**1. Introduction**

Liquefaction is one of the most important and complex topics that geotechnical engineers deal with in today's practice. The Good Friday (Alaska) and Niigata (Japan) earthquakes in 1964 are the very first earthquakes that the destructive effect of the liquefaction was observed as the slope failures, bearing failures of foundations and abutments, etc. It has been studied widely since, and so many researchers have helped liquefaction to be understood better although the topic is still complicated in many sense. The initiation of the studies starts in the 1960s by Seed and his colleagues. Seed and Ldriss in 1967 [1], Seed in 1968 [2], and Seed and Peacock in 1971 [3] set the base of the liquefaction concept by studying the clean sand samples to evaluate the cyclic resistance of the soils, and Finn et al. [4, 5], Castro [6, 7], and Youd [8, 9] are other examples that focused on the liquefaction around that time.

Cyclic loading of the saturated coarse soils causes excessive pore pressure buildup under undrained conditions. This excessive pore pressure can converge up to the total stress; meaning zero effective stress is described as liquefaction [10]. It means that the soil is no longer capable of carrying any load resulting in soil failures and/or excessive deformations of structure foundations. Therefore, this phenomenon is very crucial to take into consideration in designing a structure in liquefaction susceptible areas.

new parameters such as threshold cyclic shear strain, the dimension of the loading and other fitting parameters in relation to fine content, shear wave velocity, etc. Energy-based models focus on the stress-strain loops to calculate the enough energy to estimate the liquefaction susceptibility, and Green et al. [23] is one the most widely used models in this concept. In this study, the laboratory tests were conducted at different cyclic stress ratios (CSR), and the results were compared with the stress-based models. The details of these models and their formulation will

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas*

As mentioned before, loss of stiffness of soil is a big problem for civil engineers. Kramer et al. [24] states that estimation of the soils behavior under dynamic loading is crucial to construct any kind of structures reliable and economical. Other than laboratory studies, building codes regulate the design for a structure to be built in a specific region to estimate the dynamic loads that will be transmitted throughout the soil layers to the structure for some seismic scenarios. Ground response varies a lot with the dynamic behavior of soils and local site conditions under seismic activity. The building codes generally construct the response spectrum differently with regard to the soil class which is determined by the shear wave velocity of upper 30 m. The classification of this kind misses the local site effects on the ground response that the structure will be exposed to. Therefore, the site-specific response plays an important role to estimate the dynamic loads propagated to the soil surface. Building codes generally set some rules to necessitate the site response (i.e., ZF soil class); however, the prediction of the dynamic loads that structure would feel will

Dynamic behavior of soils is obtained in the laboratory conducting dynamic triaxial tests for medium to high and resonant columns test for low to medium shear strain levels. The behavior is modeled with the modulus reduction and damping properties of soil at varying shear strains. These values are evaluated from the stress-strain loops for every cycle to build two important curves presenting the soil

This chapter will outline the liquefaction studies into two groups which will be (i) experimental and (ii) analytical approaches. Initiation of the excess pore pressure buildup resulting ru = 1 ends up as liquefaction of soil, and it can mainly be assessed in the laboratory by the dynamic triaxial test systems. Eighteen different dynamic tests were conducted at different CSRs and loading types in order to obtain the pore pressure generation and validate the models in the literature with the recorded data. The second part of the study will focus on the nonlinear site response of the liquefied areas with the available in situ data. Five different boring logs were used in the analyses, and the nonlinear behavior of the soil layers was determined for each. It should be noted that all the soil columns were liquefied at different depths for different earthquake scenarios. The ground responses were calculated, and finally the performance of the building codes to estimate the spectral response

In this part, clean sand samples were loaded under varying cyclic stresses with different loading patterns using the dynamic triaxial test system equipped at the Eskisehir Osmangazi University Soil Dynamics Laboratory, and it is presented in **Figure 1**. The system is a fully automated pneumatic system that is capable of conducting axial strains up to 10%, and the tests can be handled as stress controlled or strain controlled. A total of 18 tests was completed to justify the performance of the excess

change drastically by the nonlinearity of soil behavior.

**2. Estimation of the excess pore pressure generation**

pore pressure generation models suggested in the literature.

be discussed later.

*DOI: http://dx.doi.org/10.5772/intechopen.88682*

nonlinearity.

**123**

of the soil columns was assessed.

