Introduction

The 27^th February 2010 subduction earthquake in Central and South of Chile with a moment magnitude M_w = 8.8 was a very strong and long movement which affected an important percentage of the national motorway and railway infrastructure (e.g.^{Buckle et al., 2012}; ^{Hube et al., 2010}; ^{Ledezma et al., 2012}; ^{Verdugo et al., 2010}). For instance, in the Romero overpass bridge built in 2001 and located in Paine, 40 km South of Santiago, structural and geotechnical related damages during this earthquake were reported. Despite the bridge was founded with 1.5 m diameter and 11 m up to 30 m deep piles due to poor subsoil resistance, it suffered significant abutment failure because the concrete retaining structure could not resist the lateral seismic loading (^{FHWA, 2011}). Although the Chada overpass bridge, 10 km South East from Romero, did not fall down, the abutment was also severely damaged, mainly due to large embankment deformations behind the abutment made with an inclined gravity wall (^{FHWA, 2011}; ^{Hube et al., 2010}). No liquefaction was observed in these places.

On the other hand, ^{Ruiz-Tagle and Villalobos (2011a}) mention several bridges with abutments made of geogrid reinforced soil walls which withstood without problems the strong 27F earthquake, namely, Costanera Norte in Santiago, San Francisco de Mostazal in Rancagua, Bonilla roundabout in Concepción, Las Ballenas in Penco-Talcahuano Interportuaria motorway, North access in Chiguayante and Temuco.

The double track skewed railway bridge of San Francisco de Mostazal close to Rancagua built in 2001, has two HDPT uniaxial geogrid reinforced soil walls of 9 m maximum height with a façade made of modular concrete blocks (Figure 1a). This geogrid reinforced wall did not suffer noticeable displacement or deformation, however the bridge superstructure displaced around 5 to 10 cm probably due to the angle of skew. Another bridge 1 km away built using traditional reinforced concrete abutment suffered lateral displacements of around 1 m, despite not be a skewed bridge.

Figure 1 Pictures of geogrid reinforced soil walls after the 27F earthquake. a) No visible movement in bridge abutment wall in San Francisco de Mostazal, b) block vertical movement and fissures in Bonilla roundabout overpass and c) curved abutment in the overpass of Ruta 78 junction in Pajaritos Avenue without noticeable movement 

Four geogrid reinforced walls of the Bonilla Bridge in Concepción with 5 m maximum height are part of a roundabout which is a key point for traffic coming from and going to the North, East and South of the country. This bridge was just being in use some days before the earthquake in February 2010 and with a programmed inauguration in March 2010. A special challenge was to cope with the low bearing capacity and compressibility of the foundation soil close to the Andalién River. To overcome this problem, 2 m deep of this silty soil was replaced by compacted sand. After the 27F earthquake, vertical displacement not larger than 5 cm occurred in the geogrid reinforced wall. These settlements caused a long gap to appear in between a row of blocks on the top of the wall. A fine crack of a couple of millimetres also appeared in the ornamental beam above on top of the wall (Figure 1b). However, the Bonilla Bridge did not suffer any damage and could be used without any problem after the earthquake.

In the overpass of Ruta 78 junction in Pajaritos Avenue in the way to Melipilla in Santiago, a 6 m high curved abutment of geogrid reinforced soil wall was built. The foundation soil was gravel and the fill material used was ignimbrite known locally as Pumacita. This volcanic material is light and therefore very good as fill since applies less lateral earth pressure, and has a relative high shear strength. This project did not suffer any visible damage and no displacement or movement was possible to record despite the curved geometry of the wall (Figure 1c).

There are other similar projects in Chiguayante, Santiago, Talca, San Bernardo, Concepción and Temuco, where geogrid reinforced soil walls were designed also for angles of internal friction of the reinforced fill between 37° and 42° and a maximum design acceleration between 0.3g and 0.4g, resulting in almost negligible damage too. The former acceleration is normally applied in projects in the country central valley (Santiago, Rancagua, Talca, etc.) and the latter in coastal areas (Constitución, Concepción, etc.).

There have been similar reported cases in other countries, for example by ^{Tatsuoka et al. (1996}, ¹⁹⁹⁸), who were probably the first to report the favourable seismic behaviour of geogrid reinforced soil walls after the 1995 Hyogoken-Nambu earthquake in Kobe, Japan. They reported several damages of different types of retaining walls, where old walls had the most serious damage, whilst gravity walls had low stability against the strong shaking and cantilever reinforced walls had a poor behaviour too. However, a geogrid reinforced soil retaining wall built in 1992 at Tanata performed successfully despite been located in one of the most severely shaken areas. They reported also other geogrid reinforced soil walls which performed satisfactorily. This led to the conclusion that this type of walls can be designed and built to resist strong earthquakes with minimum disturbance. After the 1995 Japanese earthquake this type of wall was used to replace damaged walls in Japan. The reconstruction of several railway earth retaining structures in bridges after the 2011 Tohoku earthquake, have also employed the solution of geogrid reinforced soil walls (^{Koseki et al., 2012}).

