En este artículo describimos cómo estimar el potencial licuable de arenas con algunas técnicas para estimar perfiles de velocidad de onda de corte obtenidos midiendo vibraciones ambientales y a partir de ondas generadas artificialmente. Las mediciones se realizan con facilidad, consumen poco tiempo y además resultan más baratas que otras técnicas. El método pasivo de Análisis de Microtremores (MAM) y el activo de Análisis Multicanal de Ondas Superficiales (MASW) se comenzaron a usar recientemente en estudios de licuación de arenas. En el trabajo se describe un método que se empleó en el Valle de Mexicali para caracterizar el suelo en términos de su velocidad de onda de corte con el fin de evaluar el potencial de licuación. Nuestros resultados demuestran las ventajas del método propuesto.
In this paper we describe how some techniques for estimating shallow shear wave velocity profilesobtainedfrommeasurementsofambient vibrations and from artificially generated waves can be used to assess sand liquefaction potential. The measurements are easy, quick and more economical than most other methods. The passive Microtremor Analysis Method (MAM) and the active Multichannel Analysis of Surface Waves (MASW) have only recently been adopted for liquefaction studies. We propose a method that was applied in the valley of Mexicali to characterize soil in terms of shear wave velocity to assess liquefaction potential; our results display its advantages.
Many authors have described and studied liquefaction of granular soils (Seed et al.1971; Poulos et al., 1985; Ishihara K. 1993). It occurs when vibrations or water pressure within soil cause the solid particles to cease having contact with one another. This condition is generally caused by the passage of seismic waves through loose or very loose saturated sandy soils. The soil behaves temporarily as a liquid and loses its ability to support weight. Sand boils, ground fissures or lateral spreading are typical manifestations of sand liquefaction (Marcuson, 1978).
Shear wave velocity (Vs) has been correlated with cyclic stress ratio to assess soil liquefaction potential. Vs is estimated from cross-hole or down-hole seismic surveys (Stokoe and Narzian, 1985; Tokimatsu et al., 1990; Kanyen et al., 1992; Andrus and Stokoe, 1997; Yu Shizhou, et al., 2008). In this paper we present a method in which shear wave velocity profiles are derived from Microtremor Analysis Method (MAM) and from Multichannel Analysis of Surface Waves (MASW). Combining MAM and MASW allowed us to reach a deeper penetration depth. Specifically, higher frequency waves generated by sledgehammer impacts travel through shallower depths and can be combined with lower frequency data from microtremors that travel through greater depths. The procedure also clarifies modal trends (Park et al., 2007).
We applied a combination of both techniques to a site in the Mexicali Valley, Baja California, in an area of high seismicity and high population density. Sand liquefaction has repeatedly affected Mexicali, the largest city in the region, causing extensive damage there and in towns and villages as well as in canals, roads and other facilities.
Study areaLocationMexicali is a border city that accounts for 18% of the surface of the state of Baja California. It is bounded on the north by the city of Calexico, California, USA. The site we studied is located in the Solidaridad Social Township, 5km south of downtown Mexicali and about 10km south of the border (Figure 1), along a bend in an affluent of the Colorado River.
The Mexicali Valley is within the Colorado River delta. Geologically young sandy sediments are present over the delta region. High groundwater levels and strong ground motions combined to bring about extensive liquefaction in the El Mayor-Cucapah earthquake of April 4, 2010, the largest earthquake to strike this area since 1892. It was possibly larger than the 1940 earthquake (M = 6.9) or any of the early 20th century events in northern Baja California. It had a magnitude 7.2Mw with epicenter on the western margin of the Mexicali Valley where the El Major and Cucapah faults converge, some 40km south of the Mexicali urban area.
Superficial cracks and fractures appeared along the riverbanks (Figure 2). The main fracture was 1726 m long and secondary cracks extended to about 800 m. Severe economic damage occurred to homes, the canal system and roadways. At least 151 homes suffered some degree of damage associated with the earthquake, including fissures and differential settlements (INDIVI, 2010). Earthquake induced liquefaction, lateral spreading, sand boils and flooding occurred extensively across farm lands and along rivers and irrigation canals.