The process of the pore pressure buildup mainly depends on the wave propagation throughout the soil column that is excited by an earthquake. Loose soils tend to densify when they are loaded under drained conditions, whereas if the condition happens to be undrained, the compression of the soil during cyclic loading is almost impossible. In this case, there is not enough time for water to escape from the voids; therefore it takes the seismic load reflecting as increase in the pore pressure. This pore pressure starts building up until the loading is finished. If the energy created by the excitation is big enough, the amount of the pressure will finally reach to the total stress. Since there is no effective stress anymore, the soil grains will escalate in the water and lose its strength therefore stability. Thus, the liquefaction susceptibility should be questioned in seismic areas with some basics: Is the soil coarse and loose enough for being susceptible to liquefy? Is the region active enough to produce sufficient energy to liquefy the soil? If so, does the liquefaction happen in shallow depths that will greatly affect the superstructure on it, or does it happen very deep that nothing will be felt on the ground? These are the questions that should be answered in seismically active regions to take initial precautions for possible hazards.

Although the liquefaction susceptibility is correlated with the in situ test results (SPT, CPT, Vs) or soil index parameters (relative density, fine content, Atterberg limits, etc.) in practice, today's technology gives engineers big confidence to run laboratory cyclic tests in order to understand the behavior of the soil under seismic loads. It is understandable to use empirical models to evaluate the liquefaction; because of its easiness, they are not as accurate as the real scale pore pressure models observed by the dynamic triaxial tests conducted in the laboratory. The complexity of the excess pore pressure generation models is still there, but it is the most appropriate way to estimate the dynamic behavior of coarse soils. Since the correlations do not give any information about the pore pressure generation, the possible deformations on the ground due to liquefaction is not more than an approach for them; however, the level of deformation levels can be observed in the laboratory rigorously [11]. It should also be noted that the tests can be run in varied strain amplitudes (10<sup>6</sup> –10<sup>0</sup> ).

The cyclic behavior of soils is commonly determined by the dynamic triaxial test equipment in the laboratory. Pore pressure generations models are mainly studied into three different approaches: (i) stress-based models, (ii) strain-based models, and (iii) energy-based models. The purpose of stress-based models is to relate the excess pore pressure ratio (ru) which is the normalization of the excess pore pressure by the effective stress with the number of cycles to liquefy the soil. Lee and Albaisa [12] and Seed et al. [13] studied the relation between the ru with (N/Nliq) where N is the number of loading cycle and Nliq is the number of cycle to initiate liquefaction. Later, Booker et al. [14] worked in the same model but offered different constants, and Polito et al. [15] in 2008 came up with a model consisting of fine content, relative density, and cyclic stress ratio. Finally, Baziar et al. [16] updated the formulation with some new parameters. Regarding the strain-based models, the change in volumetric strain is estimated with the cyclic shear strain along with some constants for the clean sand samples [4, 5, 16, 17]. More complex models were introduced by Dobry et al. [18–20], Vucetic and Dobry [21], and Carlton [22] with

#### *Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas DOI: http://dx.doi.org/10.5772/intechopen.88682*

new parameters such as threshold cyclic shear strain, the dimension of the loading and other fitting parameters in relation to fine content, shear wave velocity, etc. Energy-based models focus on the stress-strain loops to calculate the enough energy to estimate the liquefaction susceptibility, and Green et al. [23] is one the most widely used models in this concept. In this study, the laboratory tests were conducted at different cyclic stress ratios (CSR), and the results were compared with the stress-based models. The details of these models and their formulation will be discussed later.

As mentioned before, loss of stiffness of soil is a big problem for civil engineers. Kramer et al. [24] states that estimation of the soils behavior under dynamic loading is crucial to construct any kind of structures reliable and economical. Other than laboratory studies, building codes regulate the design for a structure to be built in a specific region to estimate the dynamic loads that will be transmitted throughout the soil layers to the structure for some seismic scenarios. Ground response varies a lot with the dynamic behavior of soils and local site conditions under seismic activity. The building codes generally construct the response spectrum differently with regard to the soil class which is determined by the shear wave velocity of upper 30 m. The classification of this kind misses the local site effects on the ground response that the structure will be exposed to. Therefore, the site-specific response plays an important role to estimate the dynamic loads propagated to the soil surface. Building codes generally set some rules to necessitate the site response (i.e., ZF soil class); however, the prediction of the dynamic loads that structure would feel will change drastically by the nonlinearity of soil behavior.

Dynamic behavior of soils is obtained in the laboratory conducting dynamic triaxial tests for medium to high and resonant columns test for low to medium shear strain levels. The behavior is modeled with the modulus reduction and damping properties of soil at varying shear strains. These values are evaluated from the stress-strain loops for every cycle to build two important curves presenting the soil nonlinearity.

