CENTRIFUGE MODEL TESTS AND NUMERICAL SIMULATIONS OF TIEBACKS FOR STABILIZATION OF SLOPES UNDER
EARTHQUAKE LOADS
Senro Kuraoka1*, Keiichi Ota2, Koji Takeya3, Keiichi Itoh4
ABSTRACT
Tiebacks, or anchors, are one of the widely used countermeasures for stabilization of slopes in Japan. Within the pa st several years, t iebacks h ave be en f ound t o undergo damages w hen subjected t o s trong e arthquakes. H ence, mechanisms of interactions be tween tiebacks a nd slopes under seismic loading need to be studied in order to develop rational design concepts for tiebacks to be applied in earthquake prone areas. In this research, dynamic centrifuge tests of model slopes with miniature tiebacks have been performed to study characteristics of loads acting on tiebacks. The results showed that the amplitudes of the oscillating axial loads on the tieback and the residual loads, after the seismic loading, depend on the angle of the tiebacks with respect to the direction of displacements of the slope near the bearing plates. While the results of centrifuge model tests showed that the amplitudes of oscillating axial loads may be large r elative t o t he pr etension l oads, dynamic numerical s imulations of a la ndslide w ith pre-existing sliding s urface suggest that i ncreases i n the ax ial l oads due t o s liding f ailure, induced during seismic loading, may be far more greater than the amplitude of the oscillating axial loads.
Key Words: Centrifuge model test, Tiebacks, Numerical simulation, Landslides, Earthquakes
INTRODUCTION
Tiebacks, or termed anchors, are one of the widely used countermeasures for stabilization of natural a nd m anmade s lopes i n Japan. Field measurements of ax ial l oads of t iebacks and centrifuge m odel tests of t iebacks have i ndicated t hat the loads on tieback oscillate, during earthquakes, such that t he pe ak load may exceed the pretension l oad (Masuda et al., 1997, Monma et al., 2000, Ota et al., 2008). Furthermore, records of reconnaissance survey after the strong e arthquakes, such as the Noto P eninsula E arthquake in 2007 (Landslide Research Team, 2007 ) and Iwate-Miyagi E arthquake in 2008 ( Japan Society o f C ivil Engineers et al., 2008 ), indicate t hat tiebacks can be damaged when subjected t o s trong earthquakes. Hence, mechanisms of interactions be tween t ieback anchors a nd s lopes unde r seismic loading need to be studied in order to develop rational design concepts for tiebacks to be applied in earthquake prone areas.
There ar e two major parts to t his pa per: the ini tial part describes the r esults of centrifuge
1 Dupity Manager, Research and Develoment Center, Nippon Koei Co.,Ltd. 2304 Inarihara Tukuba city Japan (*Corresponding Author; Tel: +81-29-871 2092 E-ma
2 Researcher, Research and Develoment Center, Nippon Koei Co.,Ltd. 2304 Inarihara Tukuba city Japan 3 Assistant General Manager, SE Co.,LTD.,6-3-1,Nishi-Shinjuku,Shinjuku-ku,Tokyo
4 Assistant Manager, Research and Develoment Center, Nippon Koei Co.,Ltd. 2304 Inarihara Tukuba city Japan
model tests and numerical simulations of homogeneous small slopes with tiebacks; the l ast part describes the results of num erical s imulations of a l andslide, with pr e-existing sliding surface, reinforced with tiebacks. The l ast part of t he pa per is i ntended t o i ndicate the possibility that t he b ehaviors of t iebacks, i nstalled i n l andslides with pr e-existing sliding surface, m ay be s ignificantly different from t he results obtained with the c entrifuge m odel tests of slopes without sliding surface.
The initial part of the paper, as mentioned above, describes the results of the centrifuge model tests that exhibit c dynamic loads on tiebacks installed in slopes subjected to seismic loads. As shown i n F ig. 1, the model s lopes were f ormed i nto a trapezoidal shape inside t he rigid container which is attached to the horizontal shaking table of the centrifuge testing machine.
Two model slopes were made with following differences; (a) angle of the slope face of one model was steeper than the other, (b) tiebacks in these two slopes were installed with different inclination with respect to the base of the slope (Fig. 2). With these two models, geometrical effects of t he s lope and t he i nclination of t iebacks on the axial l oads ha ve be en assessed through analyses of the experimental results and numerical simulations.
