Retaining walls damaged in the Chi-Chi earthquake

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Retaining walls damaged in the Chi-Chi

earthquake

Y.S. Fang, Y.C. Yang, and T.J. Chen

Abstract: This paper investigates the failure of three gravity walls due to the 1999 Chi-Chi earthquake. Characteristics of the damaged walls were carefully recorded and backfill materials behind the damaged walls were collected and tested in the laboratory. Both the simplified analysis based on the Mononobe–Okabe method and the simplified dynamic analysis based on the Richards–Elms method were adopted. For the first case, the sliding of concrete wall blocks along the construction joint was observed. It was found that, during the earthquake, the frictional resistance at the untreated construction joint was not sufficient to resist the dynamic lateral thrust. For the second case, the retaining wall settled significantly and tilted about its toe. Seismic analysis of the wall indicated that, under the same horizontal acceleration, the factor of safety against bearing capacity failure was lower than that against overturning and sliding. A stability check against bearing capacity failure for the retaining wall should never be neglected. For the third case, the retaining wall built on top of the Che-Lung-Pu fault was severely damaged by the fault rupture. During the earthquake, the vertical displacement of the hanging wall uplifted the backfill, causing the wall to overturn. Horizontal displace-ment of the hanging wall caused the wall to slide and the soil in front of the toe to heave.

Key words: analysis, bearing capacity, case study, earthquake, failure, retaining wall.

Résumé : Cet article étudie la rupture de trois murs poids causées par le tremblement de terre de Chi-Chi en 1999. Les caractéristiques des murs endommagés ont été notées soigneusement et les matériaux de remblai à l’arrière des murs endommagés ont été prélevés et soumis à des essais en laboratoire. On a adopté l’analyse simplifiée basée sur la méthode de Mononobe–Okabe de même que l’analyse dynamique simplifiée basée sur la méthode Richards–Elms. Dans le premier cas, on a observé le glissement de blocs du mur de béton le long du joint de construction. On a trouvé que, durant le tremblement de terre, la résistance au frottement le long du joint de construction non traité n’était pas suffi-sante pour résister à la poussée dynamique latérale. Dans le deuxième cas, le mur de soutènement s’est affaissé de façon significative et s’est incliné autour de son pied. Une analyse séismique du mur a indiqué que, sous la même accélération horizontale, le coefficient de sécurité contre la rupture en capacité portante de la fondation était plus faible que contre le renversement et le glissement. Une vérification de la stabilité contre la rupture en capacité portante d’un mur de soutènement ne devrait jamais être négligée. Dans le troisième cas, le mur de soutènement construit sur la faille de Che-Lung-Pu a été endommagé considérablement par la rupture de la faille. Durant le tremblement de terre, le déplacement vertical du mur suspendu a soulevé le remblai, causant le renversement du mur. Le déplacement horizontal du mur suspendu a produit un glissement du mur, et le sol en avant du pied s’est soulevé.

Mots clés : analyse, capacité portante, étude de cas, tremblement de terre, rupture, mur de soutènement. [Traduit par la Rédaction] Fang et al. 1153

Introduction

On 21 September 1999 at 1:47 a.m., a disastrous earth-quake with a magnitude of 7.3 on the Richter scale struck Taiwan. The Central Weather Bureau located the epicenter at 23.85°N, 120.82°E near the town of Chi-Chi (sometimes

translated as Ji-Ji or Gi-Gi), as indicated in Fig. 1. The focal depth was about 8.0 km. The rupture of ground along the Che-Lung-Pu fault was about 105 km long. The frequency of shaking ranged from 1.0 to 4.0 Hz. The horizontal peak ground acceleration (PGA) measured at strong ground mo-tion stamo-tion TCU-065 was as high as 774 Gal (0.79g) as listed in Table 1. In this incident, 49 542 dwellings were to-tally damaged and 42 746 dwellings were partially damaged. Most unfortunately, 2432 people were killed, and 46 people are still missing. Immediately after the earthquake, the Na-tional Science Council of Taiwan mobilized more than 1200 scientists and engineers to assess the various kinds of dam-age due to the earthquake. The authors joined the investiga-tion project and studied the failure of retaining structures due to the earthquake. For more information regarding the strong ground motion characteristics of the Chi-Chi earth-quake, the reader is referred to Tsai and Huang (2000) and

Received 2 April 2002. Accepted 31 July 2003. Published on the NRC Research Press Web site at http://cgj.nrc.ca on 31 October 2003.