This chapter will outline the liquefaction studies into two groups which will be (i) experimental and (ii) analytical approaches. Initiation of the excess pore pressure buildup resulting ru = 1 ends up as liquefaction of soil, and it can mainly be assessed in the laboratory by the dynamic triaxial test systems. Eighteen different dynamic tests were conducted at different CSRs and loading types in order to obtain the pore pressure generation and validate the models in the literature with the recorded data. The second part of the study will focus on the nonlinear site response of the liquefied areas with the available in situ data. Five different boring logs were used in the analyses, and the nonlinear behavior of the soil layers was determined for each. It should be noted that all the soil columns were liquefied at different depths for different earthquake scenarios. The ground responses were calculated, and finally the performance of the building codes to estimate the spectral response of the soil columns was assessed.

#### **2. Estimation of the excess pore pressure generation**

In this part, clean sand samples were loaded under varying cyclic stresses with different loading patterns using the dynamic triaxial test system equipped at the Eskisehir Osmangazi University Soil Dynamics Laboratory, and it is presented in **Figure 1**.

The system is a fully automated pneumatic system that is capable of conducting axial strains up to 10%, and the tests can be handled as stress controlled or strain controlled. A total of 18 tests was completed to justify the performance of the excess pore pressure generation models suggested in the literature.

Cyclic loading of the saturated coarse soils causes excessive pore pressure buildup under undrained conditions. This excessive pore pressure can converge up to the total stress; meaning zero effective stress is described as liquefaction [10]. It means that the soil is no longer capable of carrying any load resulting in soil failures and/or excessive deformations of structure foundations. Therefore, this phenomenon is very crucial to take into consideration in designing a structure in liquefaction

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

The process of the pore pressure buildup mainly depends on the wave propagation throughout the soil column that is excited by an earthquake. Loose soils tend to densify when they are loaded under drained conditions, whereas if the condition happens to be undrained, the compression of the soil during cyclic loading is almost impossible. In this case, there is not enough time for water to escape from the voids; therefore it takes the seismic load reflecting as increase in the pore pressure. This pore pressure starts building up until the loading is finished. If the energy created by the excitation is big enough, the amount of the pressure will finally reach to the total stress. Since there is no effective stress anymore, the soil grains will escalate in the water and lose its strength therefore stability. Thus, the liquefaction susceptibility should be questioned in seismic areas with some basics: Is the soil coarse and loose enough for being susceptible to liquefy? Is the region active enough to produce sufficient energy to liquefy the soil? If so, does the liquefaction happen in shallow depths that will greatly affect the superstructure on it, or does it happen very deep that nothing will be felt on the ground? These are the questions that should be answered in seismically active regions to take initial precautions for possible

Although the liquefaction susceptibility is correlated with the in situ test results (SPT, CPT, Vs) or soil index parameters (relative density, fine content, Atterberg limits, etc.) in practice, today's technology gives engineers big confidence to run laboratory cyclic tests in order to understand the behavior of the soil under seismic loads. It is understandable to use empirical models to evaluate the liquefaction; because of its easiness, they are not as accurate as the real scale pore pressure models observed by the dynamic triaxial tests conducted in the laboratory. The complexity of the excess pore pressure generation models is still there, but it is the most appropriate way to estimate the dynamic behavior of coarse soils. Since the correlations do not give any information about the pore pressure generation, the possible deformations on the ground due to liquefaction is not more than an approach for them; however, the level of deformation levels can be observed in the laboratory rigorously [11]. It should also be noted that the tests can be run in varied

The cyclic behavior of soils is commonly determined by the dynamic triaxial test equipment in the laboratory. Pore pressure generations models are mainly studied into three different approaches: (i) stress-based models, (ii) strain-based models, and (iii) energy-based models. The purpose of stress-based models is to relate the excess pore pressure ratio (ru) which is the normalization of the excess pore pressure by the effective stress with the number of cycles to liquefy the soil. Lee and Albaisa [12] and Seed et al. [13] studied the relation between the ru with (N/Nliq) where N is the number of loading cycle and Nliq is the number of cycle to initiate liquefaction. Later, Booker et al. [14] worked in the same model but offered different constants, and Polito et al. [15] in 2008 came up with a model consisting of fine content, relative density, and cyclic stress ratio. Finally, Baziar et al. [16] updated the formulation with some new parameters. Regarding the strain-based models, the change in volumetric strain is estimated with the cyclic shear strain along with some constants for the clean sand samples [4, 5, 16, 17]. More complex models were introduced by Dobry et al. [18–20], Vucetic and Dobry [21], and Carlton [22] with

susceptible areas.

hazards.

strain amplitudes (10<sup>6</sup>

**122**

–10<sup>0</sup> ).

