Seismic Assessment of Lightly Reinforced Buildings: A Study of Shear Demand vs. Supply

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1 Seismi Assessment of Lightly Reinfored Buildings: A Study of Shear Demand vs. Supply S.G. Chasioti University of Stuttgart, Germany S.J. Pantazopoulou University of Cyprus, Cyprus / Demoritus University of Thrae, Greee D.V. Syntzirma Muniipality of Komotini Publi Works Dept., Greee SUMMARY: Seismi assessment of reinfored onrete strutures as presribed by leading design ode standards suh as the EC8-III and FEMA 356 / ASCE/SEI-41 guidelines omprise a omplex system of evaluation, but the various steps of this proess are not vested with a uniform level of onfidene as ompared with the experimental results. Strength values an be estimated with suffiient auray only when the modes of failure are dutile. The level of auray degrades when onsidering brittle mehanisms of resistane, partiularly when fousing on shear transfer and the assoiated deformation apaity. Today, after several years of persistent researh inluding a vast number of experiments on olumns under yli shear/moment/axial load ombinations, the satter of our analytial estimates as ompared with the experimental shear strength values and observed modes of failure is unsettling, partiularly when dealing with strutural reinfored onrete members representative of old, substandard onstrution. In this paper, the problem of seismi shear is explored from first priniples, with ombined insight from experimental observation whenever assumptions need to be made. The proedures developed to assess shear strength of seismially loaded members are ompared against measured experimental performanes of a pertinent database of large sale olumns with substandard details, tested under lateral load reversals that simulated earthquake effets. Keywords: angle of ompression struts, shear, ontribution of onrete, modified ompression field theory 1. INTRODUCTION The proedure of estimating the strength, the deformation apaity and the expeted mode of failure in primary members of a struture, that is, the omplete proess of seismi assessment of reinfored onrete strutures, has been reently supported by bakground douments in both Europe and U.S. (EC8-III, FEMA 356 / ASCE/SEI-41, and most reently by the draft of the New Model Code by the fib). The aeptane riteria proposed, provide a omplex system of evaluation, but the various steps of this proess are not vested with a uniform level of onfidene as ompared with the experimental results. Strength values an be estimated with suffiient auray only if the involved modes of failure are dutile. The level of auray degrades when onsidering brittle mehanisms of resistane, and the assoiated deformation apaities, whih are used as a basis for omparison with deformation demands. Yet, in the proess of assessment it is ritial to determine whether flexural yielding will preede shear failure (so as to ensure dutility) or whether a brittle failure ought to be antiipated. Even when flexural yielding may be supported it is also important to dependably estimate the dutility level beyond whih shear strength may be assumed to have degraded below the flexural strength leading to a seondary post-yielding failure that limits the available deformation apaity [Pantazopoulou and Syntzirna 010]. Traditionally, post-raking shear strength had been estimated from summation of various separate resistanes, attributed to onrete, to web reinforement, to axial load, to aggregate interlok and to

2 dowel ation. It is a point of ontention as to whether these mehanisms an atually be separated and independently estimated; it is more honest to admit that these may be viewed as suessive refinements to the underlying basi truss model that was inspired by Mӧrsh more than 100 years ago, so as to improve its orrelation with the test data. After repeated efforts to identify the soure of satter between the existing models of seismi shear strength and the experimental measurements, it appears that the least understood variables are the following: (1) The inlination of the major sliding plane (i.e. the angle forming between the primary diagonal rak heralding tension failure, with the longitudinal axis of the member), as this determines the number of stirrup layers mobilized in shear () The partiipation of axial load in resisting shear (3) The role of the aspet ratio of the member on shear strength (i.e., identifying and quantifying the shear moment interation envelope). (4) The effetive area of the onrete setion mobilized in the onrete shear ontribution. Additional issues suh as the influene of bond onditions, yield-penetration over the member away from the ritial setion, availability of onfinement, slenderness