The Effect of Sand-Crumb Rubber Mixture Treatment on the Seismic Response of a Low-Rise Building Located on Liquefiable Soil

doi:10.21203/rs.3.rs-3923489/v1

One of the most effective measures to reduce earthquake risks in high-seismic areas is to reduce the input forces caused by earthquakes to the structure. The properties of rubber materials in geotechnical projects are energy absorption, dynamic deformation change as well as damping of latent energy in loads, high shear modulus and damping ratio, easy access and their economic nature. In this research, with finite difference modeling, the effect of using sand- crumb rubber layer on the seismic behavior of the model has been obtained. In the following, by changing the thickness and depth of the sand-crumb rubber layer, the seismic behavior such as floor displacement and internal forces have been investigated. This research numerically models liquefaction (UBCsand with FLAC) and predicts the effects of the sand-crumb rubber layer of different thicknesses under the foundation and evaluates the structure's damage and settlement interacting with the soil by validating the numerical model with the laboratory model and calibrating it with different ratios. The results show that liquefaction, pore water pressure excess ratio and soil settlement will be significantly reduced with the presence of sand-crumb rubber layer, and also the base shear has shown an increase, but the structural damage is reduced.

Sand-‌Crumb Rubber Mixture

Seismic Behavior

UBCsand Constitutive Model

Liquefaction

For a long time, liquefaction has always been associated with various deformation phenomena of non-cohesive saturated soils in undrained conditions under the effect of transient, uniform or repeated disturbances [1]. The production of excess pore water pressure in undrained conditions is the main cause of the phenomenon of liquefaction, which reduces the stiffness and strength of the soil. One of the most effective measures is reducing the input forces caused by earthquakes to the structure, which can achieve a more economical design for the building by damping (depreciating) the earthquake waves [2-4].

Every year, about 290 million tires are thrown away in the world, and about 50% of them are recycled and burned [5,6]. In Iran, 13 million used tires enter the environment every year, of which 25% is recycled and the rest is accumulated in the environment [7]. These bulky wastes have properties such as resistance, light weight and high drainage. Tires can be converted into rubber powder, crumb rubber, thin string and ash and used in projects depending on the need [8,9].