filled with water, and some cell and back pressures were applied in such a way that there was a difference of 5 kPa at increasing level. The saturation was controlled with the B constant to reach a value of 0.96. After saturation was accomplished, the sample was consolidated under isotropic condition approximately an hour with a confining pressure of 65 kPa. Finally, soil samples were axially loaded at different amplitude of stresses with changing loading shapes until all the samples

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas*

In order to understand the excess pore pressure generation at different cyclic stresses, three different stress levels were considered. Cyclic stress ratio is defined as the cyclic stress applied to the sample (either compression or extension) normalized by the confining pressure, and they were assigned as 0.15, 0.20, and 0.30 for the test program. All the samples were confined by the cell pressure of 65 kPa. The

As seen in the table, a total of 18 tests was programmed to see the effect of the stress level and loading characteristics. It is customary to use harmonic loading in the liquefaction studies; however, irregular loading shapes were used in this study to investigate the differences. Six different patterns were used to axially load the samples, and the double amplitude of axial stresses was kept constant at each CSRs.

Since the tests were assessed as stress controlled, the stress-based models were chosen to measure their performance with the laboratory results. Four different

In the table, N is the specific cycle that the excess pore pressure ratio to be calculated and NL is the number of cycles that liquefies the soil. *α* is a fitting constant, and although Seed and Booker propose as it is taken to be 0.7, Polito et al. advanced this constant with other parameters such as fine content (FC), relative density (Dr), and CSR. More complex model was offered by Baziar in 2011 with two different constants *θ* and *β*. These constants differ with the content of the silt in the sandy soil. Since clean sand samples were tested in this study, only related constants are shown in the table. The model Booker proposed gives almost identical results as

Seed et al.'s model does; therefore it is not presented in the following part.

A total of 18 cyclic triaxial tests was planned to gather excess pore pressure generation at different stresses with changing excitation patterns. Using the necessary information from the test data, the excess pore pressure ratios (ru) which were the ratio of the excess pore pressure recorded during cyclic loading over the

**CSR Double amp. axial str. (kPa) Type 1 Type 2 Type 3 Type 4 Type 5 Type 6** 0.15 20 X X X X X X 0.20 26 X X X X X X 0.30 39 X X X X X X

The loading shapes at CSR = 0.20 level are presented in **Figure 3**.

equations suggested by the models are presented in **Table 2**.

were liquefied.

**2.4 Observations**

**Table 1.**

**125**

**2.2 Test program and loading patterns**

*DOI: http://dx.doi.org/10.5772/intechopen.88682*

text program is shown in **Table 1**.

**2.3 Excess pore pressure generation models**

*Test program in terms of stress levels and loading types.*

**Figure 1.** *Dynamic triaxial test system at the Eskisehir Osmangazi University.*

### **2.1 Material and method**

In order to study liquefaction in the laboratory, standard sand samples are generally chosen for the tests since the cost of the undisturbed sand samples that is only possible by the freezing technique are really high. Therefore, clean Podima sand samples were used in this study. The type of sand is classified as poorly graded sand (SP) according to the unified soil classification system (USCS), and the grain size distribution is shown in **Figure 2**. The minimum and maximum unit weights of the sand were determined as 15.30 and 17.66 kN/m3 as the standards suggest, respectively. The specific gravity was determined as 2.63.

The soil samples had a diameter of 7 cm and a height of 14 cm, and the desired relative density was decided to be as 40%. Dried sand was dropped into a two parted mold, which has a membrane placed in, by a funnel with some little shaking and compacting of the sample accordingly. Later, the top header was set on the sample, and some vacuum was applied to the sample in order to hold itself, and the mold was taken apart. Following external cell placement, the cell was

**Figure 2.** *Grain size distribution of the sand used in the study.*

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas DOI: http://dx.doi.org/10.5772/intechopen.88682*

filled with water, and some cell and back pressures were applied in such a way that there was a difference of 5 kPa at increasing level. The saturation was controlled with the B constant to reach a value of 0.96. After saturation was accomplished, the sample was consolidated under isotropic condition approximately an hour with a confining pressure of 65 kPa. Finally, soil samples were axially loaded at different amplitude of stresses with changing loading shapes until all the samples were liquefied.

#### **2.2 Test program and loading patterns**

In order to understand the excess pore pressure generation at different cyclic stresses, three different stress levels were considered. Cyclic stress ratio is defined as the cyclic stress applied to the sample (either compression or extension) normalized by the confining pressure, and they were assigned as 0.15, 0.20, and 0.30 for the test program. All the samples were confined by the cell pressure of 65 kPa. The text program is shown in **Table 1**.

As seen in the table, a total of 18 tests was programmed to see the effect of the stress level and loading characteristics. It is customary to use harmonic loading in the liquefaction studies; however, irregular loading shapes were used in this study to investigate the differences. Six different patterns were used to axially load the samples, and the double amplitude of axial stresses was kept constant at each CSRs. The loading shapes at CSR = 0.20 level are presented in **Figure 3**.

