Laboratory testing procedure to assess post-liquefaction deformation potential

Laboratory testing procedure to assess post-liquefaction deformation potential

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Laboratory testing procedure to assess post-liquefaction deformation potential Jongkwan Kim ⇑, Tadashi Kawai, Motoki Kazama Department of Civil and Environmental Engineering, Graduate School of Engineering, Tohoku University, Aramaki 6-6-06, Aoba-ku, Sendai, Japan Received 30 November 2015; received in revised form 1 June 2017; accepted 4 July 2017 Available online 10 November 2017

Abstract Buildings and infrastructure suffer extensive damage due to liquefaction during strong earthquakes. The FL method has long been considered adequate for evaluating the likelihood of liquefaction, and is widely used. Due to the high frequency of large earthquakes, generally referred to as level 2 earthquakes, the necessity of multi-level assessments has been acutely felt in Japan. This requires the ductility nature of liquefied ground to be assessed. Because these earthquakes do not always occur with the motion level and waveform used in design, new assessment methods are required which take some deviation into account. Another point of consideration in developing a new method is that high quality site investigations are often either not possible or practical in the initial stage of design. Because the site investigation methods should differ depending on the site selection and the precise design of important structures, there is a clear demand for assessment methods with the flexibility to meet the particular objectives of each case. The new laboratory testing procedure proposed in this paper aims to classify soils according to their likelihood to undergo liquefaction in the event of an earthquake. With the proposed procedure, it is possible to classify soils as either ‘clearly safe’ or ‘likely to result in significant damage if liquefied’ by testing a small number of specimens. It should be noted that this test is not designed to provide for a highly accurate prediction of liquefaction or the extent of post-liquefaction deformation. Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BYNC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Keywords: Liquefaction; Laboratory test; Undrained cyclic loading; Post-liquefaction deformation

1. Introduction After the Niigata and Alaska earthquakes of 1964, reports of liquefaction damage were reported after earthquakes. The Christchurch and Tohoku (off the Pacific Coast) earthquakes of 2011 resulted in widespread liquefaction damage that has been extensively reported. Besides the damage sustained by buildings and infrastructure due to tilting and settlement (Kazama et al., 2012; Yamaguchi et al., 2012; Cubrinovski et al., 2012), the widespread occurrence of sand boiling obstructed restoration work after these earthquakes. Peer review under responsibility of The Japanese Geotechnical Society. ⇑ Corresponding author. E-mail address: [email protected] (J. Kim).

To mitigate such post-liquefaction damage, a number of tests and assessment methods have been proposed based on the results of studies conducted in the aftermath of these large earthquakes. Methods employing the stress ratio as an index (Seed and Idriss, 1971; Arulmoki et al., 1985; Iwasaki et al., 1984) for inferring resistance against liquefaction have been widely employed to determine whether liquefaction will occur under predetermined design earthquake motion. In these tests, the stress ratio is determined from an undrained constant stress amplitude cyclic shear test when liquefaction takes place at a fixed number of cycles, generally 15 or 20. In Japan, it is considered necessary to consider either level 1 or level 2 design earthquake motions in earthquake resistant design, depending on the location. The stress ratio corresponding to each design earthquake motion as suggested by design standards

https://doi.org/10.1016/j.sandf.2017.10.001 0038-0806/Ó 2017 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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(Japan Road Association, 2012; Architectural Institute of Japan, 2001) has been utilized. The likelihood of liquefaction is determined by comparing the stress ratios corresponding to liquefaction resistance and design earthquake motion in a test generally referred to as the FL method. In another method prescribed in the standards of The Overseas Coastal Area Development Institute of Japan (2009), equivalent acceleration and N-values are employed instead of the stress ratios, but the concept of comparing external loading and the resistance of ground is identical to the FL method. Both of these methods can be considered adequate in terms of their ability to assess the occurrence of liquefaction against the supposed earthquake motions. However, because of the increasing frequency of large earthquakes, regarded as level 2 earthquakes, and the uncertainty in setting design earthquake motion, demands for a more robust design have been made for an assessment method which considers not only the likelihood of liquefaction but also the extent of postliquefaction deformation. Besides these two considerations, the 2011 off the Pacific Coast of Tohoku Earthquake suggests it is also necessary to take the earthquake duration into consideration. In research on post-liquefaction deformation, volumetric strain has been the main focus of study. Lee and Albaisa (1974), Yoshimi et al. (1975), Tatsuoka et al. (1987), Nagase and Ishihara (1988) reviewed the residual volumetric strain generated after liquefaction by applying drainage after cyclic loading. On the basis of these studies, simple evaluation methods have been suggested for determining the extent of post-liquefaction settlement. Ishihara and Yoshimine (1992) established a family of curves showing volumetric strain correlated with density as well as a safety factor against liquefaction, and outlined a methodology for predicting post-liquefaction settlement. Tsukamoto et al. (2004) inferred the relationship between the factor of safety and residual volumetric strain for silty sand, using a large triaxial test apparatus and some of the acceleration time histories captured in the 1995 Kobe earthquake. In prior studies, good correlation was found between maximum shear strain during cyclic loading and liquefactioninduced settlement. In another study, Sento et al. (2004) reported that accumulated shear strain is a better indicator of liquefaction-induced settlement than maximum shear strain, and proposed an idealized relationship between post-liquefaction volume change and effective stress. Unno et al. (2006) and Unno and Tani (2008) also demonstrated that under the same loading history (i.e., of accumulated shear strain), the residual volumetric strain is the same regardless of the drainage condition. The occurrence of flow failure (including lateral flow) after liquefaction is an important criterion for classifying damage configuration. When drastic shear strain develops, especially on inclined ground, catastrophic flow failures can occur. Extensive research has been conducted on this flow after liquefaction. Yasuda et al. (1999) applied a monotonic shear loading to a liquefied specimen and