The properties of rubber materials in earthworks are such that by replacing them with a part of the soil under the foundation and using their energy absorbing properties, the dynamic properties of these materials, such as dynamic deformation and also damping the latent energy in loads, are high [10-13]. One of the other advantages of these materials is their accessibility and economy, which has enabled the use of these materials in construction projects [14-16]. The result of Madhusudan et al.'s experiments on sand-crumb rubber mixes with uniform granulation particle sizes less than 2 mm [17]. This study prevented sand and crumb rubber particles from separating and increased the mixture's damping. They found that adding rubber lowers static resistance. To investigate the shear modulus and damping ratio of granulated sand-crumb rubber mixtures, Fakharian and Ahmad [18] performed cyclic triaxial experiments on samples with different weights of granulated rubber and different consolidation ratios. After loading the samples, 0.002 and 0.004 cyclic shear strain ranges were applied up to 300 cycles [19]. Granulated rubber increased damping ratio (D) and decreased shear modulus in both shear strain ranges. In a triaxial cycle test, blended waste crumb rubber (0.1-0.8 mm) in varied amounts (0, 9, 33, and 100% by weight) with river sand and clean clay. Rubber greatly lowered density and shear stiffness of both soil types, reducing vibrations. Rubber-rich samples had lower shear stiffness depreciation at strains greater than 0.001. Rubber reduced damping ratio in this strain range. Processing rubber waste mixed with soil can be utilized as lightweight fillers for slopes, road foundations, and retaining walls subjected to seismic or traffic pressures, according to Li et al,. [20]. Shear modulus increases dramatically in tiny strains due to particle void filling, which enhances contact. Liquefaction resistance improves with crumb rubber ratio for all samples. Madhusudan et al,. [21] examined coarse sand and fine rubber mixtures under undrained cyclic simple shear. They found that sand-crumb rubber compositions delay pore water pressure. Shear stiffness decreases with axial strain in dry crumb rubber-sand mixtures. Rubber reduces sand damping. The damping ratio of crumb rubber-dry sand mixes does not diminish with loading cycles. A single layer of flexible sand-crumb rubber was tested as a low-cost seismic isolation approach for underdeveloped countries [22]. They discovered that finite element modeling or other research tools are needed to determine the ideal sand-crumb rubber layer thickness. The structure on the sand-crumb rubber layer should endure inertial forces from the seismic acceleration before the landslide. The sand-crumb rubber layer reduces earthquake reactivity and construction damage. By studying crumb rubber under minor strain circumstances, Das and Bhowmik [23,24] conducted torsional resonance column tests to investigate the dynamic characteristics of Barak river sand and crumb rubber-sand mixture. All samples showed that relative density improves dynamic shear modulus and decreases damping ratio. The damping ratio grows exponentially and the dynamic shear modulus falls with shear strain in low strain conditions. Dashti and Bray [25] used centrifuges to study foundation deformation. They discovered that shear and volumetric strains cause structural settlement and that the flowing sand layer thickness does not affect settlement. Due to earthquake drainage, large transitory hydraulic gradients near the foundation produce volumetric strains. Yang et al,. [26] tested waste tire-mixed soil based on triaxial dynamic, California load ratio, direct shear, and consolidation. Rubber's low density makes it lightweight filler that reduces settlement after combining with varied soils. Rubber has strong flexibility and energy absorption, making it useful for isolation pads, embankment support, and other applications. Plate loading tests by Moghaddas Tafreshi et al., [27] included gradual cyclic loading to a sandy soil bed with several rubber and granular soil mixture layers in a large-scale model. By dispersing weight, RSM layers alleviate vertical stress from foundation depth. Geosynthetic or geocell reinforcement can be employed with RSM layers. Increasing foundation layer rubber improves compressibility, which negates retrofitting. The ideal RSM layer thickness under gradual cyclic loads is 0.4 of the foundation diameter based on plate settlement. Low-modulus materials like sand-and-crumb rubber mixture were used to study the geotechnical seismic isolation system and dynamic interaction between the structure and foundation by Tsang et al., [28]. This study demonstrated that the GSI-RSM system improves slab-foundation horizontal and rotational responses. Silent construction uses 60% less energy and transmits more to subsoil through sliding and rotation. UBCsand effective stress constitutive model was utilized by Beaty [29] to examine liquefaction-induced shear deformations. The UBCsand model predicted displacements twice as great as centrifuge trials. The UBCsand model may be conservative because to difficulty predicting the small displacement response at shallow liquefaction areas. The current research examines how the dense layer of sand-crumb rubber with varied thicknesses affects the seismic behavior of the building on the smooth base during three near-field and three far-field earthquakes. Instead of just studying the increase in soil damping caused by the sand-crumb rubber layer and the foundation settlement due to liquefaction, this study also modeled the building frame, investigated liquefaction damage, and examined the seismic response of the structure.

In this study, finite difference software was used for numerical modeling. The seismic response of the modeled three-story building is recorded as 6 earthquake waves, both near field and far field, are applied to the soil complex and the structure. The first step is to model a single layer of loose sandy soil with liquefaction ability and different thicknesses of the sand-crumb rubber mixture. The calibration of the direct cyclic shear test by [21] was used to acquire the parameters of the constitutive model, and the findings of the centrifuge [25] experiments were utilized to validate the numerical model and determine the dimensions of the model.

The finite difference software used in this study is FLAC, which is widely used in engineering mechanics calculations [30]. FLAC software enables the liquefaction phenomenon in sandy soils by analyzing the pore water pressure with the help of UBCsand constitutive model.

2-1- Model specifications and dimensions

Choosing appropriate model dimensions is the first step in the modeling process. In this research, vertical movement under the foundation is equal to 1.75 cm for static loads. As can be seen in Fig. 1, preliminary modeling is performed assuming the dimensions of the soil environment up to twice the width of the building foundation on each side, due to the greater effectiveness of model dimensions in dynamic analysis and to achieve more accuracy in modeling.

The selected model has the dimensions given in Fig. 1: a length of 200 m, a depth of 25 meters of soil, and a depth of 2 m of underground water. There are three distinct layers of soil: a large layer of dense Nevada sand (20 m thick), a layer of river sand (3 m thick) that can be liquefied, and a thin layer of Monterey sand (2 m thick). Here, we use a sand-crumb-rubber mixture of varying thicknesses to alleviate the problem by simulating the soil beneath the foundation [31].

2–2 Structural characteristics

The general shape of the three-story structure with the length of the openings equal to 9 meters and the height of each of the floors is 4 meters, is shown in Fig. 2. Also, the specifications of the wide-wing I-shaped steel sections used are given in Table 1.