#### **2.3 Excess pore pressure generation models**

Since the tests were assessed as stress controlled, the stress-based models were chosen to measure their performance with the laboratory results. Four different equations suggested by the models are presented in **Table 2**.

In the table, N is the specific cycle that the excess pore pressure ratio to be calculated and NL is the number of cycles that liquefies the soil. *α* is a fitting constant, and although Seed and Booker propose as it is taken to be 0.7, Polito et al. advanced this constant with other parameters such as fine content (FC), relative density (Dr), and CSR. More complex model was offered by Baziar in 2011 with two different constants *θ* and *β*. These constants differ with the content of the silt in the sandy soil. Since clean sand samples were tested in this study, only related constants are shown in the table. The model Booker proposed gives almost identical results as Seed et al.'s model does; therefore it is not presented in the following part.

#### **2.4 Observations**

**2.1 Material and method**

**Figure 1.**

**Figure 2.**

**124**

*Grain size distribution of the sand used in the study.*

In order to study liquefaction in the laboratory, standard sand samples are generally chosen for the tests since the cost of the undisturbed sand samples that is only possible by the freezing technique are really high. Therefore, clean Podima sand samples were used in this study. The type of sand is classified as poorly graded sand (SP) according to the unified soil classification system (USCS), and the grain size distribution is shown in **Figure 2**. The minimum and maximum unit weights of the sand were determined as 15.30 and 17.66 kN/m3 as the standards suggest,

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

The soil samples had a diameter of 7 cm and a height of 14 cm, and the desired

relative density was decided to be as 40%. Dried sand was dropped into a two parted mold, which has a membrane placed in, by a funnel with some little shaking and compacting of the sample accordingly. Later, the top header was set on the sample, and some vacuum was applied to the sample in order to hold itself, and the mold was taken apart. Following external cell placement, the cell was

respectively. The specific gravity was determined as 2.63.

*Dynamic triaxial test system at the Eskisehir Osmangazi University.*

A total of 18 cyclic triaxial tests was planned to gather excess pore pressure generation at different stresses with changing excitation patterns. Using the necessary information from the test data, the excess pore pressure ratios (ru) which were the ratio of the excess pore pressure recorded during cyclic loading over the


**Table 1.** *Test program in terms of stress levels and loading types.*

**Figure 3.** *Example loading shapes at the level of CSR = 0.20.*


accumulation of the excess pressure started to increase again, and then liquefaction finally occurred after 5000 seconds for Type 1. Similar trends were observed for the

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas*

*DOI: http://dx.doi.org/10.5772/intechopen.88682*

Regarding the models suggested in the literature, they do not behave much different at this stress level. Although they did not do a good estimation to represent the data gathered from the sinusoidal loading, other pore pressure ratios along time were predicted alright by the models, being slightly on the conservative side. It should be noted that all three models missed the initial increases in pore pressure regardless of type of loading. Lastly, the pore pressure observed from the type five loading acts more like a harmonic loading than irregular type of loading, and models overestimated the pore pressure generation after 2000 seconds until the liquefaction developed. Overall, some model has better presentation of the observed data at certain type of loading, and some does at others. Therefore, no model perfectly

Moving on to the higher stress level, **Figure 5** shows the recorded excess pore pressure ratios at CSR = 0.20 for six different tests and corresponding estimations by the literature models. Compared to the lower stress level, the liquefaction initiation did not take that long under cyclic stress ratio of 0.20. It occurred around 130– 420 seconds for soil to lose its stability for irregular types of loading, whereas it took almost 2.5–8 times longer for soil to liquefy under harmonic loading. The literature models ideally followed the pore pressure record gathered from the three tests under loading of Type 3, Type 5, and Type 6; Baziar, being the best, did acceptable

predictions for other two tests (Type 2 and Type 4 loadings).

rest of the tests for shorter periods.

*Excess pore pressure ratios for the test data and models at CSR = 0.15.*

**Figure 4.**

**127**

matches with the test data.

#### **Table 2.**

*Models and associated equations used to compare the test results.*

confining pressure of 65 kPa were calculated for the models mentioned in the previous section. The test data and corresponding models proposed by Seed et al. [13], Polito et al. [15], and Baziar [16] at CSR = 0.15 are presented in **Figure 4**.