It i s not ed that these test conditions ha ve be en originally c onfigured f or purposes different from those described in t his pa per; t hese m odels w ere pr epared f or e xamining t he fundamental e ffects of drainage pipes f or r educing e xcess por e p ressure i n s lopes dur ing seismic loading (Ota et al., 2010), where the strengths of the slope materials and inclinations of slope faces and the tiebacks have been adjusted through trials and errors in order to prevent premature failure before applying the seismic loads. For this reason, some of the conditions such as the inclinations of the tiebacks and soil properties are not based on rigorous basis and also do not r epresent c onditions of s pecific s ites. The i ntention of t his pa per h as be en t o extract and analyze behaviors t hat a ppear t o e xhibit e ffects of geometric c onditions on the interaction between the tiebacks and slopes.
The la st pa rt of the pa per de scribes the r esults of num erical s imulations of a 100 m l ong landslide reinforced with tiebacks. The landslide mass consists of weathered sandstone and shale with pre-existing sliding surface. A sliding surface was modeled along the boundary of the l andslide m ass a nd the be drock. While the mechanical pr operties a nd the g eometrical conditions of the landslide mass are different from those of the models of the centrifuge tests, the simulated results of the landslide with tiebacks ar e p resented in o rder t o hi ghlight the possibility that the behaviors of tiebacks, installed in landslides with sliding surface, may be significantly different from those without sliding surfaces.
Fig. 1 Centrifuge testing machine and the model slope
Shaking table
Model slope
300 mm
In summary, the objectives of this paper are: (a) to assess the geometrical effects of the slope and the inclination of tiebacks on the axial loads of tieback during and after seismic loading;
(b) to predict potential behaviors of tiebacks installed in landslides with pre-existing sliding surfaces.
EXPERIMENTAL SET UP AND PROCEDURES OF CENTRIFUGE MODEL TESTS Two t ypes o f slope models, ha ving the s ame he ight o f 300 m m, are shown i n Fig. 2. The model with slope f ace a ngle of 34 °is referred to as “ gentle s lope” while the other w ill b e referred to as “steep slope” for citing purpose in this paper. The angles between the axis of the tieback and the steel base were also different: the angle in the case of gentle slope was 32°
whereas the angle was 50°in the other case. As mentioned in the introduction, these geometric conditions were ar bitrary s elected through t rials a nd e rrors i n or der t o prevent pr emature failure of the slops before application of seismic loads.
The model slopes were made with Toyoura Standard Sand (standard silica sand) and kaolin clay with a mixing ratio of 4 to 1. The sloped was formed by compacting the soil, layer by layer, while cables of the model tiebacks, inserted within greased plastic tubes, were in place during the compaction process. The strength of the soil was measured by triaxial tests (CU) and the mechanical properties of the soil are shown in Table 1.
Four m odel tiebacks, made of f lexible s teel w ires, were i nstalled in the mode l s lope with spacing of 75 m m. The bottom end of the cable was fixed to the base plate while the upper end was attached to a bearing plate, or anchor plate, that applies loads to the slope surface.
The loads on t he model tiebacks were measured with load cells. The horizontal and vertical displacements at the upper ed ge ( shoulder) of the slope were m easured b y laser sensors.
Although additional laser sensors were target towards one the anchor plates, results did not show significant trends due to noise in the measuring system.
.
Fig. 2 Two models used for the experiments: Models with gentle slope (upper left) and steep slope (upper right) Anchor plate
(Bearing plate)
Head of tieback for applying pretension
Gentle slope model Steep slope model
Targets for laser displacement sensor Targets for laser displacement sensor
Load cell
Apparent diameter of tieback: 0.16 mm Net cross section area of tieback: 0.985 mm2
Table 1 Properties of soil
Parameter Value
Unit weight (γx ) 20.1 kN/m3 Optimum moisture content(wopt ) 11.7 %
Cohesion (c’ ) 2.01 kN/m2 Internal friction angle (φ’ ) 34.1°
The procedure for centrifuge model tests is shown in Fig. 3. All the seismic loadings of the slope models were performed under constant centrifuge force of 40 g such that the height of the slope model is equivalent to 12 m in prototype scale.