Table 1

Characteristics of steel sections used in modeling [32]
Section	Section Area (cm²)	Inertia moment (cm⁴)	F_y (MPa)	Elastic modulus (MPa)
W14×257	487.7	141518.7	345	2×10⁵
W33×118	223.9	245576.5	248	2×10⁵
W30×116	220.6	205202.1	248	2×10⁵
W24×68	129.7	76170.4	248	2×10⁵

Table 2 shows the seismic mass of the structure in each floor. To calculate the specific mass of the beams, the mass of the beam is added together with the loading, but for the columns, only the mass of the column itself is calculated. The foundation of the building is a wide concrete foundation with a thickness of 0.5 meters, which is modeled using the beam element in the software, and the characteristics of reinforced concrete are considered for the characteristics of this element.

Table 2

Seismic mass of the structure (Ohtori et al., 2004)
	Seismic loading (kg)
1st and 2nd Floor	9.56×10⁵
3rd Floor	1.03×10⁶

2-3- Contact element requirements

There is an empirical rule that suggests the values of normal stiffness (k_n) and shear stiffness (k_s) for structural elements equal to 10 times the equivalent stiffness of the adjacent zone. The equivalent stiffness (unit of stress per unit of displacement) for a zone in the vertical direction, according to Eq. (1), is equal to [33]:

$$k=\hbox{max} \left[ {\frac{{\left( {K+\frac{4}{3}G} \right)}}{{\Delta {Z_{min}}}}} \right]$$

1

where K and G are respectively equal to the bulk and shear modulus and ΔZ_min is the minimum thickness of the zone adjacent to the interface in the vertical direction. If the stiffness of the materials on both sides of the contact surface is very different, this relationship is used according to the characteristics of softer materials [33]. Due to the large difference in the stiffness of the foundation and soil, the shear stiffness and bulk modulus of Monterey sand have been used to calculate the equivalent stiffness of the contact surface. In the mentioned relationship, the maximum shear modulus should be used, so to calculate the maximum shear modulus (G_max), Eq. (2) presented by Seed et al. [34] was used.

$${G_{max}}=1000\,{K_2}{\left( {\sigma _{m}^{\prime }} \right)^{0.5}}$$

2

In this regard, $\sigma _{m}^{\prime }$ is the average effective stress (lb/ft²) and K₂ is a coefficient that is different for different grain materials. The value of K₂ is selected as 70 based on the experiments of Seed et al. [34] and Kramer's research [35] for dense sand. Also, the value of $\sigma _{m}^{\prime }$ was calculated according to Eq. (3) that the value of $\sigma _{y}^{\prime }$ in the middle of the Monterey sand layer was extracted from the software.

$$\sigma _{m}^{\prime }=\frac{{\sigma _{y}^{\prime }+2\left( {1 - \sin \,(\phi )} \right)\sigma _{y}^{\prime }}}{3}$$

3

The final shear and normal stiffness values of the contact element are presented in Table 3. The shear friction angle of the contact surface is also calculated as a coefficient of the internal friction angle of the soil according to the materials that are in contact with each other. The United States Navy Engineering Center suggests a coefficient of 0.45–0.55 for concrete contact with soil [36]. In this research, the coefficient of 0.5 has been chosen and considering that the internal friction angle of Monterey sand is 40 degrees, the shear friction angle of the contact surface has been calculated as 20 degrees. It should be noted that the characteristics of the contact surface are chosen in such a way that it allows the separation and sliding of the foundation on the soil.

Table 3

Contact surface parameters
Parameter	Indication	Value
Normal tensile strength (kPa)	T_n	1
Shear friction angle (˚)	Φ_s	20
Shear stiffness (N/m/m2)	K_s	6.5×10⁹
Normal stiffness (N/m/m2)	K_n	6.5×10⁹

2-4- Characteristics of the input wave

The modeled structure under the effect of 6 far-field and near-field earthquakes applied to the model floor is selected according to Table 4 and the maximum acceleration of the input wave is scaled to 0.15g. Also, the acceleration response spectrum with 5% damping in far and near field earthquakes is shown in Fig. 3.