ratio of longitudinal bars (referring to the unsupported length between suessive stirrups) are also relevant, however they are not onsidered responsible for the dramati disrepanies between alulations and test results for this reason, they are onsidered beyond the sope of the present treatise. Development of the model requires referene to experimental evidene. For that purpose two subsets of data are used: the first subset, omprising four large sale olumns with substandard details tested under simulated seismi load by Woods and Matamoros (009) are used to illustrate some the issues listed above and to highlight their impliations in the analytial model. The seond set of data is used to test the analytial model and is used as a benhmark for evaluation of onepts onsidered in the assessment proedures. This set of data omprises nineteen olumn tests arefully seleted from the literature and onduted under ombinations of ompressive axial load and a history of lateral displaement reversals of inreasing magnitude. A oneptual model for shear was derived whereby the plane of sliding failure, web reinforement ontribution and partiipation of onrete in resisting shear fore was developed. The estimated shear strength magnitude is then used to prioritize the modes of failure and the assoiated deformation apaity (loss of load arrying apaity identified by a 0% drop in lateral load resistane after orretion for P-effets). The auray of the estimations of the various mehanisms of resistane that ontribute to shear strength depends greatly on the inlination of the dominant plane of shear sliding, marosopially assoiated with the prinipal diagonal tension rak that marks shear-related failure in reinfored onrete members. In this paper this is alulated as a funtion of the axial load and web longitudinal strain in aordane with basi onepts of onrete plane stress analysis.. EXPERIMENTAL DATABASE Test speimens used in this paper in order to derive or to alibrate the shear model were presented in Woods and Matamoros 010, Lam et al 003, Sezen and Moehle 004, Lynn et al 1996, Yavari et al 009, Aboutaha et al 1996, Aboutaha et al The olumns had details typial of pre 1970s onstrution tested either in double or single urvature, by imposed lateral load reversals. A onstant axial load is applied to most of the olumns, with the exeption of the speimens by Aboutaha et al 1996 and 1999 (tests No 1 to 3 in Tab. 1), where tests were ontinued until omplete loss of vertial load arrying apaity. Table 1 outlines speimen geometry, reinforement and loading used in the tests. The ross setion patterns are presented in Fig. ; note that all the speimens onsidered have

3 90 0 hooks for anhorage of transverse reinforement. Most of the ases tested reportedly exhibited a dominant shear failure mehanism. The speimens by Woods and Matamoros 010 and by Lam et al 003 (tests No 1 to 4 in Tab. 1) failed in shear before the attainment of yielding, identified as ondition 3 as per ASCE/SEI 41, whereas all other speimens are lassified under ondition (shear failure after flexural yielding), with the exeption of the speimens by Aboutaha et al 1996 and 1999 that failed due to insuffiient development apaity of the lap splies in the ritial region.tests No 5 to 7 by Sezen and Moehle 004, No 8 to 15 by Lynn et al and No 16 to 0 by Yavari et al. 009 are also inluded in the investigation. Table 1.Test speimen materials and details (a is a ross setion index with referene to Fig. 1) Speimen ID; Geometry l s P/f A g f Long. Reinf. Transverse Serial No angle mm MPa Reinf. b h L s /d a D bl f yl d t f yh s mm mm mm MPa mm MPa mm Spe Ø Spe Ø Spe Ø X Ø1+4Ø Spe Ø Spe Ø Spe Ø CLH Ø CLH Ø SLH Ø SLH Ø CMH Ø CMH Ø CMD Ø SMD Ø (A1) MCFS Ø (B1) MCFS Ø (C1) MCFS Ø (B1) HCFS Ø (C1) HCFS Ø FC Ø FC Ø FC Ø b, h: ross setion width and height, respetively;l s /d: aspet ratio; l s : lap splie length; P: axial load as % of f A g ; f : onrete strength; D bl,f yl : diameter and yield stress of longitudinal Reinf.; d t,f yh : diameter and yield stress of stirrups; s: spaing of stirrups; angle: inlination of the ompression stresses aording to CBPapproah with respet to the longitudinal member s axis. 1 Woods and Matamoros (010); Lam et al (003); 3 Sezen and Moehle (004); 4 Lynn at al (1996); 5 Yavari et al (009)); 6 Aboutaha et al (1996 and 1999). diretion of loading : (1) () (3) (4) (5) (6) Figure 1. Cross setion patterns of the speimens onsidered in aordane with Tab. 1