Initial pr e-tension loads of t he t iebacks w ere different i n t he ge ntle and s teep s lopes.
Approximately 100 N (160 kN i n pr ototype s cale) a nd 1 80 N (290 kN in pr ototype s cale) were applied to the tiebacks of the gentle and steep model slopes, respectively. However, the effects of difference in the pretension on the variation of loads relative to the initial loads of the tiebacks are considered to be small compared to the geometrical effects. This is because the slopes did not show significant permanent deformation with the acceleration amplitude, 200 g , applied i n t he t ests s uch t hat t he r einforcing effects of pr etension do not a ffect t he discussion on the geometrical effects of inclination of tiebacks.
The m odels w ere subjected t o a ce ntrifugal acceleration field of 40 g until the r ate of settlement ha s be come ne gligible. Then centrifugal f orce w as r educed t o 1 g i n or der t o readjust the pre-tension loads. The centrifugal force was brought back to 40 g and the shaking table was excited by a sinusoidal wave with fixed frequency at 1.5 H z, while the amplitude was increased in a stepwise fashion from 100 to 400 gal in increment of 100 gal.
Fig. 3 Procedures of the centrifuge model tests
RESULTS OF CENTRIFUGE MODEL TESTS
All t he di splacements and loads of t he ex perimental results ar e ex pressed in terms of t he prototype scale. As typical examples, the axial loads of the tiebacks installed in the gentle and steep slopes subjected to acceleration amplitude of 200gal are shown in Fig. 4. The peak axial load of the gentle slope is larger than the initial load whereas that of the steep slope is smaller than the initial load as shown in Fig. 4. It is also shown that the amplitude of the axial load of the gentle s lope is la rger t han t hat o f t he s teep slope, w here a mplitude is de fined as t ime average of the half of the maximum minus the minimum loads of each cycle.
The hor izontal di splacements ( Fig. 5) s how little ir recoverable displacement, implying th at the slope is elastically vibrating in the horizontal direction. The vertical displacements, on the other hand, indicate settlement.
Step 1: Apply pre-tension to tiebacks before application of centrifugal force
Step 2: Apply centrifugal force (40 g) until the settlement rate of the model slope has become negligible Step 3: Reduce the centrifugal force to 1 g and re-adjust the pre-tension of tiebacks
Step 4: Bring back the centrifugal force to 40 g again
Step 5: Apply seismic loads while incrementing the amplitudes in a stepwise fashion from 100 to 400gal
Fig. 4 Axial loads of tieback obtained at 200 gal: Results of the gentle slope (a) and the steep slope (b)
The same trend is obtained from tests with different acceleration amplitudes as shown in Fig.
6 (a). The difference in the amplitudes of axial loads between the gentle and steep slopes may be attributed to the direction of the cable with respect to the horizontal displacements, since it is implied that the oscillating axial loads are closely related to the horizontal displacements rather than the vertical displacements which show settlement. It can be qualitatively explained that the amplitude of th e a xial loa ds w ill be la rger when the direction of the c able a xis is closer t o t he m ajor c omponent of t he os cillating di splacements a s illustrated in Fig. 6 ( b).
Further discussion on t he mechanisms that lead to the differences in the amplitude of ax ial loads between the gentle and steep slopes i s provided in t he next s ection, w here results of numerical simulations of models with tiebacks are presented.