confirmed that there are two regions: a region where no shear stress is recovered with shearing because of the low rigidity of the soil, and a rigidity recovery region, where the rigidity of the soil is restored with shear loading. Shamoto et al. (1997) showed that shear strain is composed of two different components, i.e. a shear strain component depending on the change in effective stress, and a shear strain component independent of effective stress. The constitutive model they proposed for the evaluation large post-liquefaction shear deformation was validated by comparing their results with actual case studies. While many studies on post-liquefaction deformation have been conducted, the focus of most of the research has been either on shear strain or volumetric strain. The various methods developed for use to determine the likelihood of liquefaction, the post-liquefaction shear strain, and the post-liquefaction volumetric strain are adequate for their stated purposes. After the Kobe earthquake in 1995, and because of the higher frequency of large ‘‘level 2” earthquakes and consequent necessity for multi-level assessment, demands for a new technique to evaluate the ductility nature of liquefied ground have been made. The uncertainty in the design earthquake motion also has indicated the importance of taking deviation into account in earthquake resistant design. Since high quality site investigations in the initial stage of design are not possible and are frequently cost-prohibitive, a simple method capable of determining whether or not large amounts of damage are likely to occur in the event of an earthquake are required. In addition, since the loading history, the irregularity of earthquake waveforms, and the boundary conditions also need to be considered when making precise estimations of post-liquefaction deformation, a numerical analysis is required and a constitutive model needs to be developed. In this paper, a simple laboratory testing procedure for the assessment of the likelihood of post-liquefaction deformation is proposed. The procedure involves four consecutive tests which are carried out in the laboratory; a constant stress amplitude cyclic test, a constant strain amplitude cyclic test, a monotonic shear test, and a drainage test. The main focus of the procedure is to classify soils specimens as either likely to remain safe or likely to result in large damage if liquefied. The procedure also has potential to provide the data for parameter setting in a numerical analysis and in the development of constitutive model. 2. Cyclic shear testing procedure 2.1. The concept of the test The concept and procedure of the test method proposed in this study are shown in Fig. 1. The procedure comprises the following steps (STEP 1 to 4): constant stress amplitude cyclic shear, constant strain amplitude cyclic shear, monotonic shear, and drainage. STEP 1 is almost similar to conventional liquefaction strength test. In this step, whether liquefaction occurs against a certain stress ratio

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Constant stress amplitude cyclic shear

Test termination after drainage

Strain convergence Conventional liquefaction judgment

Constant strain amplitude cyclic shear

Stress-strain loop stabilization Considering hysteresis such as duration and the number of cycles

Monotonic shear

Judgment of flow potential

Shear stress unloading and drainage

Test termination Fig. 1. Test procedure and method.

is evaluated, and confirmation of definitely safe specimen is conducted. Additional excitation on specimen can be performed to consider the accumulation of damage in STEP 2. STEP 3 evaluates the post-liquefaction damage level roughly. In the step, a specimen having a high potential to induce large damage is classified. Shear stress is unloaded to zero and volumetric strain is measured in STEP 4. Parameters for each step, such as stress ratio (STEP 1) and the number of cycles (STEP 1 and 2), can be established by the user in accordance with the intended purpose. The proposed testing procedure may be utilized to establish the parameters for FEM numerical analysis, even though a constitutive model by which all procedures are reproduced is necessary. The details of the test procedure are explained below. A schematic of the test procedure is provided in Fig. 2.

Fig. 2. Illustration of each step.

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2.1.1. Constant stress amplitude cyclic shear (STEP 1) The constant stress amplitude cyclic shear is similar to the test method for determining the resistance to liquefaction. In this step, the specimen is subjected to a certain stress ratio corresponding to the design earthquake motion. Excess pore water pressure and strain increase in most fully saturated soils when subjected to cyclic loading. However, in the case of dense soil and clay, a small increase in the excess pore water pressure and strain result in the convergence of the shear stress-strain loop even as the cyclic loading is continued. Since the soil is regarded as a non-liquefiable material, it is considered likely to be safe under that stress ratio, and drainage is performed. The same conclusion is drawn when the strain does not reach the strain level employed as a liquefaction criterion until a certain number of cycles is accomplished. The stress ratio, the number of cycles, and the strain level in this step are flexible parameters which can be established by the users depending on their specific purpose for carrying out the test. Because of the large deformation in the shape of the specimen which takes place during the conventional liquefaction test, it is difficult to examine the post-liquefaction behavior. This implies that the strain level in STEP 1 should be in the range where the influence on the shape of the specimen is small. The liquefaction potential may be roughly judged by counting the number of cycles until a certain strain level is reached. However, it should be noted that the number of cycles does not indicate liquefaction resistance. The focus of STEP 1 is only to determine whether a given material is safe at a certain stress ratio. 2.1.2. Constant strain amplitude cyclic shear (STEP 2) In this period of heightened seismic activity, the large number of strong earthquakes which have lasted for lengthy periods of time has made it clear that the duration of the earthquake on post-liquefaction damage is also a matter of concern. The 2011 earthquake off the Pacific Coast of Tohoku was one such earthquake, lasting for over three minutes. The purpose of STEP 2 is to apply an additional cyclic loading to the specimens considered prone to liquefaction so that the duration of the earthquake can be taken into account. The number of cycles can be decided by the users according to the design earthquake motion and their purpose. STEP 2 is terminated when the predetermined number of cycles is accomplished. Since postliquefaction deformation tends to be strongly dependent on the loading history during cyclic loading, another method that applies additional cyclic loading until the stress-strain loop passes through an identical trace, namely the state of their apparent lower limit of shear modulus, can be utilized. Despite the variations in the loading history required until the state of apparent lower limit of stiffness is reached, largely due to the nature of the material and its density, it is possible to investigate and compare the postliquefaction deformation potential for specimens whose shear modulus is at its apparent lower limit.

