this magnitude of displacement.

After finding out all required parameters, hazard level corresponding each point can be calculated using Eq. 8 below. The values to be used in this equation can be obtained from Tables 2–6 depending upon the soil type which can be selected from Table 1. Fig. 2 shows the graphical representation of PGA calculation with respect to BCP-SP 07 / UBC-97 [8,12] response spectrum and the detailed flow chart of the framework is presented in Fig. 3.

(8)\mathrm{P}\mathrm{G}\mathrm{A}={\displaystyle \frac{({{\displaystyle C}}_{\mathrm{v}\mathrm{2}}-{{\displaystyle C}}_{\mathrm{v}\mathrm{1}})\times ({{\displaystyle C}}_{\mathrm{a}\mathrm{2}}-{{\displaystyle C}}_{\mathrm{a}\mathrm{1}})}{({{\displaystyle C}}_{\mathrm{v}\mathrm{3}}-{{\displaystyle C}}_{\mathrm{v}\mathrm{1}})}}+{{\displaystyle C}}_{\mathrm{a}\mathrm{1}}

BCP-SP 07 / UBC-97 [8,12] define soil profiles SA, SB, SC, SD, SE and SF. The defined C_v and C_a values are also based on soil profile types which in turn depends on the measured shear velocity.

According to BCP-SP 07 / UBC-97, SD soil profile is chosen when insufficient details are available for determination of soil profile type and SE only when engineer determines that it may be present or indicated by geotechnical data. So in this study soil type SD is considered and values corresponding this soil profile has been employed in the formula for PGA calculation.

Five (05) zones are defined by BCP-SP 07 / UBC-97. The values to be used in interpolation formula obtained from the tables above are basically interpolated between the peak values of these particular zones as the zonation is based on peak ground acceleration.

Selection of typical building & structural modeling

A typical building with 3 storeys, 3 bays and regular configuration is selected as a representative building for the building stock under consideration. A storey height of 3m and single bay width of 4.5m is considered [13]. Due to symmetry in the geometry of the representative building, only a 2D frame (Fig. 4) is considered for FE modelling. The frame is modeled as a reinforced concrete frame and is designed for gravity load only using ACI 318-02 [14]. A uniformly distributed dead load of 2.50 kN/m and live load of 2.10 kN/m is applied on the structure. The dimensions for column as per the design are 225mm×300mm and those for beam are 225mm×380mm. Based on stochastic analysis of the uncertainty parameters, the data collected from different construction sites and material testing laboratories of the country suggests the following trends. The working compressive strength for concrete is taken as 16.30 MPa with 22% coefficient of variation (COV). Similarly the yield strength of reinforcement bars is taken as 319.50 MPa with 10.70% COV. Based on field surveys, a mean concrete cover of 24 mm with 7.23% COV and a 2.43% variation in column size with 5.80% COV is considered for modeling. The detailing of provided reinforcement bars is considered so as to be in line with the findings of Badrashi et al. [13] and is depicted in Fig. 4.

The designed reinforced concrete frame is then modeled in DRAIN 3DX [15]. DRAIN 3DX is a finite element analysis software, with the liberty to choose from a wide range of elements specifically incorporating seismic performance of such elements. The representative frame is modeled in DRAIN 3DX as 2D frame by choosing element 15 of the library (fiber element) having distributed plasticity [16] for column and beam sections and is discretized. The material behavior of the frame is characterized by using constitutive models of Eurocode-2 [17]. Due to inability of DRAIN 3DX to model element loads, these loads are applied as nodal loads by further discretizing the element. Structural masses are calculated by taking reinforced concrete density of 24 KN/m³ and are modeled as lumped masses at exterior nodes of each floor level. Actual joint behavior is modeled by introducing additional nodes at top and bottom of the column and using element 08 of the library. This element has shear hinges distributed along the length of element to account for additional shear, both elastic and inelastic.

Based on findings from previous studies [18], modeling of the bar slippage and stiffness degradation induced additional deformations which are identified to simulate the actual behavior of the joints in seismic events. Additional deformations at the joints due to bar slippage are specified using zero length hinges at the column ends. A stiffness degradation factor was introduced in concrete stress- strain relationship to account for Damage accumulation in the analysis. Bond stress vs bar slips and their strength and stiffness degradation are modeled using the fiber properties of the elements. Crack openings are simulated using gap properties [19] at connection face.

Evaluation of structural capacity

Depending upon applied gravity load combination during a seismic event and resultant seismic load characteristics, the performance of a structural frame, in terms of strength and ductility, varies significantly. Different nonlinear and linear approaches are available for the analysis [20]. In this numerical study, structural response of the system is evaluated using non-linear static cyclic analysis, which provides the capacity of the structure needed for defining limit states [21]. Here, the lateral load distribution proposed by BCP-SP 07 / UBC-97 is used for the subject frame [8,12]. For uniformly distributed gravity loads, the ultimate load combination (1.4 DL+ 1.7 LL) is employed. A displacement controlled cyclic analysis is carried out on the frame with increments in displacement added until a pre-set target displacement is achieved. The result of such cyclic analysis, when plotted, produces a force-displacement envelop for the multi degree of freedom (MDOF) system. As shown in Figs. 5 and 6, the resultant force-displacement envelope is transformed to a capacity envelope for an equivalent single degree of freedom (SDOF) system as per ATC-40 [9].

Development of vulnerability curve

After the structural capacity of the building has been evaluated, calculation of hazard level corresponding to the level of damage induced to the building is required to reach at what is known as vulnerability curve. For this purpose a VBA (Visual Basics Analysis) code has been written which controls the post processing of the results obtained directly from DRAIN 3DX in accordance with the above mentioned framework. After the application BCP-SP 07 framework the desired vulnerability curve is obtained as shown in Fig. 7 below. As a general trend it can be inferred from the curve that the structure failed in a brittle way due brittle failure mode (bar pullout and joint shear failure).