Liquefaction potential: simplified empirical analysis
Three parameters are needed to assess liquefaction potential using the simplified empirical method: a) shear velocity Vs; b) the cyclic stress ratio (CSR) and c) the capacity of the soil to resist liquefaction, expressed in terms of the cyclic resistance ratio (CRR). Shear wave velocity is proportional to soil stiffness and in the simplified method, it must be corrected to account for the effect of overburden stress (Vs1). Our procedure incorporates some updates and improvements to the original simplified method (Youd et al., 2001).
For the calculation of the cyclic stress ratio, τcσv', we use an expression from the original method:
where amax is the maximum horizontal acceleration at the surface of the soil; is the acceleration of gravity; σv and σv′ are the total and effective vertical stresses respectively and rd is the coefficient of reduction of efforts. The following equations may be used to estimate average values of rd (Liao et al., 1988; Robertson and Wride, 1998).
where z is the depth below ground surface (m)
The cyclic resistance ratio, CRR, is used to set apart well-characterized sites where liquefaction occurred from those where it did not. Well-characterized sites are those where the stratigraphy is known and where field penetration resistance is available, commonly, usually from SPT or CPT tests (Figure 3). Andrus and Stokoe (1997, 2000) developed liquefaction resistance criteria from 26 earthquakes and shear wave velocities measured in the field at 70 sites (Figure 4). The curve in that figure was obtained from field observations after earthquakes with M =7.5, from the results of Vs measurements and from estimations of the cyclic stress ratio (equation 1). Their empirical CRR curve in Figure 4 separates the points in the CSR versus Vs1 space where liquefaction did and did not occur.
SPT Clean Sand base curve for magnitude 7.5 earthquakes with data from liquefaction case histories (Seed et al., 1985).
Liquefaction resistance curves by Andrus and Stokoe (2000) for magnitude 7.5 earthquakes and uncemented soils of Holocene age with case history data.
where Vs1 was defined previously; MSF is the magnitude scaling factor for earthquakes with magnitudes different from 7.5Mw; a, b are fitting parameters (a = 0.022, b = 2.8) and Vs1* is a reference shear wave velocity that depends on the amount of fines present in the sand mass:
Vs1*= 200 m/s soils with 35% fines.
Vs1*= 210 m/s soils with 20% fines.
Vs1*= 215 − 220 m/s soils with 5% fines.
The overburden stress correction is
where Vs is the measured shear wave velocity, (m/s); Pa is a reference stress (atmospheric pressure); σv is initial effective overburden stress, (kPa).
The magnitude scale factor MSF is used to translate the CRR vertically depending on the magnitude of the design or expected earthquake, i.e. MSF moves up or down the threshold for the occurrence of liquefaction given by CRR according to the size of the earthquake. It is given by:
where MW is the earthquake moment magnitude.
Field TestsThe field work presented in this paper forms part of geological and geophysical studies commissioned by local authorities after the April 4, 2010 event (Acosta Chang et al., 2010). They obtained thirty seismic profiles from MAM and MASW tests during May and June 2010 at the Solidaridad Social Township. The fieldwork also included four geotechnical soundings to carry out SPT tests down to a depth of 11 m at the sites indicated in Figure 5. We used the seven seismic profiles closest to the SPT tests to compare and correlate the liquefaction potential estimated from both SPT blow counts (N1)60 and shear wave velocity (Vs1). Stratigraphic profiles were made at each SPT site to define the local geotechnical conditions and as a support for the geophysical interpretation. These field studies did not address the issue of assessing liquefaction potential.
MASW and MAM surveys were performed deploying twenty-four 2.5Hz geophones along a linear array. Receivers were separated 1.5 m and were all connected to a multi-channel recording device.
The wave fields for MASW surveys were generated by vertical impacts of a 4.5kg sledgehammer on a steel plate coupled to the ground. Sampling rate in the MASW surveys was 0.00125 s and records had a duration of 1 s. Seismic sources (impacts) were located at three positions collinear to the geophone array. The source positions are related to the position of the first geophone. For tests L2T1, L3T7, L5T3 and L6T1, the seismic source was located at the center of the line and the other two sources at both endes with a 1.5 m offset.