This paper focuses on the static and seismic performance of a geogrid reinforced soil wall. This case is used as an example of a railway bridge's abutment built with geogrid reinforced soil walls which did not suffer major damage during the 27F earthquake.

Geogrid reinforced soil wall GRSW as bridge abutments

The 27F 2010 earthquake in Chile gave the opportunity to study the performance of this type of solution under a strong seismic event. Segmental block-faced geosynthetic reinforced soil for bridge abutments have previously demonstrated satisfactory performance and very high load carrying capacity in serviceability conditions, i.e. under no strong seismic events and mostly abroad, particularly in the USA (e.g.^{Abu-Hejleh et al., 2000}). This type of wall is easier to build and cheaper than other types of walls such as gravity or reinforced concrete cantilever retaining walls. It has also been recognised that GRSWs can improve bearing capacity when soft soils are encountered. This might even eliminate the option of deep foundations such as piles, which can have the advantage of reducing bridge bumps when entering or leaving a bridge (^{Helwany et al., 2003}). A rigid bridge abutment (reinforced concrete walls) founded on piles can induce differential settlements between the bridge and the approaching embankment causing bridge bumps. However, the use of piles is justified when there are soft soils or when scour can occur.

The GRSW solution represents a soil mass covered with segmental block facing that assist in the retaining structure construction. This facing apart from an ornamental role does not give much structural resistance. Therefore, a GRSW abutment behaves differently than that of a rigid abutment over a rigid foundation. In a GRSW abutment, the whole structure (reinforcement, block facing, fill) acts as one element which support the bridge, i.e. as a big foundation. This big foundation can reduce the large loads imposed by the bridge transferring the same load in a much wider surface, hence diminishing stresses on the foundation soil. It is worth highlighting that there is not only a reduction of stresses transmitted to the subsoil reducing settlements too, but the settlements are share by the whole structure reducing differential settlements (^{Helwany et al., 2003}). This response as one element may explain the favourable seismic response.

Railway bridge Las Gaviotas

The 55° skewed bridge Las Gaviotas was built in 2003. It is located in the Interportuaria motorway joining Talcahuano and Penco and passes above the railway and an unpaved road between Concepción and Penco. Figures 2a and 2b show pictures taken just after the 2010 earthquake of the GRSWs of 44 m long at the base and 8 m high under the bridge.

Figure 2 a) View of the motorway bridge Las Gaviotas over railway and road and b) view of the geogrid reinforced soil wall abutment 

Allowable stress design analysis of the GRSW wall

Static external stability

This project is almost on the coast therefore closer to the subduction trench between the Nazca and Continental plates and around 100 km South from the 2010 earthquake epicentre in the town of Cobquecura. The foundation soil is poor, corresponding mainly to marine and fluvial deposits close to the stream and mouth of the Andalién River. Due to these deposits, piles were needed to increase the support of the bridge in addition to the GRSW. Four piles for each abutment were designed with 1 m diameter and 22.5 m depth. The geogrids were cut to leave room for the piles. Note that only the global seismic stability analysis (presented at the end), justifies the inclusion of piles. The external static stability was evaluated complying with force and moment equilibrium as shown in Figure 3. The following calculation procedure is based mainly on the recommendations of ^{FHWA (2001)} which adopt the allowable stress design ASD. Details of the calculations can be found in ^{González (2015)}.

Figure 3 Static external force diagram of GRSW; e: eccentricity, R: resultant of vertical forces, q: overburden 

An initial value of L = 7 m was adopted for the geogrid length and the wall height H = 8 m. It is worth pointing out that experimental and numerical results have shown that in presence of geogrids the distribution of the active lateral earth pressure reduces and forms an arch shaped distribution between geogrids in comparison with triangular distributions (e.g.^{Jacobs et al., 2016}; ^{Ruiz-Tagle and Villalobos, 2011a}, ^2001b). However, the Rankine theory was adopted for simplicity to calculate the active lateral earth pressure forces F₁ and F₂. For reinforced and backfill soil it was assumed the same angle of internal friction ϕ’ = 37° and the same unit weight γ=19.1kN/m3 . Thus, the resistant and overturning moment respect to O are:

MR=12(V1+qDLL)L=3911kNm/m;MO=13F1H+12F2H=555kNm/m (1)

where V₁ is the weight of the reinforced soil, q_DL is a uniform dead load, F₁ and F₂ are active lateral earth forces. This results in an overturning factor of safety FSO=MR/MO=6.8>2.0 . The sliding force FS=F1+F2=152.6+36.6=189.2kN/m and the resistant force FR=(V1+qDLL)tanϕ=842kN/m lead to a sliding factor of safety FSS=FR/FS=4.5>1.5 .