Table 4

Characteristics of input waves and earthquake stations
Earthquake		Station	R_JB (km)	R_Rup (km)	V_s30 (m/sec)	Mw (R)	Fault mechanism	PGA (g)
Near Field	Loma Prieta (1989)	Los Gatos	3.22	5.02	1070	6.93	Reverse Oblique	0.44
	Tabas (1978)	Tabas	1.79	2.05	767	7.35	Reverse	0.85
	Chi ـ Chi (1999)	TCU ـ 102	1.49	1.49	714	7.62	Reverse Oblique	0.3
Far Field	Duzce (1999)	Lamont 1060	25.78	25.88	782	7.14	Strike Slip	0.025
	Manjil (1990)	Abbar	12.55	12.55	724	7.37	Strike Slip	0.514
	Northridge ـ 01 (1994)	Vasquez Rocks Park	23.1	23.64	997	6.69	Reverse	0.15

2-5- UBCSand constitutive model

In this research, we have used the UBCSand model to simulate the mixture of river sand-crumb rubber. This constitutive model is an effective stress plasticity model used in advanced stress-strain analyzes of geotechnical structures and has been developed mainly for granular soils that have the ability to liquefy under seismic loading (such as sands and silty sands with a relative density of less than 80%). The shear and bulk modulus are defined with the help of equations (4) and (5), and it should be noted that homogeneous elastic responses are considered in the UBCsand model [37]:

$${G^e}=K_{G}^{e}.{P_a}.{\left( {\frac{{\sigma ^{\prime}}}{{{P_a}}}} \right)^{ne}}$$

4

$${B^e}=\alpha {G^e}$$

5

G ^e and B^e show the shear modulus and bulk modulus of the elastic state, respectively. $K_{G}^{e}$, coefficient of elastic shear modulus which depends on the relative density, ne is the variable power of elastic shear modulus between 0.4 and 0.6 (usually 0.5 is chosen), $\sigma ^{\prime}$ is the average effective stress, ${P_a}$ is the atmospheric pressure and α is the correlation coefficient between the modulus Elastic shear and elastic bulk modulus are in the range of 3.2 to 3.4 and depend on Poisson's ratio. Soils parameters are shown in Table 5 [25]. Soil dilation angle (ψ) and bulk modulus (K) are necessary modeling factors. This study investigate that the dilation angle was nearly equal to zero when the layer of loose sand was considered [31]. For nearly saturated soil conditions (99% saturation), the value of 400 MPa was used for the bulk modulus of water [25]. The mechanical model is assigned using the Mohr-Coulomb model, which takes into account the soil's friction angle and cohesion.

Table 5

Characteristics of soil used in modeling (Dashti and Bray, 2013)
Parameter	Symbol (unit)	Dense Nevada Sand	Loose Nevada Sand	Monterey Sand
Relative Density	Dr (%)	90	30	85
Density	ρ (kg/m³)	1720	1580	1660
Porosity	n	0.4	0.35	0.36
Modified SPT	N_1,60	24.2	2.9	36
Friction Angle	ɸ (⁰)	37.84	33.68	40
Cohesion	c (kPa)	1	1	1
Passion Ratio	ν	0.31	0.31	0.35
Shear Modulus	G (MPa)	11.7	8	25
Permeability	Pre and Post earthquake	5.63×10^− 5	1.88×10^− 4	1.32×10^− 3
Permeability	During earthquake	1.41×10^− 5	4.69×10^− 5	3.31×10^− 4
Elastic Shear Modulus Coefficient	K_G^e	21.7×15×(‌N_1,60‌)^0.333
Elastic Shear Modulus Power	m_e	0.5
Bulk Modulus Coefficient	α	2(1 + ν) / 3(1–2ν)
Elastic Bulk Modulus Coefficient	K_B	α × K_G^e
Elastic, Plastic Bulk Modulus Power	n_e	0.5, 0.4
Plastic Bulk Modulus Coefficient	K_G^p	K_G^e ×(‌N_1,60‌)² ×0.003×100
Limit Friction Angle	ɸ_cs (⁰)	33
Maximum Friction Angle	ɸ_peak (⁰)	ɸ_cs+ 0.2(‌N_1,60‌)
Failure Ratio	R_f	0.01×(1-‌N_1,60‌)

2-6- Sand-rubber mixture behavior and modeling

Coarse-grained rubber-sand mixtures were prepared according to ASTM D-2487 [39]. The maximum specific weight according to the ASTM D-4253 standard [39] and the minimum specific weight of sand materials according to the ASTM D-4254 standard are 17.66 and 15.33 kN/m³, respectively, and for crumb rubber materials are 5.21 and 2.88 kN/m³. Figure 4 shows the particle size of rubber and sand prepared for testing [21].