Three impacts were applied in succession at each position; records were collected, stacked and stored in a PC. Stacked records were used to achieve a single record associated with each position of the source to minimize the noise- signal ratio. In the case of seismic lines L3T4, L5T1 and L9T2 the spacing between geophones was 2.0 m.
Processing and partial resultsMAM records were processed using Spatial Autocorrelation (SPAC), a well known technique to deduce a phase-velocity dispersion curve from microtremors recorded by a seismic array (Aki, 1957, 1965). The essence of the method is that, having records from seismic stations spaced at a constant distance and forming pairs of stations along different azimuths, it is possible to compute an estimate of the phase velocity of the waves crossing the array, without regard to the direction of propagation of the waves present.
If the duration of the MAM records obtained along a linear array is long enough, the recorded motion can be expected to include waves propagating along many different directions. Under this hypothesis, the equations and results that Aki (1957) obtained using the azimuthal average of the spatial cross- correlation coefficients can be applied (Chavez et al., 2006). Having a linear array is also convenient because it allows for the collection of data using the same setup as in MASW, thus avoiding re-positioning of the geophones, a task that often requires significant additional field effort.
MAM data were acquired along the same linear array as in the MASW tests. The sampling interval was 2ms and the duration of the records was 30 s. At least 30 background noise measurements were made at each seismic profile.
SPAC functions, ρ(r, ω) were defined by Aki (1957) in terms of the spatial autocorrelation of ground motion records separated a distance, r, represented as:
where c(ω) is the phase velocity associated to the frequency ω; J0 is the Bessel function of first class and zero order.
SPAC functions were estimated in this study as the average value of the real part of the coherence function calculated between each pair of records obtained with the same spacing between geophones. Thus, the above process renders a SPAC function for each geophone spacing, 23 separations in this case. As an example we show Figure 6 that displays the real part of coherence function between all possible pairs of geophones in line L5T1, with an array size of 46 m. The separation between each geophone pair is plotted on the y-axis as distance and the SPAC functions on the x-axis.
SPAC functions contain information of seismic surface wave dispersion in which phase velocity can be measured as a function of frequency. The broken line in the figure joins the frequencies, Fpcc, associated to the first zero crossings of each calculated SPAC function. The value of Fpcc decreases as the separation between pairs of stations increases, up to a separation of 25 m, approximately.
Making reference to Figure 6, in the SPAC function associated with the separation of 2 m, one can measure the frequency associated with the first zero crossing, approximately 26Hz. Because the argument of the Bessel function is, a phase velocity for 26Hz is about 136 m/s, and 220 m/s for 3Hz. This exemplifies how a different phase velocity is associated to each frequency.
Records from MAM surveys were transformed into the frequency-phase velocity space to form a dispersion image, using the Park et al., (1999) method. The above process is equivalent to the application of a ‘slant stack’ to the time signal. Dispersion curves from MASW surveys are obtained applying the same procedure except for the fact that they don’t use spatial autocorrelation. The graph in Figure 7 is a typical image that corresponds to line L5T1, with data collected for both MAM and MASW surveys.
The fundamental mode of surface waves for MAM records can be readily identified in Figure 7 in the 2-15Hz frequency range and 6-29Hz for the MASW records. The range of validity for both curves (passive and active) is limited by two straight lines having a constant wave length, 8 and 150 m as seen in Figure 7a. The Rayleigh wave fundamental mode of propagation is identified inside this range as a smooth curve formed by the maximum spectral energy with phase velocity decreasing with frequency (Park et al., 1999).
The dispersion curves from the active and passive methods (MASW and MAM respectively) were combined to obtain a single dispersion curve covering a wider frequency range (2.5 to 29Hz). As seen in Figure 7c, phase velocity reduces sharply in going from 3 to 7Hz and thereafter it reaches a constant value equal to 130 m/s. Both curves have approximately the same shape and actually overlap between 6 and 16Hz.
Dispersion curves (phase velocity- frequency) and the inversion of shear wave velocity (Vs) profiles were obtained using the procedure described in the SeisImager/ SW software manual (Geometrics, 2006). The SeisImager inversion technique is a deterministic method that depends on an initial model in which shear velocity increases with depth and in which the least square inversion is then applied (Xia, 1999b).