The bearing capacity factor of safety FSB=qu/σv , assumes a Meyerhof stress distribution σv=R/L' , where L'=L−2e , e=L/2−(MR−MO)/R , and R=V1+V2=1072.6+128.8=1201kN/m is the vertical resultant force when V₂ corresponds to overburden loads such as traffic q_LL = 12 kPa and extra dead load q_DL = 6.4 kPa. Then, the eccentricity e=0.71<1.17(=L/6) . Using Terzaghi's formulation with Vesic’ N_γ factor (66.2 for ϕ’ = 37° and 22.4 for ϕ’ = 30°), base width B = L’ and neglecting depth effects results in qu=0.5L'γNγ=3540kPa and FS_B = 16 for ϕ'=37°>2.5 and q_u = 1198 kPa, FSB=6>2.5 for ϕ’ = 30° (for soft foundation soil).

Seismic external stability

The seismic external stability can be evaluated by means of a pseudo static method as shown schematically in Figure 4. The dynamic active horizontal force imposed by the earthquake P_AE is added to the static horizontal forces due to active lateral earth pressure imposed by the retained soil and overburden. In addition, the reinforced soil mass applies a horizontal inertial force PIR=mAm , where m is the mass of the active part of the reinforced soil section assumed with a base width of 0.5H and Am=(1.45 −A)A is the maximum horizontal acceleration in the GRSW and A is a free field maximum acceleration coefficient which in Concepción is assumed to be equal to 0.4g, value measured in the centre of Concepción in the 2010 earthquake (^{Boroschek et al., 2010}). Therefore, the horizontal seismic coefficient is Am=Kh=0.42 . The vertical seismic coefficient is assumed K_v = 0. P_AE is evaluated using the pseudo static Mononobe-Okabe method, then θ=tan−1[Kh/(1-Kv)]=22.8° and the seismic earth pressure coefficient K_AE = 0.56 and the Coulomb static lateral earth pressure coefficient is K_A = 0.249 which results in ΔKAE=KAE−KA=0.315 and the seismic increment in lateral load is ΔPAE=0.5γH2ΔKAE=193.4kN/m . The 50% of ΔP_AE is then 96.7 kN/m and the inertial force PIR=mAm=(0.5H)HγAm=0.5γH2Am=257.8kN/m , where 0.5H is the assumed base width of the active mass of reinforced soil. The resistance force F_R is the same as in the static analysis, but in the sliding force F_S, the 50% of seismic increment 0.5ΔP_AE and the inertial force P_IR are added to the static lateral earth pressures F₁ and F₂. This results in a seismic factor of safety against sliding FSS=FR/FS=842/543.6=1.55>1.13 . For the overturning stability, the resistance moment M_R is equal to the static case and in the overturning moment ΔP_AE and P_IR are included as follows: MO=F1H/3+(F2+PIR)H/2+0.5ΔPAE 0.6H=2050kNm/m , which results in an overturning factor of safety FSo=MR/MO=3911/2050=1.9>1.5 .

Figure 4 Seismic external force diagram for the GRSW stability 

For the applied stress distribution and seismic bearing capacity calculations, the only difference with the static calculation is the eccentricity e restricted to L/3 rather than L/6. Thus e=MO/R , hence e=2050/1201=1.7m<2.33m , where the base width L'=L−2e=3.6m→σv=R/L'=1201/3.6=334kPa . It is worth mentioning that from theoretical and numerical analyses, it can be found that the coefficients of bearing capacity reduce with the increase of the horizontal seismic coefficient K_h (e.g.^{Soubra, 1999}). However, it was assumed for simplicity that the bearing capacity coefficients do not change for a seismic condition. Hence, qu=0.5L'γNγ=2213kPa and FSB=6.6>1.88 for ϕ’ = 37° and qu=749kPa , FSB=2.2>1.88 for ϕ’ = 30° (for soft foundation soil).

Figures 5a and 5b show the variation of the factor of safety against sliding FSs and overturning FSo with the free field maximum acceleration A and also with the angle of internal friction ϕ’ (the same for reinforced, fill and foundation soil). It can be observed that factors of safety are above 1.0, except for FSs when ϕ'<34° and A>0.4g . Therefore, according to these calculations overturning failure should not occur even for high values of accelerations and low values of angles of friction. However, sliding may occur in case of low angle of friction and high acceleration values.