Y.S. Fang1_{and Y.C. Yang. Department of Civil}

Engineering, National Chiao Tung University, 1001 Ta Hsueh Road, Hsinchu 30010, Taiwan, Republic of China.

T.J. Chen. Sinotech Engineering Consultants Ltd., 171 Nanking East Road, Sec. 5, Taipei 105, Taiwan, Republic of China.

1_{Corresponding author (e-mail: [email protected]).}

Can. Geotech. J. Downloaded from www.nrcresearchpress.com by National Chiao Tung University on 04/27/14

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Idriss and Abrahamson (2000). A dedicated issue containing 42 articles regarding the seismic aspects of the Chi-Chi earthquake was published as a Bulletin of the Seismological Society of America in October 2001.

Ueng et al. (2001) reported the geotechnical hazards ob-served after the earthquake, including landslides, soil lique-faction, foundation failures, and ground movements. Fang and Chen (1999), Huang (2000), and Fang et al. (2001) re-corded the failure of quay walls, masonry walls, gravity walls, modular-block retaining walls, and reinforced earth-retaining structures. This paper analyzes the seismic ade-quacy of three gravity retaining walls under earthquake exci-tation. Mononobe (1924) and Okabe (1924) proposed an analytical method (the Mononobe-Okabe method) to esti-mate the dynamic earth pressure against the wall under a seismic condition. Seed and Whitman (1970) described how to estimate the dynamic earth pressure based on the Mononobe–Okabe theory. Richards and Elms (1979) pro-posed a procedure (the Richards–Elms method) for the design of gravity retaining walls based on the limit-displacement concept.

In this paper, the authors introduce the behavior of retain-ing walls under seismic excitation. Three cases of gravity wall failure are reported. For the first case, sliding of con-crete wall blocks along construction joints was observed. For the second case, the retaining wall settled significantly and tilted about its toe. For the third case, the gravity wall built on top of the Che-Lung-Pu fault was severely damaged. The research team carefully measured and recorded the charac-teristics of the damaged walls. Backfill materials behind the damaged walls were collected and taken to the soil mechan-ics laboratory. Experiments were conducted to determine the physical properties and strength parameters of the backfill. Using these parameters, an analysis was done to evaluate the seismic adequacy of the damaged walls. In this paper, the simplified analysis based on the Mononobe–Okabe (M–O) method and the simplified dynamic analysis based on the Richards–Elms (R–E) method were adopted. The intention of the paper is to document several case histories of dam-aged walls such that lessons can be learned from this failure.

Seismic behavior of gravity walls

Seed and Whitman (1970) reported outward movements of retaining walls and wing walls for the 1960 Chilean and 1964 Niigata earthquakes. The behavior of a gravity retain-ing wall under horizontal acceleration a_h can be explained with the help of Fig. 2. As the ground was shaken from left to right, the dynamic earth pressure and inertia force of the wall would act from right to left. If the resistance at the base of the wall was not sufficient to defy the dynamic thrust, ac-tive wall movement would occur. If the direction of ground shaking was reversed, however, the wall would be thrown from left to right. Due to the existence of the backfill, pas-Fig. 1. Location of strong ground motion stations (TCU) and sites investigated.

Horizontal

Station Vertical East–west North–south

TCU-065 258 563 774

TCU-072 275 371 465

TCU-078 171 302 440

TCU-079 384 417 580

Table 1. Records of peak ground acceleration (cm/s2_{) (Central Weather Bureau 1999).}

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sive earth pressure would act between the wall and the soil, and only partial active wall movement could be recovered. If the wall moved outward a small amount due to each effec-tive cycle of ground shaking, with increasing effeceffec-tive cy-cles, the wall would gradually move away from the backfill. As indicated in Fig. 2, with the outward movement of the wall, the active soil wedge would slide down along the fail-ure plane, causing settlement and tension cracks in the back-fill.