2.1.3. Undrained monotonic shear test (STEP 3) STEP 3 is an undrained monotonic shear test, carried out to determine whether substantially loose ground is likely to spread laterally even if the ground is only slightly inclined, in the event that the ground liquefies. Since the recovery of the shear modulus, which is attributed to the dilatancy of soil, is not expected when lateral flow occurs on even slightly inclined ground, the potential for postliquefaction damage is assessed based on the recovery of shear modulus. The dilation characteristics of soil after liquefaction can be examined on the basis of their postliquefaction monotonic behavior. While dilative materials recover strength easily when undrained monotonic shear loading is applied, quite a large shear strain is required in the case of non-dilative materials before their strength is recovered. The risk that flow-like damage will occur in materials which exhibit dilative behavior is regarded to be low. On the contrary, that risk in non-dilative materials is considered to be quite high. Damage classification can also be performed by set criterion values of stress and strain. For shear stress, in addition to a very small gradient ground generally regarded as a target of lateral flow, the shear stress required to stop the deformation on ground of a certain gradient may be utilized as a criterion of shear stress during undrained monotonic loading. When some displacement is allowed, on ground on roads and in parks, for example, the shear strain criterion can be employed. It should be noted that the method is not suitable for use in severe conditions, for example, to determine the settlement of buildings. By employing the shear stress and strain criteria, postliquefaction monotonic behavior can be classified. If shear stress is not recovered until the shear strain criterion is reached, the potential for flow-like deformation for this material can be regarded as high. On the other hand, the potential for the occurrence of flow-like deformation is low when the shear stress is recovered prior to the development of shear strain employed as the criterion. As mentioned above, the purpose of this step is to determine whether ground will definitely incur significant damage. That is, this is a rough estimate, not a precise estimate of ground deformation for materials that were not classified as non liquefiable in STEP 1. 2.1.4. Unloading of shear stress and drainage (STEP 4) To obtain the residual volumetric strain, shear stress is unloaded and drainage is carried out following the application of monotonic loading. The volumetric strain is measured as a reference data in this step, and may be used for parameter setting in a numerical analysis. The test results can also be applied to the charts proposed by Ishihara and Yoshimine (1992) and Sento et al. (2004). 2.2. Damage assessment by the proposed test method A schematic of the liquefaction damage assessment based on the test procedure is shown in Fig. 3. Liquefaction

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damage can be classified into three types: non-liquefaction (N.L.), limited deformation (L.D.), and catastrophic deformation (C.D.).

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The shear stress and strain components can be decided by the user in accordance with their purpose, design earthquake motion, and the boundary condition. The stress

Stress Ratio

(a) γ

criterion_cyclic

SRDesign-2

N.L SRDesign-1

N.L = Non Liquefation L.D = Limited Deformation C.D = Catastrophic Deformation

Shear Strain (%)

Cyclic shear Stress Ratio

(b)

SRDesign-2 N.L

Stress level required to stop the deformation

SRDesign-1

τ

Strain level considered severe damage

γ

criterion_mono

criterion_mono

C.D

Shear Strain (%)

Cyclic shear Monotonic shear

Stress Ratio

(c) Stress level required to stop the deformation

SRDesign-2

τ

Strain level considered severe damage

criterion_mono

N.L

SRDesign-1

Varies with boundary condition

γ

criterion_mono

L.D

Shear Strain (%)

Cyclic shear Monotonic shear

Fig. 3. Schematic diagram of liquefaction assessment.

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ratio (SRdesign = s=r00 ) and the number of cyclic loading steps (N1design ) are defined by the design earthquake motion expected, and the threshold of the strain (ccriterion cyclic ) in the cyclic loading step is defined by considering the allowable displacement in the design structure and the effect on the shape of the specimen for STEP 2. The shear strain gradually increases along with the increase in the excess pore water pressure during cyclic loading. In cases where no increase is noted in either the excess pore water pressure or shear strain, or the increase is almost negligible, the stress-strain hysteresis loop converged during cyclic loading in STEP 1. In other cases, the shear strain does not reach ccriterion cyclic until N1design is applied. Such cases can be classified as non-liquefaction cases against SRdesign (Fig. 3(a)). Specimens which developed ccriterion cyclic are subjected to additional cyclic loading with a constant strain amplitude of ccriterion cyclic . The number of cycles (N2design ) of the constant strain amplitude cyclic shear (STEP 2) is defined considering the expected duration of the design earthquake motion. By applying cyclic loading until the stress-strain hysteresis loop reaches its apparent lower limit of shear modulus regardless of N2design , the potential for postliquefaction deformation can be evaluated and the decrease in the shear modulus corresponding to ccriterion cyclic in this step can be determined additionally. By applying monotonic shear loading to the liquefied specimen, it is possible to determine whether the soil is prone to catastrophic deformation behavior (C.D.). Depending on the change in the shear modulus during monotonic shear, the post-liquefaction behavior is determined. In the event that the low rigidity region (Yasuda et al., 1999) continues until quite a large amount of shear strain develops, lateral flow will occur even in the ground with a slight gradient. The definition of a large strain level is left to the discretion of the user. As mentioned in the concept of the test, postliquefaction behavior can be classified by employing the shear stress and strain criteria. The criteria in monotonic loading are the shear stress (scriterion mono ) required to stop the lateral flow of inclined liquefied ground and the shear strain (ccriterion mono ) which represents allowable displacement in the target ground, respectively. In some conditions, the shear stress does not recover to scriterion mono until ccriterion mono is reached. In such cases, the potential for catastrophic deformation, such as lateral flow, must be regarded as high (Fig. 3(b)). Ground classified as C.D. is regarded as high priority when considering countermeasures against liquefaction. On the other hand, if shear stress reaches scriterion mono before the development of ccriterion mono , no flow-like damage will occur even if some deformation takes place (Fig. 3(c)). In such cases, a numerical analysis is required to consider the boundary conditions and evaluate the precise nature of deformation. Since the initial shear stress imposed by the gradient of the ground affects the cyclic and monotonic behavior of the ground, no precise