Figure 5 Variation of the factor of safety versus the acceleration and angle of friction a) against sliding and b) overturning 

LRFD methodologies

The previous analyses were based on the method of allowable stress design ASD, where uncertainty in applied loads and material resistance is incorporated in a factor of safety. Another method of analysis is the load and resistance factor design LRFD, which accounts for uncertainty in resistance and load using pre-established factors. This methodology has been adopted by ^{FHWA (2009)}, where the design consists in applying limit states for different cases of load and resistance combinations under static and seismic conditions. Load combinations include permanent and transient loads using minimum and maximum load factors, where the more critical combinations are selected. The LRFD methodology considers the evaluation of the external and internal stability analysis of MSE walls as in ASD analyses. The British norm BS 8006 (2010) is also based on the limit state philosophy, in particular the ultimate and service limit state, using partial factors. This methodology is very similar to that of the LRFD adopted by ^{FHWA (2009)}, in respect to the increase of loads and reduction of resistance as well as using different load combinations. A comparison of these methods can be found in ^{Galindo (2014)}. The following results based on ^{FHWA (2009)} and BS 8006 (2010) have been carried out using the software ^{Geo5 (2015)}. Figure 6a shows results of the variation of the static factor of safety against sliding versus angle of friction comparing the three design methodologies. ^{FHWA (2001)} corresponds to the ASD design method explained before, ^{FHWA (2009)} is for the LRFD method under the most critical conditions and BS 8006 (2010) applies limit state analysis. It can be observed that although results are different, the trend is similar and factor of safety values are above 1. The same can be observed in Figures 6b and 6c for the static overturning and bearing capacity factors of safety. The lowest values of factor of safety are given by ^{FHWA (2009)}.

Figure 6 Variation of the static factor of safety with the angle of friction for different calculation methodologies, a) against sliding, b) overturning and c) bearing capacity 

The results of seismic factor of safety variation with the angle of friction are shown in Figures 7a, 7b and 7c. In general, it can be noticed that the values of factors of safety diminish, reaching values below 1.0 for sliding and bearing capacity when angles of frictions are below 32°. Although the three methods have different results, they provide almost the same trend and for angles of friction above 35°, they indicate that stability is reached with a factor of safety of at least 1.2.

Figure 7 Variation of the seismic factor of safety with the angle of friction for different calculation methodologies, a) against sliding, b) overturning and c) bearing capacity 

Global stability analysis

The GRSW can be subjected to instability conditions from outside the reinforced structure that can pass through the GRSW. This problem is normally analysed using slope stability analysis tools. Figure 8 shows the results of a global static stability analysis considering the geogrids and soil properties. A Bishop method for the calculation of the sliding factor of safety is adopted, where for the minimum global factor of safety of 1.64 the potential failure surface develops in the wall toe and moves upwards through the reinforcements.

Figure 8 Static global stability analysis with software ^{GGU (2015)}, FS_g = 1.64 

Figure 9 shows a pseudo-static analysis adopting K_h = 0.42, resulting in a factor of safety of 0.97. Since there was no noticeable damage in Las Gaviotas GRSW, let alone failure, a possible reason is that the analysis shown in Figure 9 does not include the piles which may have acted as an extra reinforcement. Other possible reason is that a ground maximum acceleration less than 0.42g occurred in the site. Other reason could be that the shear strength properties of the soil, specially the soil in contact with the geogrids and behind them, may have mobilized friction angle values higher than 37°. This latter explanation has been pointed out before as highly likely related to the favourable performance of GRSW in Japan (^{Tatsuoka et al, 1998}).

Figure 9 Pseudo-static global stability analysis with software ^{GGU (2015)}, FS_G, = 0.97 

Final comments

This work presented a back-calculation of a geogrid reinforced soil wall GRSW designed as abutment for Las Gaviotas Bridge after the occurrence in 2010 of the 8.8 moment magnitude earthquake in Concepción, Chile. This structure did not suffer any noticeable damage during the earthquake. The calculation procedures are mainly based on the allowable stress design ASD approach by ^{FHWA (2001)} recommendations. The results of this re-assessment shows that static and seismic stability comply with external and internal stability. Other calculation procedures were also performed for Las Gaviotas Bridge case such as the load and resistance factor design LRFD adopted by ^{FHWA (2009)} and the limit state method also with load factors and load combinations adopted by BS 8006 (2010). Although, some differences in the results were found compared with those obtained using the ASD approach, in general, they also comply with external and external and static and seismic stability. It was found that instability problems can appear in case of maximum accelerations larger than 0.4g and soil angles of frictions below 34°. A factor of safety below 1.0 was also found in the seismic global stability analysis for a horizontal acceleration of 0.42g and angle of friction of 37°. This situation led to the decision of including piles for the improvement of the abutment and bridge seismic global stability. Further research is needed to include arch effects in the calculation of lateral active earth pressure between geogrids as well as using seismic bearing capacity coefficients. Moreover, it would be important to evaluate displacements numerically and experimentally in field tests or ideally monitoring real GRSWs.