Site 1: sliding along construction joints

The damaged retaining wall was located along Taiwan Provincial Highway 14 and is labeled as site 1 in Fig. 1. The gravity wall was built to retain a steep excavation for high-way construction. The wall was 4.7 m high, 2.0 m thick at the base, and 0.6 m thick at the top as illustrated in Fig. 3. The retaining structure was constructed by placing concrete in five pours. It should be mentioned that no special treat-ment had been provided at the construction joints of the wall. During the Chi-Chi earthquake, the upper parts of the wall gradually moved away from the backfill along the con-struction joints. Eventually, the top two blocks fell down to the side ditch of Highway 14 as indicated in Fig. 4. The damaged zone was approximately 20 m long. Based on field observations, it was suspected that the frictional resistance at the flat construction joint was not sufficient to resist the dy-namic earth pressure and the inertial force of the upper part of the wall. It was clear that a more detailed analysis would be needed

Soil testing

After the earthquake, the authors joined the damage re-connaissance team organized by the National Science Coun-cil of Taiwan. Backfill materials behind the damaged walls were collected at the site and tested in the soil mechanics laboratory of the National Chiao Tung University. Physical property tests and standard Proctor compaction tests (ASTM 2000) were conducted. Physical properties for backfill ob-tained from sites 1, 2, and 3 are summarized in Table 2, and

Fig. 2. Seismic behavior of gravity wall. Fig. 3. Profile of the damaged retaining wall at site 1.

Fig. 4. Outward movement of the gravity wall along construction joint.

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gradation curves of the soil samples are illustrated in Fig. 5. In the field, the contractors are generally required to com-pact the soil to at least 90% of standard maximum dry den-sity. To simulate the performance of the backfill in the field, the soil sample at its optimum moisture content was com-pacted in the laboratory with the standard Proctor method and then tested with the direct shear apparatus. Seed and Chan (1959) reported that samples compacted dry-of-optimum tend to be more rigid and stronger than samples compacted wet-of-optimum. From a practical point of view, in this study the soils collected from the sites were com-pacted at the optimum moisture content and then sheared to failure. The strength parameters obtained are listed in Ta-ble 2 and were used in the stability analyses of the retaining walls.

Seismic pressure based analysis

Kramer (1996) stated that gravity walls are customarily designed by one of the following two approaches: a seismic pressure based approach, or a permanent displacement based approach. Gravity walls have traditionally been designed on the basis of seismic earth pressure. The Mononobe–Okabe method is commonly used to estimate the dynamic earth pressure due to earthquakes. The total active thrust P_AEcan be expressed as [1] PAE = H −k Kv AE 1 2 1 2 γ ( )

where the dynamic active earth pressure coefficient K_AE is given by

[2] K_AE = − −

+ + + + −

cos ( )

cos cos cos ( ) sin ( ) sin (

2 2 ₁ φ β θ θ β δ β θ φ δ φ θ δ β θ β − + + −         i i ) cos ( ) cos ( ) 2 [3] θ = −       − tan 1 1 k k h v

γ is the unit weight of soil, H is the height of the wall, φ is the internal friction angle of soil,δ is the wall friction angle,

i is the slope of the ground surface behind the wall,β is the

slope of the back of the wall to the vertical, k_h is the hori-zontal seismic coefficient (= ah/g, where ah and g are the

horizontal acceleration and gravitational acceleration, re-spectively), and kvis the vertical seismic coefficient (= av/g,

where avis the vertical acceleration). Pseudo-static

accelera-tions are generally considered smaller than anticipated peak accelerations. Whitman (1990) reported that values corre-sponding to one third to one half of the peak ground surface acceleration were commonly used with factors of safety (FSs) of 1.0–1.2. Under the combined effect of static and earthquake load, the NAVFAC DM-7.2 design manual of the U.S. Department of the Navy (1982) recommends that an FS between 1.1 and 1.2 is acceptable. It is reported that gravity walls designed by the traditional approach have gen-erally performed quite well in earthquakes.

Site No. Location Unified classification of backfill Specific gravity, G_s Optimum moisture content (%) Maximum dry unit weight, γd,max(kN/m3) Cohesion, c (kN/m2₎ Internal friction angle,φ (°)

1 Provincial Highway 14, kilometre 38 SC–SM 2.51 12.2 17.6 0.8 35.7

2 Provincial Highway 21, kilometre 71 SC 2.51 24.9 15.6 1.7 31.0

3 Taiwan Cinema Culture Town SP 2.62 11.3 18.1 1.1 38.8

Table 2. Properties of backfill materials.

Fig. 5. Grain-size distribution of backfill materials at sites 1–3.