assessment of post-liquefaction deformation is intended in this procedure. 3. Examples of the proposed test procedure using a torsional shear test 3.1. Test apparatus The proposed test procedure was performed using a torsional shear test apparatus capable of applying axial stress and shear stress independently (refer Fig. 4). The test apparatus is composed of a loading part and a triaxial cell. Axial and shear stresses are regulated by separate stepping motors controlled by a personal computer, while a pore water pressure controller regulates the back pressure and pore water pressure. Injection and drainage are both controlled by the pore water pressure controller which converts the rotary motion of the motor to the linear motion of a piston, and allows the amount of drainage to be precisely measured. The resolution of shear strain is 2  105 , and the pore water controller can regulate the pore water volume with resolution of 6:3  105 cm3 . 3.2. Test procedure This test used fine silica sand (Iide silica sand #7) and sand-silt mixture prepared by mixing 10% of DL Clay to the fine silica sand. The physical properties of sand and sand-silt mixture are presented in Table 1. To make the specimens as uniform as possible, each specimen, with an outer diameter of 70 mm, an inner diameter of 30 mm, and a height of 100 mm, was divided into 5 layers, and each layer was compacted until the predetermined weight of soil was satisfied. The specimens were pre-consolidated at a pressure of 20 kPa, and CO2 gas was circulated from the bottom to the top, followed by de-aired water, finally applying back pressure to saturate the specimen. The specimens with a B value of over 0.95 were consolidated to 100 kPa. The consolidated specimens were subjected to the two types of cyclic loading, then monotonic loading and drainage, in that sequence. Constant stress amplitude cyclic shear was applied with a shear stress ratio (SRdesign ) of 0.2 and 0.4 assuming design earthquake motions of level 1 and 2, respectively. A stress ratio of 0.2 was set referring to design earthquake motion level 1 described in the Specifications for Highway Bridges (Japan Road association, 2012). A design earthquake motion of level 1 is defined as an earthquake with a peak ground acceleration between 200 Gal and 300 Gal, and a high possibility for in-service inspection. Earthquake motion level 2 is defined as the strongest earthquake that can occur in the future, in a certain place. According to Yamazaki et al. (1998), soil deposits with a Standard Penetration Test (SPT) N-value of over 25 rarely were liquefied, suggesting that the critical equivalent N-value is 25 for a large earthquake with an equivalent acceleration of about

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Fig. 4. Torsional shear apparatus.

Table 1 Properties of soil.

Soil particle density qs ðg=cm3 Þ Maximum void ratio emax Minimum void ratio emin Median grain size D50 (mm) Plasticity index

Iide silica sand 7

DL Clay

Sand with DL Clay 10%

2.69 1.015 0.626 0.28 N.P

2.67 1.67 0.82 0.015 N.P

2.69 0.94 0.5 0.25 N.P

500 Gal. Referring to the above results, a soil deposit with an SPT N-value of 25 can be assumed to be nonliquefiable against a level 2 design earthquake motion. Based on the recommendations for Design of Building Foundations (Architectural Institute of Japan, 2001) and Specifications for Highway Bridges, the stress ratio corresponding to an SPT N-value of 25 was derived to be 0.4. Therefore, a stress ratio of 0.4 was employed as a representative value for a level 2 design earthquake motion. It

should be noted that these stress ratios (SRdesign ) are examples utilized in this study, and are not part of a designated method. Under cyclic loading, saturated specimens develop shear strain with increasing excess pore water pressure. Liquefaction has been assumed to occur when shear strain reaches a specific value during cyclic loading. In this study, liquefaction was assumed to take place at single amplitude of 2.5% (ccriterion cyclic ) in accordance with a previous liquefaction test conducted using a hollow torsional shear system (Yoshimi et al., 1989; Sharafi and Baziar, 2010). In the case of dense soil, effective stress does not necessarily decrease and the stress-strain hysteresis loop converges while the specimen is being subjected to cyclic loading. To classify such cases, namely the non-liquefaction cases, the average effective stress for each cycle was determined and compared with those from the former cycle. When the ratio of the two values is more than 99.5%, the stress-strain loop was considered to have converged, and drainage was carried out.