Fig. 5 Horitaontal ( a) a nd v ertical d isplacements (b) of upper e dge o f t he gentle s lope m odel obatined at acceleration amplitude of 200 gal
Fig. 6 Amplitudes of axial loads of the gentle and steep slope models (a ), illustration of direction of the cables with respect to the horizontal displacement component (b)
0 20 40 60 80 100 120 140 160
0 100 200 300 400 500
Amplitude of acceleration (gal)
Amplitude of axial force (kN)
Gentle slope Steep slope Amplitude of
axial load
Gentle slope model
Steep slope model Tieback
Tieback
Steel base
Steel base 50°
Horizontal displacement 32°
Horizontal displacement
(a)
(b)
-50 -25 0 25 50
0 2 4 6 8 10 12 14 16 18 20
Time [sec]
Horizontal displacement [mm]
200 gal Gentle slope
↓Towards the toe of the slope
-50 -25 0 25 50
0 2 4 6 8 10 12 14 16 18 20
Time [sec]
Vertical displacement [mm]
200 gal Gentle slope
↑Settlement
(a) (b)
Vertical displacement
Horizontal displacement 100
120 140 160 180 200
0 2 4 6 8 10 12 14 16 18 20
Time [sec]
Axial load [kN] 200 gal
200 220 240 260 280 300
0 2 4 6 8 10 12 14 16 18 20
Time [sec]
Axial load [kN]
200gal
(a) (b)
Residual load Residual load
The residual loads of the tiebacks are defined as the remaining axial load after the seismic loading as i ndicated in Fig. 4. The r esidual l oads of steep slope m odel t end t o decrease as acceleration amplitude of the seismic wave increases as shown in Fig. 7, whereas opsite trend is found with the gentle slope model. This trend may be attributed to the direction of the cable with respect to the irrecoverable ve rtical di splacements, or s ettlements. The ax ial l oad of tieback of the steep slope is more likely to decrease than in the case with gentle slope, since the direction of the cable in the steep slope is closer to the direction of the settlement than in the case with the gentle slope as illustrated in Fig. 7.
Fig. 7 Residual loads of the gentle and steep slope models (left ), ill ustration of direction of the cables with respect to the settelment (right)
NUMERICAL SIMULATION OF CENTRIFUGE MODEL TESTS
Finite e lement analysis of t he gentle s lope m odel, us ed i n t he c entrifuge m odel t ests, w as performed i n or der t o examine t he r elationship be tween t he di rection of t he c able of t he tieback and the axial loads of the tiebacks. Three dimensional FE mesh, shown in Fig. 8, was generated such that the width of the model is equal to the interval, 3 m, of the four tiebacks in the prototype scale. The soil was modeled with Ramberg-Osgood model, since the stress-stain curves obtain from the cyclic deformation tests of the soil used in the centrifuge tests show that t he s ecant s hear m odulus i s de pendent on confining s tresses. The parameters for t he model are given in Table 2.
Table 2 Parameters f or t he soil model
Parameter value
Unit weight, γ 20.1 kN/m3
Poisson’s ratio、ν 0.45
Initial shear modulus, Go 83,500 kN/m2
Reference strain, γ 3.19×10-5 Maximum damping ratio, hmax 0.22
Fig. 8 Finite element mesh of the gentle slope model
The measured and simulated axial loads, horizontal displacements, and vertical displacements at acceleration amplitude of 200 gal are given in Figures 9 t hrough 11. Differences between
0 50 100 150 200 250 300 350
Before excitation
200 300
Amplitude of acceleration [gal]
Residual load [kN]
Steep slope Gentle slope
Gentle slope
Steep slope
Tieback
Tieback Steel base
Steel base 58°
Settlement Settlement
40°
Location of displacements shown in Figures 10 to 12
12 m
the measured and simulated results are noted: Fig. 9 s hows that the amplitude of simulated axial loads is two times larger than that of the measured axial loads. The amplitude of t he simulated horizontal displacements is close to that of the measured displacement as shown in Fig. 10. H owever, t he s imulated hor izontal displacements i ndicate i ncreasing t rend of irrecoverable component, w hereas s uch t rend i s not f ound w ith t he m easured ho rizontal displacements. The trend of settelment, on the other hand, is consistent between the measured and simulated results (Fig. 11). No attempt was made to improve the agreement between the measured and s imulated be haviors, s ince the a mplitude of the hor izontal di splamcent is reasonably cl ose be tween the m easrued and simulated results s uch that ef fects of t he inclination of the cable can be examined, using this finite element model.
-150 -100 -50 0 50 100
0 2 4 6 8 10 12
Time [sec]
Axial load [KN]
Experiment Simulation
Fig. 9 Measured and simulated axial loads of tiebacks during seismic loading
-0.035 -0.030 -0.025 -0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020
0 2 4 6 8 10 12
Time [sec]
Horizontal displacements [m
Experiment Simulation
Fig. 10 Measured and simulated horizontal displacements at the upper edge of the slope
-0.025 -0.020 -0.015 -0.010 -0.005 0.000 0.005
0 2 4 6 8 10 12
Time [sec]
Vertical displacements [m
Experiment Simulation
↑隆起
↓沈下
Fig. 11 Measured and simulated vertical displacements at the upper edge of the slope
Addtional simulation was performed with the same gentle slope model, while chaging the axis of t he tieback such that it is perpendicular t o the s lope face. The results shown i n Fig. 12, substantiate the previous statement that the amplitude of the axial loads tend to be larger when the direction of the cable axis is closer to the direction of major component of the oscillating displacements.