4 3. DETERMINING THE COMPONENT OF UNCERTAINTY To illustrate the unertainty and satter in the urrent state of the art regarding shear strength estimation for reinfored onrete members the first four of the speimens listed in Tab.1, whih had failed in shear prior to yielding of the ritial setion are used as referene, as the experimental shear fore sustained may be ompared diretly to the nominal alulated shear strength V n before any degradation takes plae. Analytial strength estimations are obtained from expressions inluded in the urrent assessment standards (i.e. the Model Code 010, the EC8-III, and the ASCE/SEI 41). An enhaned version of the expression provided by ASCE/SEI 41 for the onrete ontribution (Table 3),is that of the CBP whih inludes an enabling hek that the raks must have losed in order to aount for this ontribution (i.e., N/A g f >( s1 - s ) f y /f ) aording with Pantazopoulou and Syntzirma (010). Figure (a) plots results from various alternative estimations of prevailing olumns strength for the four olumns (i.e., the least lateral fore estimate required to sustain either flexural failure or shear failure aording with the various alternative assessment models mentioned). Note the satter between the alulated alternatives and the test result. Figure (b) plots the estimated strength at shear failure against the test values. The test and alulated values of rotation apaity, u, of the four speimens, is given in Fig. (); these are obtained from the expliit expressions provided by the Assessment Standards. Here, in order to test the auray of the rotation expressions of the CBP (this method assoiates u to the hord rotation at the onset of loalization of failure in the weakest mehanism of resistane), shear strength V n was set equal to the test value, V test [Syntzirma and Pantazopoulou 010]. The estimated hord rotation at loss of axial load apaity as estimated by ASCE/SEI 41 is also plotted in Fig. (). Test CBP setting V n =V test MC010 t ASCE/SEI V failure (kn) EC8-III ASCE/SEI 41-axial. loss V n (kn) 5 u % (a) (b) () Spe No Figure. Comparison of (a) prevailing olumns strength, (b) shear strength and () ultimate deformation (rotation apaity u ), between test values and Models estimations in aordane with Tab.1 The satter between the various alternatives illustrates the urrent state of understanding of seismi shear note that the examples onerned elasti (prior to flexural yielding) reported modes of shear failure. It is also worth noting that the fundamental approah of the CBP model performed well with respet to the deformability estimates when the shear strength unertainty was mitigated. This finding undersores the signifiane of orretly estimating shear strength as a ruial step towards reduing the reported satter. It was mentioned before that the inlination of the sliding plane (i.e. the angle between the prinipal diagonal tension rak that identifies shear failure and the member axis) ontrols both the so-alled onrete ontribution omponent, V, (through the inlination of the ompressive strut parallel to the rak) and the number of stirrups mobilized in transverse tension; the latter has been traditionally assoiated with a 45 o Mӧrsh-type truss, whih appears to disagree with experimental evidene. Figure 3 highlights the observed plane of failure and the number of stirrups mobilized in the ase of the first four speimens listed in Table 1 (elasti shear failures). Considering the development apaity of the typial stirrup from the point of intersetion with the diagonal tension rak to the hook end (the

5 orresponding lengths are speified on Fig. 3), the estimated web steel ontribution, V w, as determined from the CBP model for the example olumns are listed in Table. The differene between V test and V w is the estimated onrete ontribution, V, whih is given in the last row of the table. This is ompared in Fig. 4 (a), with the analytial estimates obtained from a few well known models and Code expressions (listed in Table 3). Speimen No 1 Speimen No Speimen No 3 Speimen No 4 14 mm =6 ο 343 mm 9 mm 115 mm 11 mm =76 ο 35 mm 141 mm 46 mm 35 mm =77 ο 34mm 01mm 167mm 134mm 100mm 67mm 33mm =71.5 ο Figure 3. Test Speimens No 1 to 4. Formation of diagonal raking. Table.Calulation of the real onrete ontribution in shear resistane with respet tofig. 3. Speimen No 1 Speimen No Speimen No 3 Speimen No 4 V test V w meas.(kn) V al. (kn) Table 3. Expressions for the alulation of onrete ontribution. Model Code 010, V k f zb Rd v k w Ls EC8-III tot g h CBP model CBP-modified Tureyen&Frosh 003 ASCE/ SEI 41 ACI318-99, eq.(11-3) 0.16 max(0.5;100 ) min f 0.8A min N; 0.55 A f ( MPa) N f d N y if ( ) V k( ) ;( ) otherwise 0 s1 s g f A MPa V A f f Ls 0.5 f A g g N f d N y if ( ) V k( ) ;( ) s1 s w f b MPa A f f Ls 0.5 f A g g otherwise V 0 V f b psi 5 w ( ) 0.5 f N V ( ) A MPa g L / d s 0.5A f g V f b d psi w ( )