The first thing to point out in the figure is that the liquefaction happens in various times for different types of loading, although the double amplitude axial stresses are the same for all the six tests. The longest time to liquefy the clean sand sample happened to be almost 18,500 seconds for the sinusoidal type of loading, whereas this duration came out to be in an interval of 3500–8600 seconds for irregular type of loading. As seen in the upper left side of the figure, the recorded pore pressure buildup differs a lot with regard to other types. An initial increase was recorded in a short time, and it fluctuated for almost 10,000 seconds, and then the

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas DOI: http://dx.doi.org/10.5772/intechopen.88682*

**Figure 4.** *Excess pore pressure ratios for the test data and models at CSR = 0.15.*

accumulation of the excess pressure started to increase again, and then liquefaction finally occurred after 5000 seconds for Type 1. Similar trends were observed for the rest of the tests for shorter periods.

Regarding the models suggested in the literature, they do not behave much different at this stress level. Although they did not do a good estimation to represent the data gathered from the sinusoidal loading, other pore pressure ratios along time were predicted alright by the models, being slightly on the conservative side. It should be noted that all three models missed the initial increases in pore pressure regardless of type of loading. Lastly, the pore pressure observed from the type five loading acts more like a harmonic loading than irregular type of loading, and models overestimated the pore pressure generation after 2000 seconds until the liquefaction developed. Overall, some model has better presentation of the observed data at certain type of loading, and some does at others. Therefore, no model perfectly matches with the test data.

Moving on to the higher stress level, **Figure 5** shows the recorded excess pore pressure ratios at CSR = 0.20 for six different tests and corresponding estimations by the literature models. Compared to the lower stress level, the liquefaction initiation did not take that long under cyclic stress ratio of 0.20. It occurred around 130– 420 seconds for soil to lose its stability for irregular types of loading, whereas it took almost 2.5–8 times longer for soil to liquefy under harmonic loading. The literature models ideally followed the pore pressure record gathered from the three tests under loading of Type 3, Type 5, and Type 6; Baziar, being the best, did acceptable predictions for other two tests (Type 2 and Type 4 loadings).

confining pressure of 65 kPa were calculated for the models mentioned in the previous section. The test data and corresponding models proposed by Seed et al. [13], Polito et al. [15], and Baziar [16] at CSR = 0.15 are presented in **Figure 4**. The first thing to point out in the figure is that the liquefaction happens in various times for different types of loading, although the double amplitude axial stresses are the same for all the six tests. The longest time to liquefy the clean sand sample happened to be almost 18,500 seconds for the sinusoidal type of loading, whereas this duration came out to be in an interval of 3500–8600 seconds for irregular type of loading. As seen in the upper left side of the figure, the recorded pore pressure buildup differs a lot with regard to other types. An initial increase was recorded in a short time, and it fluctuated for almost 10,000 seconds, and then the

**Models Equation Notes**

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

� � *α* = 0.7

� �<sup>1</sup>*=<sup>a</sup>* � � *α* = 0.7

� �<sup>1</sup>*=<sup>a</sup>* � � *<sup>α</sup>* <sup>¼</sup> <sup>0</sup>*:*<sup>01166</sup> � *FC* <sup>þ</sup> <sup>0</sup>*:*<sup>007397</sup> � *Dr*

n o<sup>2</sup> <sup>r</sup> <sup>0</sup>*:*<sup>6</sup> <sup>≤</sup>*<sup>θ</sup>* <sup>≤</sup> <sup>0</sup>*:*<sup>8</sup>

þ 0*:*01034 � *CSR* þ 0*:*5058

0*:*0 ≤*β* ≤0*:*25

*<sup>π</sup>* sin �<sup>1</sup> 2 *<sup>N</sup> NL* � �<sup>1</sup>*=<sup>a</sup>* � 1

*<sup>π</sup>* sin �<sup>1</sup> *<sup>N</sup> NL*

*<sup>π</sup>* sin �<sup>1</sup> *<sup>N</sup> NL*

þ *β*

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>2</sup>*<sup>N</sup> NL* � 1

<sup>2</sup> <sup>þ</sup> <sup>1</sup>

*<sup>π</sup>* sin �<sup>1</sup> *<sup>N</sup> NL* � �<sup>1</sup>*=*2*<sup>θ</sup>* � �

*Models and associated equations used to compare the test results.*

**Figure 3.**

**Table 2.**

**126**

*Example loading shapes at the level of CSR = 0.20.*

Seed et al. [13] *ru* <sup>¼</sup> <sup>1</sup>

Booker [14] *ru* <sup>¼</sup> <sup>2</sup>

Polito et al. [15] *ru* <sup>¼</sup> <sup>2</sup>

Baziar [16] *ru* <sup>¼</sup> <sup>2</sup>

**Figure 5.** *Excess pore pressure ratios for the test data and models at CSR = 0.20.*

As the axial stress increases, the pore pressure buildup behavior under sinusoidal loading converges to the one loaded by the irregular type. There is still a mismatch at the initial, but after 400 seconds, all three models presented the data alright for the Type 1 loading. It is obvious that most of the time the model proposed by Baziar [16] is the closest to the recorded data, and Polito's model [15] gives the upper limit out of the three models, whereas the other model stayed in between two.