-100 -50 0 50 100
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Time(sec)
Axial load (kN)
Angle with surface 90°
Angle with surface 114°
-3.5E-02 -3.0E-02 -2.5E-02 -2.0E-02 -1.5E-02 -1.0E-02 -5.0E-03 0.0E+00 5.0E-03 1.0E-02
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Time (sec)
Horizontal displacement (m) Angle with surface 90°
Angle with surface 114°
Fig. 12 Simulated axial loads (left) and horizontal displadcements at the shoulder of the slope (right) of gentle slope with different inclination of tiebacks
NUMERICAL SIMULATION OF A LANDSLIDE WITH SLIDING SURFACE
Numerical simualtions were performed in order to demonstrate the possiblity that the loads of tiebakcs, installed in landslides with pre-exsiting sliding surface, may show trends different from t hose s hown b y the c entrifuge m odel t ests. The l andslide consists of w eathered sandstone and there are six tiebacks per unit width of 3.5 m as shown in Fig. 13. The landslide and the bedrock are modeled as elastic materials with the properties shown in Table 3. The sliding surface, with the parameters given in Table 4, is modeled with normal and tangential springs, while shear failure is governed by the Mohr-Coulomb criterion. The groundwater was assumed to rise 1 m durig seismic loading such that the pore pressure on t he sliding surface was increased by an amount equibvalent to a pressure head of 1 m.
The seismic wave for this simulation was selected from the conventional wave data used for earthquake resistance deisgn in Japan. The acceleration data of Hyogo-ken Nanbu earthquake measured at t he K obe Marine O bservatory, ha ving pe ak a cceleration near 800 gal, was applied in the simulation.
Two cases of s imulations w ere p erformed: i n one cas e t he sliding s urface was m odeled to permit sliding; in the other case, the strengths of the sliding surface were set to high values such that sliding does not occur under strong seismic loading. The latter case will be referred to as the model without silding surface.
Fig. 13 Landslide model with sliding surface for dynamic numarical simulation
Bedrock
80 m Groundwater level
Tiebacks Sliding surface
-10.0 -5.0 0.0 5.0 10.0
0 5 10 15 20 25 30
Time (sec)
Acceleration m/sec2
Kobe Marine Observatory
Input Bed rock
Groundwater level
Free filed boundary
Free filed boundary
Table 3 Mechanical properties of the landslide and the bedrock Names of layers Elastic modulus, E
(kN/m2) Poisson’s ration, ν Unit weight γ (kN/m3)
Surficial Layer 5.8×104 0.4 18
Main body of the
landslide 7.2×105 0.4 18
Bedrock 4.0×107 0.3 23
Table 4 Mechanical properties of the sliding surface Cohesion, c
(kN/m2) Angle of internal friction, φ (degrees)
Normal stiffness, Kn
(kN/m3)
Shear stiffness, Ks
(kN/m3)
25.0 33.0 3.1×105 1.0×105
Responses of the axial loads of the tieback, nearest to the toe of the landslide, and the horizontal displacements at the center of gravity of the landslide are shown in Fig. 14 and Fig.
15, respectively. Comparison of the axial loads and the horizontal displcaments show that the behaviors of axial loads are closely related to those of the horzontal displacments. A distinct difference in the responses of axial loads are found between the case with and without the sliding surface; the axial loads in the case with the sliding surface increased in a monotonic fashion with minor vibration mode, whereas the axial loads of the case without the sliding surface only show oscillating behavior. Morevoer, the peak axial load of the case with sliding surface is much larger than the peak axial load of the case without sliding surface.
The results obtained from these simulations imply that increases in the axial loads due to sliding failure may be far more greater than the amplitude of the oscillaing axial loads such as those observed through the centrifuge model tests described in this paper.