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Seed and Whitman (1970) suggested that the total active thrust PAE could be resolved into the static active thrust PA

and the dynamic increment∆P_AE components: [4] P_AE = P_A + ∆P_AE

P_Aacts at H/3 above the base of the wall, and∆P_AE acts at 0.6H above the base of the wall. The magnitude and the point of application of ∆P_AE suggested by Seed and Whit-man were adopted in this study for estimation of overturning moment of the wall. The static active thrust P_Ais calculated using Coulomb theory with the cohesion of soil neglected.

The cross section of the collapsed wall at site 1 is shown in Fig. 3. It is clear in Figs. 3 and 4 that sliding failure oc-curred along the construction joint A–B. Therefore, stability analysis was carried out only for the upper two blocks of the wall. It is true that, due to the earthquake excitation, sliding failure could occur along any of the construction joints. To limit the scope of this study, however, the FSs were only de-termined for blocks 4 and 5 of the wall which actually failed. The coefficient of friction at joint A–B was assumed to be 0.5. It is obvious that the actual value of the friction coefficient depends on the roughness of the upper and lower surfaces in contact.

The wall friction angleδ between the backfill and the wall is commonly assumed to be between φ/2 and 2φ/3. The study by Seed and Whitman (1970) indicated that, forδ = 0 andδ = φ/2, the seismic active coefficients K_AE determined using the Mononobe–Okabe theory were nearly identical. It was concluded that values of K_AE computed for δ = φ/2 could be considered satisfactory for most conditions. In this study, it was assumed that δ = φ/2. Assuming the backfill had been compacted to a relative compaction of 90% before the earthquake, the unit weight of the compacted backfill would be 17.8 kN/m3. For the gravity wall, the unit weight of concrete was assumed to be 23.6 kN/m3_.

To evaluate the stability of a retaining wall, the NAVFAC DM-7.2 design manual (U.S. Department of the Navy 1982) requires checks for (i) resistance against overturning, (ii) re-sistance against sliding, (iii) allowable pressures on the base, (iv) settlement, and (v) overall stability of the wall. For the wall damaged at site 1, it is obvious that the resistance against sliding would be the point of emphasis. The factor of safety against sliding (FSsliding) can be expressed as

[5] FS_sliding R D = ∑ ∑ F F

whereΣ FRis the sum of the horizontal resisting forces, and

Σ FDis the sum of the horizontal driving forces. The factor

of safety against overturning (FSoverturning) about the toe can

be expressed as [6] FSoverturning R O = ∑ ∑ M M

whereΣ M_R is the sum of the resisting moments about the toe, andΣ MOis the sum of the overturning moments about

the toe. The computation of FS against sliding and overturn-ing under earthquake excitation is introduced in most soil dynamics textbooks, such as those by Das (1993) and Kramer (1996).

The variation of FS of the wall (blocks 4 and 5) as a func-tion of the horizontal seismic coefficient kh is shown in

Fig. 6. Since for most earthquakes the horizontal accelera-tion components are considerably greater than the vertical components, Seed and Whitman (1970) concluded that k_v can be neglected for practical purposes. In this study, the vertical ground acceleration was neglected. Under the static condition (k_h= k_v= 0), the FS against sliding obtained using the Mononobe–Okabe method was found to be 2.18. Das (1999) suggested that, under a static condition, the FS against sliding, overturning, and bearing capacity failure should be at least 1.5, 2.0, and 3.0, respectively. It was obvi-ous that the gravity wall was safe from sliding without the earthquake excitation.

Figure 6 shows that the FS against sliding decreased with increasing horizontal ground acceleration. As the horizontal acceleration exceeds 0.24g, the FS against sliding would be less than 1.0. This means the frictional resistance at the construction joint A–B would be insufficient to resist the dynamic soil thrust. In Table 1, the peak horizontal accelera-tions in east–west and north–south direcaccelera-tions measured at station TCU-072 during the Chi-Chi earthquake were 0.38g and 0.47g, respectively. These values are apparently greater than the yield acceleration of 0.24g. It is possible that, as mentioned in the second section of this paper, the wall moved a small amount due to each effective cycle of ground shaking. After several effective cycles, the wall gradually moved away from the backfill and eventually fell into the side ditch. In Fig. 6, sliding failure is shown to be more likely to occur than overturning, since the FS against sliding is significantly lower than the FS against overturning for the same k_h value.

Fig. 6. Factor of safety (FS) of wall at site 1 as a function of seismic coefficient.