**2.5 Discussion**

**Figure 6.**

**Figure 7.**

**129**

Out of 18 cyclic triaxial tests to understand the soil liquefaction susceptibility, it is observed that the shape of the loading or in other words frequency content of the excitation plays an important role to cause instability. Earthquakes are never harmonic types of excitations, and using sinusoidal loading in order to understand the soils dynamic behavior may mislead the interpretation. **Figure 7** explains how many

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas*

*DOI: http://dx.doi.org/10.5772/intechopen.88682*

*Excess pore pressure ratios for the test data and models at CSR = 0.30.*

*The effect of loading on the change of number of cycles to liquefy soil.*

Final set of tests were carried out at a high stress (CSR = 0.30) and recorded excess pore pressure ratios over time, and corresponding literature predictions are presented in **Figure 6**. It is obvious that the increasing stress level causes soil to liquefy at low number of cycles. For all the types of loading, it did take only 1– 10 cycles for soil to lose its rigidity meaning not more than 100 seconds. As seen in the figure, all of the literature models predicted the pore pressure generation almost perfectly for the test done using Type 2 loading. Regarding the others, the data are underestimated by all the models especially the test data observed from the harmonic loading. It is hard to estimate the performance of the models to represent the data under Type 5 loading since it took only 1 cycle (10 seconds) to liquefy the soil.

There is one question that can arise to understand the behavior of the liquefaction occurred when harmonic loading was applied: Did the soil liquefy at 100 seconds or earlier like 30 seconds where the first time ru value reached 1.0? During the specific test, the deformation of the soil was carefully observed with the naked eye along with the computer screen. Although ru came to 1.0 around 30 seconds, the soil was not totally unstable and still was able to resist more loads. Therefore, the total stability lost was waited to terminate the test, and it lasted almost 100 seconds.

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas DOI: http://dx.doi.org/10.5772/intechopen.88682*

**Figure 6.** *Excess pore pressure ratios for the test data and models at CSR = 0.30.*

#### **2.5 Discussion**

As the axial stress increases, the pore pressure buildup behavior under sinusoidal loading converges to the one loaded by the irregular type. There is still a mismatch at the initial, but after 400 seconds, all three models presented the data alright for the Type 1 loading. It is obvious that most of the time the model proposed by Baziar [16] is the closest to the recorded data, and Polito's model [15] gives the upper limit

Final set of tests were carried out at a high stress (CSR = 0.30) and recorded excess pore pressure ratios over time, and corresponding literature predictions are presented in **Figure 6**. It is obvious that the increasing stress level causes soil to liquefy at low number of cycles. For all the types of loading, it did take only 1– 10 cycles for soil to lose its rigidity meaning not more than 100 seconds. As seen in the figure, all of the literature models predicted the pore pressure generation almost perfectly for the test done using Type 2 loading. Regarding the others, the data are underestimated by all the models especially the test data observed from the harmonic loading. It is hard to estimate the performance of the models to represent the data under Type 5 loading since it took only 1 cycle (10 seconds) to liquefy the soil. There is one question that can arise to understand the behavior of the liquefaction occurred when harmonic loading was applied: Did the soil liquefy at 100 seconds or earlier like 30 seconds where the first time ru value reached 1.0? During the specific test, the deformation of the soil was carefully observed with the naked eye along with the computer screen. Although ru came to 1.0 around 30 seconds, the soil was not totally unstable and still was able to resist more loads. Therefore, the total stability lost was waited to terminate the test, and it lasted almost 100 seconds.

out of the three models, whereas the other model stayed in between two.

*Geotechnical Engineering - Advances in Soil Mechanics and Foundation Engineering*

*Excess pore pressure ratios for the test data and models at CSR = 0.20.*

**Figure 5.**

**128**

Out of 18 cyclic triaxial tests to understand the soil liquefaction susceptibility, it is observed that the shape of the loading or in other words frequency content of the excitation plays an important role to cause instability. Earthquakes are never harmonic types of excitations, and using sinusoidal loading in order to understand the soils dynamic behavior may mislead the interpretation. **Figure 7** explains how many

**Figure 7.** *The effect of loading on the change of number of cycles to liquefy soil.*

cycles are needed to liquefy soil sample for different types of loading at a double amplitude of 26 kPa stress, just to give an example.