The curve derived using this framework indicates initial cracking starts at 0.0284 g PGA value. MDR increases linearly up to 0.083 g with corresponding 8.1% damage but then concrete crushing in compression and cracking in tension takes place along with gap fiber event in first and 2nd storey columns, during next cycle. This adds to the vulnerability of the structure as the curve becomes further steep. As can be seen from the graph that the MDR goes on increasing with a very less increase in PGA value. This happens due to the pull out in 1st storey left interior column reinforcing bars at 22% MDR. This pull out then spreads further to the other parts of structure and MDR increases to 43%. At an MDR value of 71% corresponding to 0.27 g pullout induces in the 2nd storey columns as well, thus enhancing the vulnerability and shifting the behavior towards brittleness. Between an MDR of 43% and 71% there are no visible kinks in the plot. This can be attributed to the fact that the alternate crushing of concrete in compression and yielding of steel in tension neutralizes the effect of sudden change in behavior. After further splitting out of re-bars of the 2nd storey’s columns, concrete failure takes places in subsequent cycles and ultimately makes the building to collapse at 0.297 g.

A number of damage scales are available in literature but here in this research HAZUS-99 [22] damage scale [23,24] is used to obtain PGA values for different damage levels. The damage scale defined three damage levels (i.e. slight, moderate and collapse). Vertical lines marked on the vulnerability curves indicate the PGA value at which these damage levels are reached. Up to slight damage the trend is almost linear, after which steepness increases and increased further after moderate damage level is reached and the building collapsed after 10.74% increase in PGA value.

To elaborate the results further and to check the suitability, the vulnerability curve of the same building is derived with the framework of Kyriakides et al. [11]. This curve derived with Eurocode-8 [25] elastic response spectrum with class “B” soil type (Being closer to the soil type used in this framework) is then compared with the one just derived above (Fig. 8). Vulnerability curve with Euro code clearly overestimate the damage initially up to 0.210 g and after this value the damage is well underestimated until the building frame collapsed. Thus, it overestimate the associated hazard first and then underestimate it eventually representing the damage a little of ductile type rather than brittle. In order to made it clearer bar chart corresponding to different damage levels is shown in Fig. 9, which shows slight damage of the building at a PGA value 4.90% lower than the one obtained with BCP-SP 07. Similarly moderate damage have a PGA value 11.92% higher and collapse at PGA value of 15.12% higher than the one obtained with BCP-SP 07 framework.

Difference in behavior can also be observed from the curve derived with BCP-SP 07 framework. This curve attains moderate damage level with a 29.68% increase in PGA value following attainment of slight damage. The collapse level reached with just 7.98% increase in PGA value at which moderate level is reached. While the previous framework by Kyriakides et al. [11] requires 40.67% & 8.40% increase in PGA value to change the state of damage from slight to moderate and then moderate to collapse, respectively. So, the framework by Kyriakides et al. [11] indicated the building less brittle up to moderate level. On the other hand at collapse level the failure trend is much more sudden and the depicted increase in PGA value for changing the damage moderate to collapse does not vary considerably from what is indicated in the current BCP-SP 07 framework.

Comparison with existing past earthquake damage data

Only a limited amount of damage data was available after Kashmir earthquake of 2005. In a recent study by Ahmad et al. [26], the available data has been compiled and empirical vulnerability curves have been derived. The analytical vulnerability curves derived in this study are then compared with the empirical one by Ahmad et al. [26] as shown in Fig. 10. Although the extent of damage data is limited yet the curve could be further projected based on the pattern of the curve. Comparison of analytical curve indicated a relatively gradual increase in MDR than the empirical curve but after the 50% damage is reached, the Empirical curve underestimates the MDR. An early damage accumulation is observed with analytical curve due to brittle failure modes. The analytical curve derived using the framework by Kyriakides et al. [11] compares well with the empirical curve until the slight damage is reached but after this point it under estimates the damage. The collapse point of the same is also compare well with the the empirical one but a considerable difference can be seen in the region between slight and collapse damage states. Thus, the curve derived with the framework by Kyriakides et al. [11] gives a better approximation at lower PGA but at higher PGA the predicted response is not much accurate.

Damage states marked on vulnerability curves indicated that the slight damage approach earlier in empirical curve while moderate and collapse states reach at relatively higher PGA when the empirical curve is considered. This shows that the analytical curve suggests an early onset of moderate and collapse damage states. However, these states may be delayed until a higher PGA, when explained through the empirical curve. The little difference is attributed due to the limited damage data which was also site specific. Safely it can be concluded that the pattern of damage as indicated by analytical curve is almost similar to the empirical one.

Conclusions

1) From the derived curve it is obvious that the building failed in a brittle manner with bar pullout as a dominant failure mode.

2) No warning signs will be indicted once the moderate damage level is reached. Building collapse will occur with just 8% increase in PGA value after the moderate damage appears.

3) The typical buildings even designed with PSC-86 are vulnerable to earthquakes and will perform better in Zones 1,2A, 2B but are not suitable for Zones 3 and 4.

4) The framework by Kyriakides et al. [11] with Eurocode Response Spectrum, gives better approximation at lower PGA but at higher PGA a better approximation of seismic performance is obtained with BCP-SP 07.

5) Comparison with empirical curve indicated under estimation of damage at lower PGA (0.25g) and overestimation at higher PGA. A little difference is attributed due to the availability of limited and site specific damage data.

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