The initial shear wave velocity model is generated from the information provided by the phase velocity curve assuming that penetration depth is about one third of the wave length associated to each of the measured phase velocities. The procedure considers n-1 layers with a constant thickness; the nth layer is twice as thick. In our calculations we used seven layers and, starting from the initial model, proceeded on to the nonlinear iterative inversion procedure.
Figure 8 shows the dispersion curves combining the results of MASW and MAM surveys for the Solidaridad Social Township. We estimated shear wave velocity (V) profiles at depths varying from 1.8 up to 30 m (figure 9), approximately. In this specific case the method stops being reliable at depths larger than 30 m.
Results
The graphs in Figure 9 show the shear wave velocity profiles obtained from the MASW and MAM dispersion curves. This information has been summarized in Table 1. Regarding liquefaction potential, there are four significant seismic units:
Unit 1. It goes from about 3.5 to 10 m in depth. Shear wave velocities vary from 125 to about 174 m/s; lowest values were found in L5t1 and L3T4, located close to the location of soundings SPT 3 and SPT 2, respectively (see Figure 5). Shear wave velocities en line L6T1, close to SPT 5, were about 162 m/s. Values in the remaining three lines, L9T2, L3T7 and L5T3 average 170 m/s.
Unit 2. It goes from 10 to 17 m in depth. Shear wave velocities in lines L9T2, L3T7, L5T1 and L6T1 are about 160 m/s and around 185 m/s in lines L5T3 and L2T1 and slightly larger in line L3T4.
Unit 3. Shear wave velocity values in this unit are scattered within the 189 to 241 m/s range, in depths that go from 17 to 26 m.
Unit 4. Shear wave velocity is more widely scattered in this unit, varying from 218 to 312 m/ s at depths that go from 26 m down to the maximum depth monitored with our dispersion curves, 30 m.
The shallowest strata cannot be identified from MAM/MASW measurements, as the dispersion curve cannot be reliably estimated for frequencies above 1.9Hz due to the spatial aliasing limit. As seen in figure 10, the upper most strata are clayey soils reaching depths of as much as 2 m. These clays are not liquefiable; their presence hinders the dissipation of pore pressures and enhances the formation of sand boils when the underlying sandy soils liquefy. Water table was located about 10 m below the surface at sounding SPT1 but is much shallower at the other sites, 3 to 5 m.
Penetration resistance of these sandy soils is seldom larger than 20 blows and applying the simplified method (equations 1 to 3) from the blow counts obtained from soundings SPT 1, SPT 2, SPT 3 and SPT 5, their high potential for liquefying was ratified. In applying equation 1, the value of amax = 0.23g was taken from the maximum ground acceleration recorded at the Tamaulipas station during the El Mayor-Cucapah event. The epicentral distance between our study site and the Taumalipas station is approximately the same for the El Mayor-Cucapah earthquake. The clean sand CRR curve in figure 2 [CRR-(N1)60] applies only for earthquakes with a magnitude equal to 7.5. We used the I.M Idriss (1997) correction factors to scale down the CRR curve to magnitude 7.2 as in the April 4, 2010 earthquake, following the recommendations of the NCEER workshop (Youd, et al., 2001). We also performed analyses assigning a larger amax value (=0.45 g), as recommended in the Civil Engineering Design Manual from the Mexican electricity board (CFE, 2008) and also included a complementary analysis with amax= 0.35g. Figure 11, show that the ground below the water level is potentially liquefiable for the three maximum accelerations used in the al analyses to the maximum depth explored with the SPT soundings.
Liquefaction potential was also assessed from the shear wave velocity profiles shown in Figure 12 and obtained from the MAM and MASW surveys. Maximum ground acceleration values and correction factors to scale down the CRR curve of Figure 4 to a 7.2 magnitude were the same as those used in the SPT analyses.
The stratigraphical interpretation of the seismic profiles can only be done down to the maximum explored depth in the SPT soundings, 11 m, as shown in Figure 10. It is to be expected that deeper strata are also sands or sandy non plastic soils, as can be inferred from the shear wave velocity values obtained form MAM and MASW surveys and from the geological and physiographical conditions at the Solidaridad township (Jaime A., 1980). These sandy soils having shear wave velocities of less than about 200 m/s are also liquefiable, according to our analyses. However, a vast number of past experiences have shown that liquefaction seldom occurs at depths larger than about 20 m (Seed and Idriss, 1971; Ovando and Segovia, 1996; YU S., Tamura M. and Kouichi H., 2008).