6 A signifiant parameter ontrolling the relevane of the analytial estimates with the experimental results appears to be the area of onrete setion ontributing to V (Table 3): in most ases, the assumed effetive shear area was equal or nearly equal to the area of the ross-setion web: A g =b w d, or 0.8A g, or zb w (where z the depth of the Mӧrsh truss). Tureyen and Frosh (003) use the depth of ompression zone, instead, leading to a muh better approximation of the results, although the expression was alibrated for beams, thereby not aounting for the effet of the axial load. The CBP approah, modified aordingly also illustrates improved orrelation with the test results. Figure 4 (b) plots the observed values for the angle of inlination of the shear sliding plane relative to the transverse axis of the member for all the ases examined; note that the angle ranges between 6 o and 76 o, i.e. very far from the 45 o assumption. Thus, the ompressive strut whih is through to be approximately parallel to the sliding plane is very steep for olumns as ompared to what is observed in beam tests (i.e. tests with low axial load whih have formed the basis of alibration of the Mӧrsh truss). 500 V (kn) (a) (b) ( o ) Spe.No Spe.No Figure 4. (a) Estimated onrete ontribution to a member s shear strength (b) Observed angle of the prinipal sliding plane measured with respet to the olumn s transverse axis SHEAR STRENGTH: NEW APPROACH AND CORRELATION WITH TESTS In this setion the onrete ontribution omponent is established from first priniples. As a point of departure it is larified that onrete diretly supports shear only over the ompression zone of the member,, where raks may be assumed to have losed. So the effetive area A v, ontributing to shear resistane is taken equal to b w. Here two different member ross setions of a olumn undergoing lateral sway under earthquake ation are onsidered for analysis (Fig. 5). The ross setion shown in Fig. 5(b) is loated at the member end; fores F, C s and T s1 are the resultants of the ompression stress blok, stresses in ompression reinforement and tension reinforement, respetively ( s1 and s are the ompression and tension reinforement ratios, respetively, alulated over the area of the web, b w d). Similarly, the ross setion shown in Fig. 5() represents the nominal state of stress at the member s midpoint (setion m). Setion e C s = s b w d f s F,e T s1 = ρ s1 bd f s1 F,m Setion d x d x L s m N (a) (b) M () v e =F,e /b w N Figure 5. (a) Column under lateral sway, (b) Equilibrium of normal fores at setion e, () Nominal normal fores at setion m (atually the long. reinforements might be in tension due to shear).

7 If v is the mean axial stress of the olumn ross setion in Fig.5 (b), the stress tensor in the ompression zone is: ( e) ftk ftk 0 ftk ftk ftk ftk 1 ftk (4.) where, at the onset of diagonal raking of the web, the priniple tensile stress (e) is limited by the tensile strength of onrete f tk =0.5 f, whereas =F,e /b w the mean normal onrete ompressive stress in the end ross setion (i.e. the ompression fore resultant at the end setion normalized with the onrete area under ompression). The shear stress is related to the flexural moment at the end ross setion when onsidering that V=M/L s where L s the member s shear-span: V M b b L s Upon substitution to (4.), Eqn. 4.4 is obtained for : M M v x b Ls ftk 1 3 b Ls ftk ftk f tk (4.4) The orientation of prinipal axes,, in the end ross setion is obtained with referene to the longitudinal member axis, using basi mehanis aording with Eqn. 4.5: ftk 1 1 ftk ftk tan /( x y ) ; ftk 0.5 f f f 1 f tan ; tan f f 0.5 f tk (4.5) where represents the normalized stress ratio in the onrete ompression zone of the member (note that the value of is muh higher than o = N/ f b w d whih represents the reported in tests, nominal axial load ratio, a value that ours at the point of infletion in the absene of flexural moment). Using the above equations, the only parameter to be defined is the stress level of the member at whih shear raking initiates in the ompression zone. Defining this point in the resistane urve of the member, the values of ating moment M sh,r and ompression zone depth an be easily alulated. Here it is impliitly assumed that the first main rak formation due to diagonal tension will also define the inlination of the shear sliding plane. As shown in Fig. 6 (a), extensive raking generally preedes the onset of longitudinal reinforement yielding as manifested by a substantial redution of effetive flexural stiffness, while the member is still in the apparent elasti range of response. A point of referene in defining the point of web raking is that where the post raking stiffness loss is severe so that the effetive EI tends to its seant value at the onset of yielding (this orresponds to stabilization of raking as identified by the red mark in Fig. 6 a and b).