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In this example, cyclic loading was conducted until a shear strain of 2.5% was reached without employing the N1design . Specimens that experienced liquefaction during the first step were subjected to 2.5% single amplitude cyclic loading during constant strain amplitude cyclic shear in STEP 2. Provided the stress-strain hysteresis loop is identical to what it was during which the cyclic loading, the specimens can be regarded to be at the apparent lower limit of the shear modulus condition, which means no further reduction in the shear modulus occurs on the surface. In such a case, STEP 2 can be terminated at the apparent lower limit of shear modulus to evaluate the post-liquefaction deformation potential. In the past, the post-liquefaction deformation of diverse materials has been examined under a constant loading history. However, the dependence on the loading history makes it difficult to compare their potential for post-liquefaction damage (Sento et al., 2004; Unno et al., 2006). It is possible for all specimens to reach the state of their apparent lower limit of shear modulus regardless of the differences in their loading histories. That is, the potential for post-liquefaction deformation can be examined irrespective of the loading history. The loading history of a specimen until it acquires the apparent lower limit condition varies according to the type of material. Thus, the number of cycles N2design was not employed. The number of cycles until the shear strain reached 2.5% during STEP 1 and the stress-strain hysteresis loop became stable during STEP 2 was counted. It should be noted that the apparent lower limit does not coincide with the genuine lower limit of the shear modulus since additional cyclic loading after the apparent lower limit has been reached can induce larger deformation (this will be discussed in a later section). To judge whether the stress-strain loop was identical, the shear stress was measured at every 0.25% change in shear strain and compared to the value observed during the same shear strain in the prior cycle. When more than 36 of a total of 40 locations measured indicated a difference of less than 0.1 kPa, the stress-strain hysteresis loop was considered identical and the next step was conducted. The last cycle and the one before it during which cyclic loading was terminated according to the criterion mentioned above are shown in Fig. 5. The small difference between the loops smaller than 0.1 kPa was attributed to the noise generated from the measuring. Specimens with a shear modulus which decreased to their apparent lower limits were continuously subjected to monotonic shear unless one of two conditions was satisfied: the development of shear strain beyond 30%, or recovery of a shear stress of 50 kPa before the former condition was reached. Justification for these is described as follows: according to the Recommendations for Design of Building Foundations (Japan), displacement in excess of 40 cm is considered likely to result in tremendous damage. A shear strain of 30% (ccriterion mono ) was introduced as a criterion

0.6

n-1 cycle n cycle

0.4

Shear stress (kPa)

912

Under 0.1 kPa

0.2 0.0 -0.2 -0.4 -0.6 -3

-2

-1

0

1

2

3

Shear strain (%) Fig. 5. Stress-strain hysteresis loop at last cycle (n cycle) and that of former cycle (n-1 cycle) during constant strain amplitude cyclic shear.

for judging the potential of catastrophic damage such as flow, assuming the existence of a 1–2 m thick liquefiable layer. Post-liquefaction deformation depends mainly on the small resistance regions where shear strain increases sharply with extremely small shear stress (Yasuda et al., 1999). It should be noted that gradient of the shear stress-strain loop is almost constant when the shear stress exceeds 50 kPa. In this study a shear stress of 50 kPa (scriterion mono ) was designated the termination condition. In practice, the shear stress criterion can be adjusted according to the in-situ conditions, such as the gradient of the slope and the height of the adjacent embankment. In this example, the amount of shear strain required to restore a shear stress of 50 kPa was evaluated. The unloading of shear stress and drainage was performed when one of the two abovementioned conditions was achieved. 3.3. Test cases Details of the test cases adopted in this study are shown in Table 2. The relative densities, stress ratios, and fines contents differed from case to case. The relative density of each sample was determined based on JIS A 1224, even though it is restricted to soils with a fines content of less than 5%, so that the test results can be compared with those reported in other research which adopted the relative density. Shear stress ratios of 0.2 and 0.4 were adopted for cases 1 to 5 and 6 to 8, respectively, considering design earthquake motion levels. Cases 9 to 11 contained 10% of DL Clay, which is a non-plastic fines, by weight so that the effect of the fines content could be evaluated. The particle size distribution of sand, DL Clay, and sand-silt mixture is illustrated in Fig. 6. Since Yilmaz et al. (2008) reported no clear relationship between the grading characteristics and the cyclic resistance even among gap-graded soils, the test results were examined without considering

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Table 2 Test cases and results. Case

Dr (%)

qd ðg=cm3 Þ

FC (%)

s=r0c

N1

N2

c1 (%)

c2 (%)

cacm;1 (%)

cacm;2 (%)

ev (%)

1 2 3 4 5 6 7 8 9 10 11 12 13

34 46.5 54 63.5 72.6 35.6 53.3 75 34.8 56.3 74 54 54.5

1.43 1.47 1.49 1.52 1.55 1.43 1.49 1.56 1.53 1.61 1.68 1.49 1.49

0 0 0 0 0 0 0 0 10 10 10 0 0

0.2 0.2 0.2 0.2 0.2 0.4 0.4 0.4 0.2 0.2 0.4 0.2 0.2

0.5 1.5 3.5 12.5 7 0.13 0.22 4.5 1 7.5 4 5.5 5

2.25 3.25 3.25 3.5 – 2.75 3.75 6.25 4.75 6.25 10.25 3.25 2.75

– 30 20.6 13.3 – – 17.6 7.5 – 16.1 8.0 – –

6.6 4.6 3.0 2.8 – 4.7 2.4 2.4 5.0 4.2 4.0 4.0 7.0

25.5 35.7 38.3 44.4 1.2 30.0 40.0 80.6 51.3 76.5 121.9 242.3 437.7

78.9 91.1 76.5 68.3 1.2 85.4 72.7 93.2 106.1 104.5 134.0 298.3 490.7

5.4 3.5 3.0 2.1 0.1 4.3 2.7 1.6 5.0 3.4 2.1 3.9 4.0

the effect of gap-grading of the sand-silt mixture. In order to determine the effect of earthquake duration, an additional cyclic loading of 20 and 40 cycles (cases 12 and 13) were applied to the specimens, after which the apparent lower limit of shear modulus was reached. 4. Test results based on the proposed method

100

Percent finer by weight (%)

Silica sand #7 DL Clay Sand silt mixture (Silica sand #7 + DL Clay 10%)

60

40

20

0

1E-3

0.01

0.1

Particle size (mm)

Fig. 6. particle size distribution of material.