The maximum size of the rubber crumb particles was 2 mm (ASTM,D. 2007) and the steel wires in the tires were completely removed before shredding [40].

Also, the ratio of pore water excess versus the number of loading cycles diagrams with the increase of crumb rubber content from zero to 100% are given in Fig. 5. As can be seen, with the increase in the percentage of rubber particles, the maximum ratio of pore water excess decreases.

The hysteresis curves obtained from the direct cyclic shear test are a benchmark for determining the parameters of the UBCsand model, which is given in Fig. 6. As can be seen, with the increase in the percentage of rubber particles, significant energy consumption has been achieved in the rings.

In this research, seven numerical models with different percentages of sand and crumb rubber were generated and analyzed, as shown in Table 6:

Table 6

Modeling of this research
No	Name	Modeling
1	Liquefiable Layer	Loose fluid layer of river sand under the foundation
2	Non ـ Liquefiable Layer	Dense sandy soil without loose layer under foundation
3	RSM10 ـ Down	The weight combination of 10% rubber crumb with 90% sand and replacing it with the entire liquefiable layer (5 meters)
4	RSM30 ـ Top	The weight combination of 30% rubber crumb with 70% sand and replacing it up to the top of the liquefiable layer (2 meters)
5	RSM30 ـ Mid	The weight combination of 30% of rubber crumb with 70% of sand and replacing it up to the middle of the liquefiable layer (3.5 meters)
6	RSM30 ـ Down	The weight combination of 30% rubber crumb with 70% sand and replacing it with the entire liquefiable layer (5 meters)
7	RSM50 ـ Down	The weight combination of 50% rubber crumb with 50% sand and replacing it with the entire liquefiable layer (5 meters)

The above modeling has been done with the help of UBCsand constitutive model. In the second model, the layer of loose soil with the ability to liquefy is replaced with a layer of non-liquefiable dense sand to compare the results of model number 1 and 2 to check the effect of the existence of a loose layer in the soil. In the third to seventh models, sand-crumb rubber mixture with different percentages and thicknesses was used, which replaced all or part of the loose fluid layer below. The granulation curve of each of the above models is given in Fig. 7.

In this section, the validation of the soil to obtain the dimensions of the model using centrifuge test results and numerical modeling by Dashti and Bray [25] has been discussed. Then we examine the results of the direct cyclic shear test of [21] for sand- crumb rubber mixture with different rubber ratios. Also, the results of the simulations performed considering the interaction of soil and structure have been discussed. The results of these analyzes are presented in two sections: soil and building frame. In the soil section, the optimization of sand-crumb rubber mixture, and the investigation of liquefaction occurrence and in the building frame section, the investigation of the horizontal movement of floors, base shear, foundation settlement and damages caused by liquefaction are presented.

3-1-Soil environment

Dashti and Bray [25] modeled the presence of a liquefiable soil layer under the foundation using centrifuge tests and numerical modeling. By applying the earthquake wave, they have investigated the changes in pore water pressure and acceleration in the model. In this research, to validate the constitutive model and obtain the meshing size in the UBCSand constitutive model, the soil environment was simulated as a free field without a building frame, and it was matched with the results of others [25]. Figure 8 shows the numerical model made by Dashti and Bray [25] and the present research.

According to Dashti and Bray [25] research, the applied seismic wave for dimensional validation and numerical simulation meshing is the north-south component of the Kobe earthquake in Japan, which was recorded at the Port Island station. The maximum acceleration of the incoming wave is equal to 0.15 g. Figure 9 shows the accelerogram of the Kobe earthquake.

The comparison of the results of the ratio of excess pore water pressure at the bottom, middle and top of the liquefiable loose sand layer can be seen in Fig. 10, respectively. In Fig. 10b, it can be seen that the most consistent results are obtained in the center of the liquefiable sand layer and in comparison with the numerical modeling of [25], it confirms the correctness of the numerical simulation results.

With the hysteresis curves and changes in pore water excess ratio from cyclic direct shear test [21], single element modeling is done by FLAC software. In the following, calibration has been done for RSM0, RSM10, RSM30, RSM50 mixtures by using different ratios of sand-rubber crumb mixture (Fig. 11).