8 M II III EI M=M r M=M sh,r M=M r I EI M=M sh,r (a) (b) Figure 6. Defining the point of shear rak initiation When applying Equation 4.5 to the speimens desribed in Table 1 it was found that the angle varies between 5 o to 35 o with respet to the member s longitudinal axis (this is a range of 65 to 55 degrees with respet to the transverse axis of the member, a finding that omplies with the experimental values of Fig. 4 b). In this ase the onrete ontribution, is given by the shear stress resultant over the ompression zone of the ritial setion, V = b w, whereas the orresponding steel ontribution, V s, is obtained from the sum of fores of the total number of stirrup legs parallel to the plane of ation and interseted by the inlined rak plane: No of stirrups interseted by the shear plane: d s tan (4.6) d Vw As, tr f y, tr s tan (4.7) The methodology developed in this setion was applied to the entire olletion of tests studied in Table 1. Results are plotted for the nominal shear strength V n in Fig. 7a whereas Fig. 7b plots the estimated speimen strength, V failure, when onsidering the hierarhy of failure. Values in Fig. 7a with estimated shear strength higher than that measured in the tests do not neessarily imply lak of orrelation: these are example where failure was eventually ontrolled by alternative modes as illustrated in Fig. 7b whih ompares the test value with the strength of the prevailing mode. Here, ases where the alulated values of V failure are equal although they are obtained from different models whereas the orresponding V n values differ are again those that are ontrolled by an alternative, weaker mode of failure other than shear e.g. flexural and lap-splie failure. Note the signifiant improvement in the estimated values when apaity-based prioritizing of failure is employed to organize the various mehanisms of resistane (CBP method, omparison of Fig. 7a with Fig. 7b) after the introdued modifiations to the estimated plane of sliding and the effetive area of the ross setion ontributing to shear resistane. 5. CONCLUSIONS Through systemati evaluation of experimental results onerning brittle olumns that failed in shear prior to flexural yielding under ombined axial load and lateral load reversals, this paper explored the defiienies in the existing methods of estimation of seismi shear strength of reinfored onrete members. Beause shear strength is an essential tool in seismi assessment, used in order to: identify the strength hierarhy of the various mehanisms of resistane, to determine the prevailing mode of failure and eventually to estimate the dependable deformation apaity of reinfored onrete, it is essential for the improvement of performane based design that the exessive of satter assoiated with the analytial methods of its estimation be mitigated. In this paper, an alternative method of alulation of both shear strength ontributions (i.e. those owing to onrete and to web reinforement) is established from first priniples. An important outome is the angle of inlination of diagonal tension failure in the ritial zones of the member, whih also defines the number of

9 V failure V shear stirrups mobilized in tension to resist shear. It is onluded that, onsistently with experimental evidene, the strut angle that aounts for seismi shear of olumns is muh steeper than the 45 o assumption made in the established assessment standards. Test results are orrelated suessfully partiularly when aounting for a redued effetive shear area (supporting the onrete ontribution omponent) restrited to the ore of the member s ompression zone. AKCNOWLEDGEMENT Work presented in this paper was onduted under partial support from Institute for Constrution Materials, University of Stuttgart, Germany and Demokritus University of Thrae, Greee. 900 V n (kn) Test ASCE/SEI 41 (a) CBP-proposed EC8-III 600 TEST Σειρά EC8-III 300 Σειρά5 0 Spe υποστύλωμα No. 900 V failure (kn) Test ASCE/SEI 41 CBP-proposed EC8-III (b) Spe No. Figure 7. Comparative study of strength indies proposed by C.B.P. model, EC8 III, C.B.P. and ASCE/SEI 41 vs. the experimental values. EXAMPLE For the 1 st speimen of the Table 1 (Woods and Matamoros 010), here the shear strength V n aording to the new approah presented in hapter 4 is alulated. f 0.5 f MPa tk In order to form the diagram of how stiffness deays with inreasing ross setion urvature (Fig. 6b), fiber analysis for the end ross setion till the point of yield is performed. The point where the first shear rak is formed and defines the moment M sh, r is identified by the red mark on the Figure 8, and orresponds to a strain of 0.1 to the reinforement under tension. In this ase, M sh,r =197 knm and the ompression zone depth is 337 mm.