cacm ¼

t

jc_ ðtÞjdt

ð1Þ

0

where c_ ðtÞ is the shear strain rate at time t. In this study, the accumulated shear strain was employed as an index to represent the loading history. 4.1. Cyclic shear process

The test cases and results are shown in Table 2. Dr , FC, and s=r0c , refer to the relative density, fines contents, and stress ratios, respectively. N1 and N2 are the number of cycles during constant stress amplitude cyclic shear and constant strain amplitude cyclic shear. c1 , c2 , cacm;1 , cacm;2 , and ev are the levels of shear strain at which the shear stress recovered to 50 kPa during monotonic shear, the residual shear strain after the unloading process, the accumulated shear strain during the cyclic loading process, the accumulated shear strain of entire test process, and the residual volumetric strain, respectively. The blanks for c1 in Table 2 imply that shear stress was not regained to the value of 50 kPa until 30% shear strain was reached. In the effective stress analysis, the accumulated shear strain used as an index to represents the damage of soil was determined by

80

Z

1

The different results according to the density of the specimens are shown in Figs. 7 and 8. In Fig. 7, shear strain developed and reached 2.5% in medium dense sand with the application of cyclic loading. On the other hand, the stress-strain hysteresis loop converged with a slight increase in the excess pore water pressure in dense soil (Fig. 8). However, when the stress ratio was increased from 0.2 to 0.4, the shear strain increased and liquefaction took place (Fig. 9). The results indicate that specimens with a relative density over 75% can be regarded as not liquefiable at a stress ratio of 0.2, but liquefiable at a stress ratio of 0.4, which suggests a stronger motion. Thus, case 5 is classified as non-liquefaction when the design earthquake motion corresponds to a stress ratio of 0.2. As mentioned earlier, this step is not intended to directly evaluate the liquefaction resistance, but a rough assessment is possible by taking the number of cycles N1 into consideration. The results for the sample containing a DL Clay content of 10% are shown in Fig. 9(b). A comparison with Fig. 9(a) confirms that although the DL Clay does not affect the liquefaction resistance, it does augment the ductility of liquefied soil. In energy terms, ductility represents the energy dissipation capacity. Cohesive and dense materials, in general, are regarded as more ductile than sandy or loose materials (Kazama et al. 2000; Yoshimi and Tokimatsu, 1991). By comparing the number of cycles (N1 and N2), it was possible to roughly compare liquefaction resistance and postliquefaction ductility. Figs. 10 and 11 show the number of cycles N1 and N2 versus the relative density. N1 increases as the relative density increases irrespective of whether it is a sand or sand-silt mixture. Though N1 cannot be understood as the liquefaction resistance, it was possible to compare specimens subject to identical stress ratios.

914

J. Kim et al. / Soils and Foundations 57 (2017) 905–919

Shear stress (kPa)

Decrease of mean effective stress 20

20

10

10

0

0

-10

-10

-20

-20

(a) 0

20

40

60

80

100

(b) -3

-2

-1

Mean effective stress (kPa)

0

1

2

3

Shear strain (%)

Shear stress (kPa)

Fig. 7. (a) Effective stress path and (b) the stress-strain hysteresis loop (case-4, Dr = 63.5%, s=r00 ¼ 0:2).

20

20

10

10

Convergence of mean effective stress

0

Convergence of stress-strain loop

0

-10

-10

-20

-20

(a) 0

20

40

60

80

Mean effective stress (kPa)

100

(b) -3

-2

-1

0

1

2

3

Shear strain (%)

Fig. 8. (a) Effective stress path and (b) the stress-strain hysteresis loop (case-5, Dr = 72.6%, s=r00 ¼ 0:2).

The effect of DL Clay on the ductility of liquefied soil (N2) is illustrated in Fig. 11. While N2 increases with relative density irrespective of fines content, the specimens containing DL Clay were more ductile than clean sand. Using just a small number of specimens, the proposed test procedure makes it possible for the effect of fines on the potential for liquefaction and the ductility of liquefied soil to be roughly examined. 4.2. Monotonic shear process The shear stress versus shear strain relationship during the post-liquefaction undrained monotonic loading and the unloading process is shown in Fig. 12. When the liquefied specimen was subjected to monotonic loading, shear strain increased sharply with extremely small shear stress until the stiffness of the specimen recovered. Yasuda et al. (1999)

and Shamoto et al. (1997) referred to the range in which shear strain developed without any increase in shear stress as the ‘‘small resistance region” and characterized it as ‘‘shear strain independent of effective stress”. There is no doubt that this region plays a crucial role in the post-liquefaction shear strain development. In the case of a relative density of 35%, the small resistance region remained at a shear strain of 30% since shear stiffness was not recovered until a shear strain of 30% was reached, while other specimens showed the recovery of stiffness before the development of 30% shear strain. Since the proposed method comprises several steps, nonuniformities mentioned above, such as water film and strain localization, may occur and affect the results of following steps. However, the presence of non-uniformities above mentioned was not observed in this test. Loading history additionally applied after the stressstrain loop converged showed an observable clear effect

J. Kim et al. / Soils and Foundations 57 (2017) 905–919

20

14

(a) Dr=75% ' / c = 0.4

Clean sand Sand silt mixture

12

FC=0%

Number of cycles N1

Shear stress (kPa)

40

915

0

-20

10

/

' c

= 0.2

8 6 4 2

-40 -3

-2

-1

0

1

2

0 30

3

40

50

60

70

Relative density (%)

20

Fig. 10. Relationship between relative density and number of cycles N1 under stress ratio of 0.2.