3-2- Validation of building frame

In order to verify the results of the three-story building frame simulation, the structural members are first simulated with rigid supports in FLAC. Then, subjected to seismic analysis by applying earthquake waves, the building frame is simulated in ETABS. With the help of time history analysis of axial force values, bending anchor and the shear created in the building frame has been studied in two modes of static and vibration analysis [41, 42]. The results of previous research show software validation and interaction studies [43–45].

4-1- Investigating the condition of the soil

4-1-1- pore water excess ratio ()

4-1-1- pore water excess ratio (r_u)

In this research, first, by examining the different ratios of sand-crumb rubber (RSM10, RSM30, RSM50) which have been replaced by the entire liquefiable layer (thickness of 5m), the pore water excess ratio has been estimated. As shown in Fig. 12, with the increase of sand-crumb rubber ratio, the pore water pressure ratio decreases significantly in the center of the liquefiable layer. In combination with a weight percentage of 30% (RSM30) mixture, the amount of liquefaction is reduced to an acceptable level and approaches the state of non-liquefiable layer. Meanwhile, the model with 10% by weight (RSM10) mixture, it is significantly different from the condition of the non- liquefiable layer. With 50% by weight (RSM50) mixture, the proportion of excess pore water pressure in the liquefiable layer is almost not created. Therefore, in this research, RSM30 has been selected for sand-crumb rubber mixture ratio.

The average ratio of excess pore water pressure (r_u) for the top, bottom and middle of the liquefied layer are shown in Fig. 13 and Fig. 14, for near-field earthquakes and far-field earthquakes, respectively. As can be seen in both Fig. 13 and Fig. 14, the excess pore water pressure ratio (r_u) is the maximum in the middle of the layer and the minimum at the top of the liquefiable layer of river sand. Near-field earthquakes produce higher r_u than far-field earthquakes, the maximum r_u in near-field earthquakes for the bottom, middle, and top of the layer is 42, 34, and 11.5% respectively, higher than the r_u in far-field earthquakes. Therefore, it is concluded that the r_u of the liquefiable layer is almost 80% higher than the non- liquefiable layer.

According to Fig. 13, the pore water excess ratio decreases significantly with the increase in the thickness of the sand-crumb rubber layer. It should also be noted that increasing the thickness of the sand-crumb rubber layer from 2m to 5m, can reduce r_u by about 60%.

4-2- Investigating the condition of the building frame

4-2-1- Base shear

Figure 15 shows the values of the maximum absolute value of base shear during near-field and far-field earthquakes.

According to Fig. 15, it can be said that the liquefaction phenomenon reduces the base shear by about 20%. By increasing the thickness of the sand-rubber crumb layer under the foundation, the possibility of liquefaction is reduced and when the sand-rubber crumb layer is the thickest (5m), the minimum base shear is obtained. Also, in near-field earthquakes, the base shear values are about 30% higher than in far-field earthquakes. The reason for this difference is the very low stiffness and high damping of the liquefiable layer, which prevents the transmission of waves to the structure. Increasing the ratio of crumb rubber reduces the pore water pressure and increases the effective stress in the layer. Also, greater stiffness and less damping are obtained, which increase the acceleration of the structure and increase the base shear rate.

4-2-2- Maximum horizontal acceleration of floors

In this section, the maximum horizontal acceleration changes at the connection points of the beams to the column (1) in Fig. 2 have been investigated under the horizontal component of far-field and near-field earthquakes. Figure 16 shows the maximum horizontal acceleration at different levels of the building frame. According to the results in Fig. 16, it can be said that the minimum and maximum values of PHA for far-field, near-field earthquakes, and different thicknesses of sand-crumb rubber mixture are at the end of the column and at the roof level, respectively. By increasing the thickness of the sand-crumb rubber layer from 2m to 5m, the average PHA values can increase by about 37%. According to Fig. 16, in near-field earthquakes, the PHA values at the base level are about 30% and at the roof level are 37% more than far-field earthquakes, which is due to the phenomenon of resonance.

4-2-3- Lateral and relative displacement of floors

Determining the amount of displacement is important to eliminate or reduce the damage caused by hitting nearby buildings during an earthquake. The lateral displacement values of the floors have been investigated by determining the lateral displacement of the structure for points A, B and C (Fig. 17) for different floors of the building compared to the displacement of the foundation.