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Permanent displacement-based analysis

This approach allows the designer to take into consider-ation the wall inertia effect and leads to the conclusion that there might be some lateral movement of a wall even for mild earthquakes. Design procedures based on Richards and Elms (1979) and Whitman and Liao (1985) procedures for estimation of permanent displacement are available. In the Richards and Elms analysis, the weight of the wall Ww

re-quired to prevent wall motion is expressed as [7] Ww=  H −k Kv AE CIE    1 2 1 2 γ ( )

The coefficient K_AEcan be determined using eq. [2], and the wall inertia factor C_IEis given by

[8] C k IE b v b (1 = + − + − −

cos ( ) sin ( ) tan ) (tan tan )

β δ β δ φ

φ θ

where tanφ_bis the friction coefficient at the base of the wall. The FS to take into account the effects of dynamic soil pres-sure and wall inertia is defined as

[9] FS

w

= W

W

where W is the weight of the wall for equilibrium in the static condition. For this method, an FS of 1.5 is generally required. The variation of FS against sliding based on the method proposed by Richards and Elms (1979) is also shown in Fig. 6. It is clear that as the horizontal ground ac-celeration exceeds 0.15g, the FS would be less than 1.0, which means that the frictional resistance at the construction joint will not be able to resist the horizontal soil thrust and wall inertia force. When the ground shaking is equal to or greater than the yield acceleration, permanent wall displace-ment will occur.

Figure 7 shows how the variation of soil property affects the results of analysis. Based on the laboratory test results, the internal friction of the backfill is assumed to be 35.7°. Under the horizontal shaking of 0.15g, the calculated FS against sliding (R–E method) is 1.06. If the φ angle of soil is reduced to 34.0°, however, the FS against sliding (R–E method) would drop to only 0.95. The analytical results are relatively sensitive to the variation of soil strength. It is pos-sible that locally poor compaction or the presence of weaker soil triggered the 20 m long wall failure at site 1, not failure for the whole length of wall.

The Foundation Design Code of Taiwan adopted the Mononobe–Okabe method to determine the dynamic earth pressure under seismic loading. Central Taiwan, the most se-verely damaged area, was included in zone 2 of the seismic zoning chart of Taiwan. The design horizontal acceleration recommended for zone 2 is only 0.23g. On 21 September, however, the horizontal PGA measured at stations TCU-072 and TCU-065 was 0.47g and 0.79g, respectively. Under such a strong vibration, the retaining walls designed with a hori-zontal acceleration of 0.23g probably could not remain sta-ble. About 2 months after the earthquake, the damaged wall at site 1 had been repaired. Shearing reinforcements were fabricated at the construction joint as indicated in Fig. 8. During construction, steel H-piles were driven to resist the

potential movement of the steep slope. The installation of a shearing key would be another efficient method to prevent sliding failure at the construction joint.

Site 2: bearing capacity failure under the

toe

The damaged retaining wall was built near Sun-Moon Lake and is labeled as site 2 in Fig. 1. The gravity wall was built to retain the steep slope for the construction of Provin-cial Highway 21. After the Chi-Chi earthquake, the retaining wall settled significantly and tilted about its toe as shown in Fig. 9. Little lateral movement of the wall was observed. The active soil wedge behind the wall collapsed, however a large portion of the wall body remained undamaged. The beetle-nut plantation on the uphill slope remained stable dur-ing the earthquake.

The wall was 2.5 m high, 1.25 m thick at the base, and 0.5 m thick at the top, as shown in Fig. 10. Weep holes were fabricated in the wall 0.25 m apart horizontally. The dam-aged zone was about 40 m long. Figure 1 shows that site 2 is quite close to the epicenter of the Chi-Chi earthquake. It is possible that the unexpected strong ground motion is the main cause of the damage. Adequacy of the gravity wall un-der seismic excitation is discussed in the following section. Seismic adequacy

The variation of FS for the gravity wall at site 2 as a func-tion of the horizontal seismic coefficient k_h is shown in Fig. 11. It was assumed that the foundation soils had been compacted and had the same properties as the backfill. The resisting force against sliding at the base of the wall can be expressed as [10] ∑ = ∑   +   F_R Vtan 2 B c 3 2 3 φ

Fig. 7. Variation of FS as a function of soil strength.

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whereΣ V is the sum of the vertical forces, B is the width at the base of the wall, and c is the cohesion.