Shear velocity profiles obtained from all the MAM and MASW measurements were plotted in a single graph, Figure 13 (see also Table 1). Results show that the lowest shear wave velocities in sandy soils were obtained in lines L3T4 and L5T1, which have the highest risk of liquefaction. Overall, sand strata between depths 5 and 17m are highly prone to liquefy again for earthquakes inducing peak ground accelerations of at least 0.23g and Mw magnitudes of 7.2. Strata between 17 and 25 m may also liquefy but are not as susceptible. Liquefaction potential analyses using SPT blow counts and Vs are equivalent in that both yielded the same results.
Having established CRR, a factor of safety against liquefaction can be determined for each CRR value at any depth, as a function of Vs1.
According to this, liquefaction will occur whenever that factor is less than unity. Making it equal to 1 and substituting values in equations 1 to 6, we estimated the minimum values of shear wave velocity (critical shear wave velocity, Vsc) required to bring about liquefaction, for different peak ground accelerations, amax, assuming the same earthquake magnitude, Mw = 7.2.
The plots of Figure 14, amax, against Vsc, define two trend lines that characterize two zones in the Solidaridad Social Township. The first one represents data obtained from seismic profiles L9T2, L3T7 and L5T3, that are all clustered around the geotechnical sounding SPT 1 in a zone where the water table is rather low (9.6 m). The second trend line includes the rest of the seismic profiles at locations near the standard penetration tests SPT 2, SPT 3 and SPT 5. Water table in these sites is higher, between 3.4 to 4.8 m, since they are closer to the riverbank. Data in the figure demonstrate that, given a value of V sites near the riverbank will liquefy with lower a, values than the sites clustered around SPT-1. This illustrates the manner in which groundwater influences liquefaction susceptibility, it decreases with increasing water table depth, that means under these conditions no liquefaction will take place in the superficial layers as they dry out or become partially saturated. Groundwater level is not stationary; so seasonal variations can alter the vulnerability of sand strata to liquefaction, especially in the uppermost soil layers.
Conclusions
Results presented in this paper showed that the combination of active and passive methods (MAM and MASW) is a viable and low cost procedure to obtain reliable shear wave velocity profiles in urban environments. Our shear wave velocity profiles were derived from 30 m deep seismic lines that were utilized to obtain shear wave velocity profiles form MAM and MASW records and then to evaluate the liquefaction potential of the sandy soils at a site in the Solidaridad Social Township, 5km south of the city of Mexicali.
Liquefaction potential was estimated for the April 4, 2010 earthquake using a well known simplified empirical procedure adapted to be used in terms of shear wave velocity values. In our simplified liquefaction analyses we used an amax, value recorded at a nearby station and the actual Mw magnitude of the 2010 event. We also performed complementary analyses with two other amax values.
Geotechnical soundings were also performed after the El Mayor-Cucapah event and we also used the results of SPT sounding to assess liquefaction potential; we compared these results with those obtained applying the simplified empirical procedure from the seismic profiles we obtained with the MAM/MASW shear wave velocity profiles. Our results showed that both analyses are equivalent.
The procedure we presented and discussed has evident advantages over traditional methods for assessing the potential for sand liquefaction as it does not require geotechnical boreholes (SPT or CPT soundings) nor does it need drilling of boreholes to carry out field tests to obtain shear wave velocity profiles from conventional geophysical profiling methods (up-hole, down-hole or cross-hole tests). The instruments for measuring vibrations in MAM or MASW surveys are standard geophones and analysis of vibration records is relatively simple.
The liquefaction potential analyses presented here pointed out that the soils will liquefy again, should another large earthquake hit the region. Successive liquefaction events in the same site have been known to occur in the past and are not uncommon.
Finally, it must be emphasized that effective characterization of soil deposits may require the use of several seismic profiling methods in order to obtain suitable information to suffi understand relevant subsurface conditions for a particular project or situation.