The permanent lateral displacement of the building frame floors based on the intended earthquakes is shown in Fig. 18. The results of Fig. 18 are as follows:

As the height of the structure increases, the amount of lateral movement increases significantly.
The presence of sand-crumb rubber layer increases the amount of lateral movement. The liquefiable layer transfers less displacement to the structure, but the layer with sand-crumb rubber transfers more displacements to the structure due to the reduction of liquefaction ability.
By increasing the thickness of the sand-crumb rubber layer, the lateral displacement increases and becomes similar to the non- liquefiable state.
The maximum amount of lateral displacement created in the roof level was related to the Chi-Chi earthquake, which was about 10 cm, and this shows the necessity of installing the discontinuity seam in the structures.
The amount of lateral displacement in near-field earthquakes is about 40% higher than in far-field earthquakes, which clearly shows the damage caused by hitting the nearby building.

Figure 19 show that liquefaction reduces the maximum ratio of horizontal displacement in the floors of the structure. Also, the maximum amount of horizontal displacement ratio is observed in the first floor and similarly, it decreases with increasing height. The maximum ratio of horizontal displacement in near field earthquakes is about 50% higher than that of far field. It can be seen that with the increase in the thickness of the sand-rubber crumb layer, the maximum ratio of horizontal displacement in the floors increases.

4-2-4- Foundation Settlement

The final settlement of the structure after the end of the earthquake is one of the most influential factors that occur when an earthquake occurs due to the phenomenon of liquefaction and causes irreparable damage to the structure. In this research, the settlement history of the structure in the center of the foundation after the earthquake was studied; this is shown in Fig. 20. The results from Fig. 20 are given below:

The final settlement of the foundation in the liquefaction state in near-field and far-field earthquakes is about 130% and 40% more than the case without liquefiable layer, respectively.
The final settlement in near-field earthquakes is about 42% higher than in far-field earthquakes.
The presence of a sand layer of rubber crumb can reduce the final settlement to an acceptable level due to the high relative density of this layer of 80% and reducing the possibility of liquefaction under the building foundation.
By increasing the thickness of the rubber crumb sand layer, the amount of final settlement decreases in near-field and far-field earthquakes.

4-2-5- Structural damage

Asymmetric settlement during liquefaction damages the building and its neighbors. Asymmetric foundation settlement is reduced by the modeled structure's symmetrical parts and stress. This study ignored sand boiling, which causes massive asymmetric settlements. Table 6 evaluates liquefaction-related structural damage using Burland [46] and Boscardin and Cording [47] criteria. Near field earthquakes increase the building's deflection ratio, which indicates high structural risk, while the non-liquefiable layer's is within the acceptable limit. The building's foundation's sand-crumb rubber layer can mitigate liquefaction and settlement. The building on the liquefied layer suffers moderate to severe damage from near-field earthquakes and mild to severe damage from far-field earthquakes, according to Buscardin and Cording's damage assessment guidelines [47]. Less settlement occurs because the sand-crumb rubber layer reduces foundation liquefaction (Table 7). As per Burland's instructions [46], structure damage from near-field earthquakes is moderate to extremely severe, and damage from far-field earthquakes is moderate. The structure damage has decreased from extremely severe too mild as the sand-crumb rubber layer thickness has increased (Table 7).

More structural damage is caused by near-field earthquakes than far-field ones. The liquefaction phenomenon is crucial to building destruction, as a liquefaction layer under the structure can cause mild to severe damage. Use dense sand-rubber crumb materials to reduce structural settling, settlement damage, and liquefaction.

Table 7

Assessment of structural damage
Earthquake		Building damage assessment
		Liquefiable layer		Non ـ Liquefiable layer
		[47]	[46]	[47]	[46]
Near Field	Loma Prieta	M ـ SE	Moderate	SL	Slight
	Tabas	SE ـ VSE	Severe and Very Severe	SL	Slight
	Chi ـ Chi	M ـ SE	Moderate	M ـ SE	Slight
Far Field	Duzce	M ـ SE	Moderate	SL	Moderate
	Manjil	M ـ SE	Moderate	SL	Negligible
	Northridge	SL	Moderate	NEGL	Negligible
		RSM30 ـ Top		RSM0 ـ Mid
Near Field	Loma Prieta	M ـ SE	Moderate	M ـ SE	Moderate
	Tabas	SE ـ VSE	Severe	M ـ SE	Slight
	Chi ـ Chi	M ـ SE	Moderate	M ـ SE	Moderate
Far Field	Duzce	M ـ SE	Moderate	M ـ SE	Moderate
	Manjil	M ـ SE	Moderate	M ـ SE	Moderate
	Northridge	M ـ SE	Moderate	SL	Slight
		RSM30 ـ Down
Near Field	Loma Prieta	SL	Slight
	Tabas	M ـ SE	Slight
	Chi ـ Chi	M ـ SE	Slight
Far Field	Duzce	SL	Slight
	Manjil	NEGL	Very Slight
	Northridge	NEGL	Very Slight
NEGL = Negligible SL = Slight damage M ـ SE = Moderate to Severe damage SE ـ VSE = Severe to Very Severe damage