(b) Dr=74% ' / c = 0.4 FC=10%

12

10

0

-20

-40 -3

-2

-1

0

1

2

3

Shear strain (%) Fig. 9. The stress-strain hysteresis loop during cyclic loading; (a) Dr = 75%, s=r0c ¼ 0:4 (case-8), (b) Dr = 74, s=r0c ¼ 0:4, and FC = 10% (case-11).

on the post-liquefaction monotonic behavior, as can be seen in Fig. 13. In the specimen (Case-3) without the additional loading, the shear stress of 50 kPa was restored during undrained monotonic loading at a shear strain of 20%, whereas in the two cases (Cases 12 and 13) with the additional loading, a shear stress of only 7 kPa was achieved until the shear strain reached 30%, with almost no difference noted between the two specimens. 4.3. Residual volumetric strain Volumetric strain is plotted against relative density in Fig. 14. The residual volumetric strain correlates well with relative density irrespective of the fines and the stress ratio. The cases subjected to additional cycles are also plotted as diamond in Fig. 14. After additional cyclic loading, the residual volumetric strain was about 1% larger than cases without any additional loading history. However, it should

Number of cycles N2

Shear stress (kPa)

40

Clean sand Sand silt mixture

8

6

4

2

0 30

40

50

60

70

80

Relative density (%) Fig. 11. Relationship between relative density and number of cycles N2.

be noted that there was no difference in the volumetric strain between cases where an additional 20 cycles were applied and cases where 40 cycles were applied. It can be therefore concluded that although loading history affects the residual volumetric strain, its effect peaks out at some point. According to Sento et al. (2004), post-liquefaction volumetric strain depends on the accumulated shear strain indicating loading history. The post-liquefaction volumetric strain was plotted against the accumulated shear strain as proposed by Sento et al. (2004) in Fig. 15. Although the data corresponding to the relative density under 40% is scattered, agreement is good when relative density is over 40% (using an accumulated shear strain for the entire test process cacm;2 ). As mentioned, the effect of loading history is gradually reduced and then peaks out. This can be explained in terms of the margin of void ratio, which

J. Kim et al. / Soils and Foundations 57 (2017) 905–919 '

/

70

c

= 0.2

c

= 0.4

FC=10% /

(2-1) Dr=35.6% (2-3) Dr=53.3% (2-5) Dr=75%

' c

= 0.2

(3-1) Dr=34.8% (3-3) Dr=56.3%

FC=10%, /

' c

6

= 0.4

(4-5) Dr=74% (Dr=34%)

5

Dr=40%

(Dr=34.8%) (Dr=35.6%)

(3-3)

50

(2-5)

Residual volumetric strain

Shear stress (kPa)

v

60

'

/

(1-1) Dr=34% (1-2) Dr=46.5% (1-3) Dr=54% (1-4) Dr=63.5%

(%)

916

(4-5) (2-3)

40

(1-3)

(1-4)

(1-2)

30 20 10

(3-1) (2-1) (1-1)

5

10

15

20

25

30

35

Shear strain (%)

Shear stress (kPa)

(Dr=53.3%)

2

Dr=70% (Dr=74%)

(Dr=63.5%)

Dr=80%

(Dr=75%)

1

Proposed lines by Sento et al. (2004) Iide silica sand Iide silica sand with DL Clay of 10%

0

100

200

300

Accumulated shear strain

400

500

(%) acm,2

indicates the capacity for deformation. This means that there are restrictions to post-liquefaction deformation even if additional loading is applied indefinitely. The results in Figs. 14 and 15 demonstrate that accumulated shear strain can be designated as an index to represent the loading history at least for clean sand, and silty sand with a little fines content. In addition, comparable results to those reported in earlier research indicate that the post-liquefaction volumetric strain obtained through the proposed test procedure can be reasonably utilized.

50 No loading history additional 20 cycles additional 40 cycles

30

20

10

5. Estimating the damage potential

0 0

5

10

15

20

25

30

35

Shear strain (%) Fig. 13. Effect of additional loading history on post-liquefaction stress recovery characteristic (case-3, 12, and 13).

6

Residual volumetric strain (%)

(Dr=54%)

Fig. 15. Relationship between accumulated shear strain and residual volumetric strain.

Fig. 12. Test results of monotonic shear.

40

Dr=60%

(Dr=56.3%)

3

(Dr=54.5%)

(Dr=54%)

(Dr=46.5%)

0

0 0

Dr=50%

4

*Additional loading was applied after shear modulus reached to its lowel limit(cases 12 and 13)

5

4

3

2 Clean sand, / Clean sand, /

1

' c

= 0.2 '

c

= 0.4

*

Clean sand FC = 10% 0 0

20

40

60

80

Relative density (%) Fig. 14. Residual volumetric strain versus relative density.

100

The potential for damage was evaluated and is described in Table 3. The results shown in Fig. 7 where the excess pore water pressure and the stress-strain loop converged can be regarded as non-liquefaction. In these cases, the possibility that liquefaction would occur in the event of the design earthquake motion is quite low. As such, it is not necessary to carry out a detailed liquefaction assessment or to implement any countermeasures. Examples of the damage level potentials are provided in Fig. 16, where (a) represents catastrophic deformation and (b) represents limited deformation. Very loose samples and the two samples subjected to additional loading fell into the catastrophic deformation category, which means the potential for flow is high. In this case, countermeasures are recommended, and attention should be promptly paid to ensuring these soils are strengthened. In the case of soils deemed likely to undergo limited deformation, a numerical analysis should be used to assess precisely how much deformation is likely. The normalized cumulated dissipation energy (Kazama et al., 2000) was also determined for use as an index to represent soil ductility using the following equation: Z t 0 0 W=rm0 ¼ 1=rm0  sðcÞ  c_ ðtÞdt ð2Þ 0