Fig. 14 Axial loads of tiebacks during seismic loading: (a)with and without the sliding surface, (b) enlarged plot of axial loads in the case without sliding surface
Fig. 15 Horizontal displacements at the center of gravity of the landslide: (a)with and without the sliding surface, (b) enlarged plot of displacements in the case without sliding surface
300 320 340 360 380 400
0 5 10 15 20 25 30 35 40
Time (sec)
Axial load (kN)
Measured axial load
300 400 500 600 700 800 900 1000 1100
0 5 10 15 20 25 30 35 40
Time (sec)
Axial load (kN)
Sliding plane No sliding plane Measured axial load
(a) (b)
-0.20 -0.18 -0.16 -0.14 -0.12 -0.10 -0.08 -0.06 -0.04 -0.02 0.00
0 5 10 15 20 25 30 35 40
Time (sec）
Hirizontal displacement (m)
Cenetr of gravity
-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
Time (sec）
Horizontal displacement (m)
Cenetr of gravity
(a) (b)
CONCLUSIONS
The results of centrifuge model tests and numerical simulations of the homogeneous slopes without sliding surface imply that the angle of the tieback with respect to the direction of the displacement near the bearing plate is one of the influential factors that affect the axial loads.
For ex ample, the amplitudes of the a xial loa ds may tend to be s mall if the cabl e i s perpendicular to the direction of the displacements of the surface near the bearing plate.
The results of centrifuge model tests also indicated that residual loads of the tiebacks, after the seismic loading, may become larger or smaller than the pretension loads, depending on t he angle of inclination of the tiebacks with respect to the displacements of the slope face. The trends of residual loads and the amplitude of the axial loads indicate that the orientation of the cable may have significant effects on the axial loads and deformation of the slopes such that careful consideration may be needed when designing the orientations of the tiebacks.
Centrifuge model tests of the homogeneous slopes without sliding surface indicated that peak load o f the tieback, dur ing s eismic lo ading, can be come higher t han t he pr etension l oad.
However, numerical simulations of a landslide with pre-existing sliding surface suggest that the axial loads may monotonically increase with relatively small oscillation, if the strength of the sliding surface is low such that the landslide mass moves along the sliding surface. The results obt ained from the s imulations a lso implied that inc reases in the a xial loa ds due to sliding failure may be far more greater than the amplitude of the oscillaing axial loads such as those observed t hrough the centrifuge m odel t ests de scribed i n t his pa per. It is, therefore, implied that mode of the displacements, during earthquake, is one of the important factors that need to be properly estimated for tiebacks to be applied in earthquake prone areas.
REFERENCES
Japan S ociety of C ivil E ngineers, Japanese G eotechnical S ociety, Japan Association for Earthquake E ngineering, a nd The J apan Landslide S ociety (2008). “Report on the Iwate-Miyagi N airiku E arthquake i n 2008 ,” Home page of Japan Society of Civil Engineers.(in Japanese)
Landslide R esearch T eam, E rosion a nd S ediment C ontrol R esearch G roup, P ublic W orks Research Institute (2007). “ 2007 Noto Peninsula earthquake,”Home page of Landslide Research Team, Erosion and Sediment Control Research Group, P ublic W orks Research Institute.
Masuda, T., Jujii N., Yamada H., and Okazaki K. (1997). “ The Stability Analisis of the Walls with the Anchor on the Earthquake,” Proceedings of the Annual Conference of the Japan Society of Civil Engineers, Vol.52, pp.396-397.(in Japanese)
Monma, K ., C hida, Y ., a nd K ojima, S . (2000). “Report on t he the I wate-Miyagi N airiku Earthquake in 2008,”.Civil Engineering Journal, 42-9, pp.58-61. (in Japanese)
Ota, K., Ito, K., Kuraoka, S., and Takeya, K. (2008). “Centrifuge Model Tests of Slopes with Acnhors Subjected to Seismic Loadings,” Proceedings of the Annual Conference of the Japan Society of Civil Engineers, Vol.52, pp.396-397.(in Japanese)
Ota, K., Ito, K., Kuraoka, S., and Takeya, K. (2010). “ Centrifuge Model Tests of Tieback Anchors and Drainage Pipes for Stabilization of Slopes under Eearthquake Loads,” to be publised in the Proceeding of Fifth International Conference on Recent Advances in Geotechncal Earthquake Engineering and Soil Dynamics, May2010.