The results of this research show that the presence of sand-rubber crumb layer reduces the excess pressure of pore water and as a result reduces the phenomenon of liquefaction. This causes significant reduction of settlement and less damage in the structure.

In this research, the replacement of the sand-crumb rubber layer with different thicknesses instead of the loose sand layer, the seismic behavior of the building and the liquefaction phenomenon of the soil under the foundation have been investigated. The aim of this research was to numerically model the liquefaction phenomenon and predict the effects of the sand- crumb rubber layer of different thicknesses under the foundation of the building. Based on the obtained results, it can be said that the layer with a thickness of 5 meters, weight combination of 30% crumb rubber with 70% sand, replacing with the entire liquefiable layer, is the best possible choice from a practical point of view, which reduces pore water pressure, settlement, base shears and structural damages. The results obtained from this research show:

In general, near-field earthquakes cause more excess pore water pressure ratio, more settlements in the soil under the foundation, more lateral displacement, and a greater maximum lateral displacement ratio than far-field earthquakes.

The presence of liquefiable layer causes a significant increase in the maximum excess pressure of pore water and structural settlements compared to the state of non- liquefiable layer. The maximum amount of r_u created in the middle and the minimum amount of r_u is reported at the top of the liquefiable layer, respectively. The results show that the occurrence of liquefaction causes a decrease in base shear in the building and also causes a significant increase in the settlement of the center of the foundation and asymmetric settlement of the foundation.

The presence of liquefiable layer does not have much effect on the amount of horizontal movement of the structure. The maximum and minimum PHA values for all models occur at the end of the column and at the roof level, respectively. The presence of liquefiable sand layer in the UBCSand constitutive model has not had a significant effect on the maximum horizontal acceleration values.

Based on the results obtained from the ratio of excess pore water pressure on the sand-crumb rubber mixtures replaced by a liquefiable layer with a thickness of 5m and a content of 10, 30 and 50% by weight, it is shown that the RSM30 has a significant effect on reducing the phenomenon of liquefaction and settlement of the structure.

By increasing the thickness of the sand-crumb rubber layer from 2m to 5m, the ratio of excess pore water pressure decreases by about 60% for near-field and far-field earthquakes, and it becomes similar to the condition of soil with a non-liquefiable layer.

Replacing dense sand-crumb rubber layer with loose river sand materials can have the greatest effect on settlement and excess pore water pressure; protect the foundation from the effects of asymmetric settlement and consequently the damage caused by these settlements.

The presence of a dense sand-crumb rubber layer has a significant effect on the amount of structural damage and can be used as a solution to deal with the effects of structural damage. Also, different sand-crumb rubber ratios have good effects on the phenomenon of liquefaction, but analyzes should be done to make it cost-effective and obtain the optimal rubber content.

Here are some suggestions for future work:

Modeling with changes in the water level (saturation and drying of the soil layer) and considering hydraulic gradients
3D modeling in FLAC-3D software for concrete and asymmetrical buildings in loading
Investigating the phenomenon of sand boiling and post liquefaction analysis and the effect of sand-crumb rubber mixture in it and the use of different mixtures of non-granular soil with crumb rubber

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

Availability of data and material

The data that supports the findings of this study are available within the article.

Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Funding / Grant information

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Authors' contributions

Benyamin Tareghian: Conceptualization, Methodology, Software, Data curation.

Mohammad Saleh Baradaran: Writing - Original draft preparation, Writing - Reviewing and Editing, Visualization, Validation.

Ali Akhtarpour: Supervision, Validation, Methodology, Reviewing and Editing.

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Graphical Abstract

The Effect of Sand-Crumb Rubber Mixture Treatment on the Seismic Response of a Low-Rise Building Located on Liquefiable Soil

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Abstract

Figures

1- Introduction

2- Materials and methods