Table 3 Damage assessment and normalized cumulated dissipation energy. Case

Damage level potential

Normalized cumulated dissipation energy W =r0m0

1 2 3 4 5 6 7 8 9 10 11 12 13

Catastrophic deformation Limited deformation Limited deformation Limited deformation Non-liquefaction Catastrophic deformation Limited deformation Limited deformation Catastrophic deformation Limited deformation Limited deformation Catastrophic deformation Catastrophic deformation

0.0023 0.0052 0.0069 0.0085 0.0003 0.0041 0.0103 0.0313 0.0069 0.0126 0.0360 0.0091 0.0117

Normalized cumulated dissipation energy

J. Kim et al. / Soils and Foundations 57 (2017) 905–919

917

0.014 0.012 0.010 End of cyclic loading

0.008 0.006 '

Dr = 55%, 0.004

c

= 100kPa '

Clean sand, /

c '

Clean sand, /

0.002

FC=10%, /

c '

c

= 0.2 = 0.4

= 0.2

0.000 0

20

40

Accumulated shear strain

60 acm,1

80

(%)

Fig. 17. Normalized cumulated dissipation energy of relative density of 55%

50

(a) Dr=34% ' / c = 0.2

Shear stress (kPa)

40 30 20 10 0 -10 -20 0

10

20

50

30

(b) Dr=63.5% ' / c = 0.2

40

Shear stress (kPa)

30 20 10 0 -10 -20 0

10

20

30

Shear strain (%) Fig. 16. The stress-strain hysteresis loop of the overall test procedure; (a) case-1 and (b) case-4.

where r0m0 , ðsðcÞ, and c_ ðtÞ are the initial mean effective stress, shear stress, and shear strain rate at time t, respectively. The relationship between accumulated shear strain

and the normalized cumulated dissipation energy during cyclic loading is presented in Fig. 17. Even in cases where the relative density of each specimen was the same, the dissipated energy during cyclic loading differed according to the loading history and fines content. The energy dissipation of the specimen subjected to a stress ratio of 0.4 was more rapid than that subjected to a stress ratio of 0.2 with the same accumulated shear strain. Furthermore, the specimen with a 10% DL Clay content demonstrated larger energy dissipation than clean sand, indicating that the DL Clay increased the ductility of the specimen. The values taken at the end of cyclic loading for all the cases indicated by the black circles in Fig. 17 are plotted against relative density and accumulated shear strain cacm;1 in Fig. 18. A comparison of the normalized cumulated dissipation energy and relative density indicated that dissipation energy varies with the stress ratio (Fig. 18(a)). Fig. 18(b) also showed that dissipated energy varied with accumulated shear strain depending on the material properties and stress ratio. The relationship between residual volumetric strain and residual shear strain is shown in Fig. 19, along with the damage potential level of each specimen. Residual shear strain was obtained when the shear stress reached zero during the unloading process. The boundary of residual volumetric strain and residual shear strain was shown to be divided at the same point where the damage potential level is divided. The residual volumetric strain and residual shear strain of about 4% obtained in this test represented the boundary between catastrophic deformation and limited deformation. 6. Conclusions This study proposed a new liquefaction assessment procedure that indicates the potential for liquefaction damage among an assortment of soil specimens as highly unlikely,

J. Kim et al. / Soils and Foundations 57 (2017) 905–919

Normalized cumulated dissipation energy

918

Clean sand, /

0.035

Clean sand, /

' c ' c

(a)

= 0.2

0.025

FC = 10%, /

'

c

= 0.2

FC=10%, /

0.025

= 0.4

0.020

0.020

0.015

0.015

0.010

0.010

0.005

0.005

0.000 20

= 0.4

c

(b)

40

60

80

100

'

= 0.2

'

= 0.4

c c

Additional cyclic loading was applied after shear modulus reached to its lower limit(cases 12 and 13)

0.000 0

= 0.2

'

*

Clean sand FC=10%, /

0.030 c '

' c

Clean sand, /

= 0.4

*

Clean sand FC = 10%, /

0.030

Clean sand, /

0.035

0

100

200

300

Acuumulated shear strain

Relative density (%)

400 acm,1

500

(%)

Fig. 18. (a) Normalized cumulated dissipation energy versus relative density; (b) Normalized cumulated dissipation energy versus accumulated shear strain cacm;1 .

residual volumetric strain. This effect was restricted, however, due to limitations imposed by the margin of the void ratio. The observed residual volumetric stain was interpreted in terms of accumulated shear strain, and compared to values reported in a previous study. It was concluded that volumetric strain obtained through the proposed test procedure can be utilized reasonably and the introduction of accumulated shear strain provided an acceptable interpretation of liquefaction-induced volumetric strain. In addition, the relationship between residual volumetric strain and accumulated shear strain was shown to be bilinear, not linear.

6 Catastrophic deformation Limited deformation Non-liquefaction

Residual volumetric strain (%)

5

4

3

2

1

0 0

1

2

3

4

5

6

7

8

Residual shear strain (%) Fig. 19. Residual volumetric strain versus residual shear strain.

likely to deform to some extent, or likely to cause catastrophic damage. The proposed procedure took the constant stress amplitude cyclic shear, constant strain amplitude cyclic shear, monotonic shear, and drainage, in that order, into consideration. The method used to classify the post-liquefaction damage as non-liquefaction, limited deformation, and catastrophic deformation was discussed. An example of the proposed procedure was presented by means of a hollow cylindrical torsional shear test apparatus. The test results of this procedure provided the following: It was shown that although a 10% DL Clay content in clean sand increased the ductility of the soil after liquefaction, no effect was found on the post-liquefaction monotonic behavior or the residual volumetric strain. Additional loading history applied after the shear stressstrain reached its apparent lower limit of shear modulus was found to affect the post-liquefaction behavior and

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