to between 3500 and 18,500 seconds, and these values drop to 130– 1100 seconds at CSR of 0.20. Even a small difference in the applied stress

*Estimation of Excess Pore Pressure Generation and Nonlinear Site Response of Liquefied Areas*

iii. There are many stress-based models to estimate the pore pressure buildup in the literature, and three of them were used here to see their performance to estimate the laboratory data. Models have better representation of the pore pressure generation at the low to medium stress levels for irregular loading patterns, and at high stress levels the capability to estimate the data is not that well. Among the models, the model Baziar et al. [16] suggests relatively does better jobs, and Polito et al.'s [15] model is being on the safer side all the time. However, the performance of all three to predict the recorded data does not

iv. The dynamic triaxial tests take some time to set the sand sample appropriately and evaluate the data to understand the behavior, but other levels of relative

v. The latest point is that the effect of fine content should also be investigated, and if the opportunities (budget, facility, etc.) are possible, undisturbed samples should directly be taken out of the site to see if the real in situ samples are represented well by the laboratory approaches in order to

Japan, Chile, the USA, Italy, Iran, and Turkey are some of the most important earthquake-prone countries, and they have been exposed to devastating activities over the last decades causing damaged buildings and many fatalities. One of the most essential regions for liquefaction studies in the literature is the Duzce/Sakarya Region in Turkey which was immensely affected by Kocaeli and Adapazari (Duzce) earthquakes in 1999. Liquefaction susceptibility in structural design should be considered in zones consisting of loose sand soils because it may cause significant damages as excessive settlement and sinking of the structures. This can only be

In this section, the nonlinear site response of liquefied areas will be investigated

Five different boring log data were used in the analyses to evaluate the ground response in a liquefied prone zone. The soil profiles consist of almost 90% of silty sands (SM), and some low-plasticity clays, gravelly sands, and clayey sands can be found in very shallow depths. A summary table showing the information about the

All the borings are 20 m long having shear wave velocity (Vs) values changing

using the well-documented in situ data taken from the city of Sakarya which is surrounded by Istanbul, Yalova, Duzce, and Bilecik. The region lays on the extension of the North Anatolian Fault Zone [25], and it is neighboring two local faults (Sapanca and Duzce), and the map is presented in **Figure 8**. The area suffered a lot,

and many liquefied zone were inspected during Duzce Earthquake in 1999.

from 145 to 290 m/s. The average Vs of upper 30 m for each profile was also determined to be able to use it in the estimation of the surface response spectra

densities and confining pressures should be tested to have better

understanding of the pore pressure generation concept.

evaluate the response of the pore pressure buildup.

**3. Nonlinear site response of liquefied areas**

possible by the nonlinear site-specific analysis.

**3.1 Introduction and studied area**

logs is presented below.

**131**

amplitude may cause a drastic drop in the number of cycles.

differ that much.

*DOI: http://dx.doi.org/10.5772/intechopen.88682*

One clear point can be made from the figure that the variety of loading and its dominant frequency are effective on the number of cycles that would initiate the liquefaction. Although the excess pore pressure buildups are similar for the first 5 cycles, Type 1 with the harmonic shape diverges from the rest of the group, and the number of cycles needed for liquefaction occurs to be at least 2.5 times later than the others. With regard to the irregular type of loadings, they even act differently, and the number of cycles to liquefy the soil varies between 10 and 40 which can be considered a wide interval. Thus, the potential of liquefaction triggering should be studied with different types of loading when needed.

The essence of the results in terms of number of cycles to liquefy soil samples is shown in **Tables 3** and **4**.

It should be noted that the variation is a lot for different cyclic stress ratios. For example, Type 3 and Type 4 loading patters need similar number of cycles to liquefy the soil at CSR = 0.15, whereas it changes for increasing CSRs. Harmonic loading always takes more time/cycle to generate pore pressure than others, and every irregular loading type has its varying frequency-dependent characteristics at increasing stresses. Therefore, the excess pore pressure generation is not only affected by the frequency content of the loading alone, but also the stress levels along with it play important role in estimating liquefaction triggering.

As a summary, three different stress levels at varying loading shapes were used to run dynamic triaxial tests in order to determine the generation of excess pore pressures under cyclic excitations. The desired relative density and confining pressure for all 18 tests were constant as 40% and 65 kPa, respectively. There are a few clear points that are worth to emphasize:



**Table 3.**

*Number of cycles to initiate liquefaction for different types of loading.*


**Table 4.** *Soil profiles.* to between 3500 and 18,500 seconds, and these values drop to 130– 1100 seconds at CSR of 0.20. Even a small difference in the applied stress amplitude may cause a drastic drop in the number of cycles.