Under a static condition, the FS against sliding is only 1.15. This value is unacceptable for design, since it is less than the required FS of 1.5. In Fig. 11, the FS against sliding decreases with an increase in the horizontal acceleration. With the Mononobe–Okabe method, the FS against sliding would be less than 1.0 for a horizontal acceleration greater than 0.05g. With the Richards–Elms method, the wall would start to slide as the horizontal acceleration exceeds 0.025g. It is clear in Fig. 10 that the wall is relatively short and thick

and should exhibit good resistance against overturning. In Fig. 11, at any k_hvalue, the FS against overturning is appar-ently higher than that against sliding. This analysis indicates that the wall should slide instead of overturn under seismic shaking. This finding is contrary to the wall behavior ob-served in the field.

Tatsuoka et al. (1998) reported that, under a seismic load, gravity and semigravity walls could display bearing capacity failure under the toe. As indicated in Fig. 12, the incremen-tal seismic forces ∆P_AE and k_hW would increase the contact

pressure at the toe, qmax. If qmaxexceeds the ultimate bearing

Fig. 9. Overturning of gravity wall at site 2. Fig. 8. Shearing reinforcement at construction joint.

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capacity, q_ult, of the underlying soils, settlement would occur at the toe, causing the retaining wall to tilt. The FS against bearing capacity failure is defined as

[11] FS₌ qult

q_max

The ultimate bearing capacity of the foundation soil was determined with the following equation proposed by Meyerhof (1963):

[12] q_ult = cNcFcsFcdFci + qNqFqsFqdFqi

+ 0.5γBN_γF_γsF_γdF_γi Fig. 12. Assumed contact pressure at the base of the wall. Fig. 11. Factor of safety of wall at site 2 as a function of

seis-mic coefficient.

Fig. 10. Profile of damaged wall at site 2.

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where Nc, Nq, and Nγ are bearing capacity factors; Fcs, Fqs,

and F_γsare shape factors; Fcd, Fqd, and Fγdare depth factors;

and F_ci, F_qi, and F_γiare load inclination factors. It should be noted that the resultant force acting at the base of the wall is not vertical, and the load inclination factors would signifi-cantly influence the estimated qultvalue. Unfortunately, due

to limited funding, the strength parameters c₂and φ₂ of the foundation soil were not available for this case. It was as-sumed that the properties of the soils under the wall were similar to those of the compacted backfill. In the analysis, the parametersγ₂= 17.5 kN/m3_,_φ

2= 31°, and c2= 1.7 kN/m2

were adopted for the foundation soil.

The variation of FS against bearing capacity failure is also indicated in Fig. 11. Under the same seismic coefficient, the FSs obtained are slightly lower than the FS against sliding. During the Chi-Chi earthquake, the horizontal PGA recorded at the nearby station TCU-079 was 0.59g. Under such a strong seismic vibration, the overturning wall movement was most probably triggered by insufficient bearing capacity un-der the toe. Based on this case study, it could be concluded that a stability check against bearing capacity failure for the gravity wall should never be neglected.

It should be noted in Fig. 11 that, even under static load-ing, the FSs against sliding and bearing failure are very low. Figure 13 shows how the variation of soil friction angle af-fects the analytical results prior to the earthquake. Based on the laboratory tests, the angleφ of the compacted backfill is assumed to be 31.0°. In Fig. 13, ifφ is reduced to 29°, bear-ing failure would be more likely. However, the FS against bearing failure increases rapidly with an increase inφ. If φ is increased to 33°, the FS against bearing failure would be 2.18, and sliding becomes the possible mode of failure.

Site 3: retaining wall damaged by fault

rupture

Figure 14 shows the failure of a gravity wall located at the Taiwan Cinema Culture Town (site 3) near the township of Wu-Fung. The wall was constructed right above the Che-Lung-Pu fault. During the earthquake, the fault rupture caused the wall to slide and overturn. Figure 14 shows that the power pole tilted along with the retaining wall. The body of the wall remained unbroken, however. Ground heave in front of the toe is quite obvious in Fig. 14. The backfill be-hind the wall cracked, and the buildings constructed on the backfill were severely damaged by the ground deformation and strong ground shaking.