10 EI (knm) EI ( 10 3 ) (knm ) v MPa / tan No of stirrups rossed: 1. Therefore V w =5 Kn The shear stress over the ompression zone is: E E E E MPa urvature φ (1/mm) ( 10-5 ) (1/mm ) Figure 8. Defining the point of shear rak initiation for the Spe. No. 1 o And the onrete ontribution to the member s shear apaity: V = 0.8b w = =91 kn, where in this ase the depth of the ompression zone is 00 mm, beause orresponds to the ross setion point of yield. The shear apaity of Spe.No.1 is: V n =91+5=343 kn. REFERENCES Tureyen, A.K. and Frosh, R.J. (003). Conrete shear strength: Another perspetive. ACI Strutural Journal 10:5, Aboutaha, R.S., Engelhardt, M.D., Jirsa, J.O., and Kreger, M.E. (1996), Retrofit of onrete olumns with inadequate lap splies by the use of retangular steel jakets. Earthquake Spetra 1:4, Aboutaha, R.S., Engelhardt, M.D., Jirsa, J.O., and Kreger, M.E. (1999), Experimantal investigation od seismi repair of lap splie failures in damages onrete olumns. ACI Strutural Journal 96:, Lam, S.S.E., Wu, B., Wong, Y.L., Wang, Z.Y., Liu, Z.Q. and Li, C.S. (003), Drift apaity of retangular reinfored onrete olumns with low lateral onfinement and high-axial load. ASCE Journal of Strutural Engineering 19:6, Lynn, A., Moehle, J.P., Mahin, S., and Holmes, W. (1996), Seismi evaluation of existing R.C. building olumns. Earthquake Spetra 1:4, Sezen, H. and Moehle, J. (004). Strength and deformation apaity of R.C. olumns with limited dutility. 13thWorld Conferene on Earthquake Engineering. No 79. Woods, C. and Matamoros, A.B. (010). Effet of longitudinal reinforement ratio on the failure mehanism of R/C olumns most vulnerable to ollapse. 9thU.S. National and 10th Canadian Conferene on Earthquake Engineering. No Yavari, S. Elwood, K., Lin, S. H., Wu, C.L., Hwang S.,J., and Moehle J. (009). Experimental study on dynami behavior of multi-story reinfored onrete frames with non-seismi detailing. ATC & SEI 009 Conferene on Improving the Seismi Performane of Existing Buildings and Other Strutures. p.p ASCE/SEI 41 (007). Seismi Rehabilitation of Existing Buildings, Amerian Soiety of Civil Engineers. CEB-FIP Model Code (010). Chapter 6:Interfae Charateristis; Chapter 7:Design. Elwood, K., Matamoros, A., Wallae, J., Lehman, D., Heintz, J., Mithell, A., Moore, M., Valley, M., Lowes, L., Comartin,C., and Moehle, J. (007), Update to ASCE/SEI 41 Conrete Provisions. Earthquake Spetra 3:3, Euroode 8 (005). Design of strutures for earthquake resistane Part.3: Assessment and retrofitting of buildings, European Committee for Standardisation. FEMA 356 (000). Prestandard and ommentary for the seismi rehabilitation of buildings, Federal Emergeny Management Ageny. Pantazopoulou, V. and Syntzirma, D. (009). Code expressions for deformation apaity of lightly reinfored onrete members a omparative study. ACES Workshop:Advanes in Performane-Based earthquake Engineering. Syntzirma, D.V., and Pantazopoulou, S.J. (006), Deformation apaity of R.C. members with brittle details under yli loads. ACI Speial Publiation Vol. 36: 1-. ACI (1999), Building Code Reguirements for Strutural Conrete, Amerian Conrete Institute. Syntzirma, D.V., and Pantazopoulou, S.J. (010), Deformation apaity of lightly reinfored onrete members omparative evaluation. ACES Workshop:Advanes in Performane-Based earthquake Engineering, Series Geotehnial, Geologial, and Earthquake Engineering, Vol. 13, Springer.