The failure mechanism of the damaged wall is illustrated in Fig. 15. The gravity wall is 4.0 m high and 0.4 m thick at the top. The retaining wall was built on top of the Che-Lung-Pu fault. Figure 16 is an oblique aerial photograph showing the fault rupture cutting through the Taiwan Cinema Culture Town. Lee et al. (2000) investigated the surface fault rupture due to the Chi-Chi earthquake. It was reported that the vertical and horizontal displacements measured at Wu-Fung were 2.0 and 1.3 m, respectively. The maximum verti-cal fault rupture reported for the Chi-Chi earthquake was as much as 7.0 m. It is clear in Fig. 16 that the buildings constructed along the fault were severely damaged by the ground deformation and strong ground shaking. The vertical

and horizontal PGA measured at station TCU-065 near site 3 were 0.26g and 0.79g, respectively. Figure 15 shows that during the earthquake the vertical displacement of the hang-ing wall uplifted the backfill, caushang-ing the wall to overturn. Horizontal displacement of the hanging wall pushed the wall, causing it to slide, and the soil in front of the toe, caus-ing it to heave. It may be concluded that it is of critical im-portance for the designer to locate the active faults near the site and not to construct any structure on top or even near active fault zones.

Figure 17 shows the variation of FS against sliding and overturning for the wall as a function of the horizontal seis-mic coefficient. It should be mentioned that the change of FS in Fig. 17 is solely due to the effect of ground shaking. The procedure of analysis is the same as that for the walls at sites 1 and 2. Under a static condition, the FSs against slid-ing and overturnslid-ing are greater than the required values of 1.5 and 2.0, respectively. The wall should be safe from slid-ing and overturnslid-ing without earthquake excitation. Based on the Richards–Elms method, as the horizontal acceleration exceeds 0.17g, the FS against sliding would be less than 1.0. In Fig. 17, the FS against overturning is apparently greater than the FS against sliding under the same seismic coeffi-cient kh. The wall should be safe from overturning up to a

horizontal acceleration of 0.50g. It may be concluded that failure of the retaining wall was mainly caused by excessive fault displacement.

Conclusions

This paper has investigated the failure of retaining struc-tures due to the 1999 Chi-Chi earthquake. Stability analysis was performed with both the Mononobe–Okabe and the

Fig. 13. Variation of FS as a function of internal friction angle,φ.

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Richards–Elms methods. Based on the case study for three gravity walls, the following concluding remarks are made.

For the first case, the sliding of concrete wall blocks along the construction joints was observed. With the Mononobe– Okabe method, as the horizontal acceleration exceeded 0.24g, the FS against sliding at the construction joint would be less than 1.0. With the Richards–Elms method, the mini-mum horizontal acceleration to initiate any sliding is 0.15g. When the ground shaking is equal to or greater than the yield acceleration, permanent wall displacement will occur. During the Chi-Chi earthquake, the horizontal PGA

mea-sured in the east–west and north–south directions was 0.38g and 0.47g, respectively. It would be reasonable to infer that the wall moved a small amount due to each effective cycle of ground shaking. After several effective cycles, the wall gradually moved away from the backfill and eventually fell into the side ditch. The installation of shearing keys or shearing reinforcements would be effective methods to pre-vent sliding at the construction joint.

For the second case, the retaining wall settled significantly and tilted about its toe. Tatsuoka et al. (1998) reported that, under a seismic load, gravity and semigravity walls could display bearing capacity failure under the toe. If the contact pressure under the toe, q_max, exceeds the ultimate bearing ca-pacity, qult, of the underlying soils, settlement would occur at

the toe, causing the retaining wall to tilt. Seismic analysis of the wall indicates that, under the same horizontal accelera-tion, the FS against bearing capacity failure was lower than the FS against overturning and sliding. The overturning wall failure was most probably triggered by the insufficient bear-ing capacity beneath the toe. It is concluded that a stability check against bearing capacity failure for the gravity wall should never be neglected.

For the third case, the retaining wall built on top of the Che-Lung-Pu fault was severely damaged by excessive fault displacement. During the earthquake, vertical displacement of the hanging wall uplifted the backfill, causing the wall to overturn. Horizontal displacement of the hanging wall caused the wall to slide and the soil in front of the toe to heave. The failure of the retaining wall was mainly due to the excessive fault rupture. It is of critical importance for the engineer not to construct any structure on top of or near an active fault.

Fig. 15. Schematic diagram of the wall damaged by fault rup-ture.

Fig. 14. Sliding and overturning of retaining wall at site 3.

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Acknowledgements

The writers wish to acknowledge the National Science Council of the Republic of China (NSC 89-2921-Z-319-005-10) for the financial assistance that made this investigation possible.

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