Investigation of the seismic behavior of grouted sandy gravel foundations using shaking table tests

Abstract

Sandy gravel foundations exhibit non-linear dynamic behavior when subjected to strong ground motions, which can have amplification effects on superstructures and can reveal insufficient lateral resistance of foundations. Grouting methods can be used to improve the seismic performance of natural sandy gravel foundations. The strength and stiffness of grouted sandy gravel foundations are different from those of natural foundations, which have unknown earthquake resistance. Few studies have investigated the seismic behavior of sandy gravel foundations before and after grouting. In this study, two shaking table tests were performed to evaluate the effect of grouting reinforcement on seismic performance. The natural frequency, acceleration amplification effect, lateral displacement, and vertical settlement of the non-grouted and grouted sandy gravel foundations were measured and compared. Additionally, the dynamic stress-strain relationships of the two foundations were obtained by a linear inversion method to evaluate the seismic energy dissipation. The test results indicated that the acceleration amplification, lateral displacement amplitude, and vertical settlement of the grouted sandy gravel foundation were lower than that of the non-grouted foundation under low-intensity earthquakes. However, a contrasting result was observed under high-intensity earthquakes. This demonstrated that different grouting reinforcement strategies are required for different sandy gravel foundations. In addition, the dynamic stress-strain relationship of the two foundations exhibited two different energy dissipation mechanisms. The results provide insights relating to the development of foundations for relevant engineering sites and to the dynamic behavior of grouted foundations prior to investigating soil-structure interaction problems.

Graphical abstract

Keywords

sandy gravel foundation / grouting-treated reinforcement / shaking table test / seismic behavior

1 Introduction

Sandy gravel soil is composed of sand, gravel, and pebble soil. It is widely distributed in river valleys and coastal areas, usually as a thick overburden on the bedrock. Sandy gravel soil has high compressive strength and low-shear modulus which exhibits low lateral resistance when subjected to strong ground motions. It has been observed from previous earthquake events that the seismic wave amplitude is increased by the overburden layer, which aggravates the damage caused to a superstructure [1–4]. This has led to the utilization of natural sandy gravel soils with a larger bearing capacity while avoiding potential factors such as uneven settlement. The bearing capacity of sandy gravel foundations under static loading conditions is sufficient to fulfill the static bearing capacity requirements due to their high compressive strength. However, the lateral resistance of sandy gravel soils is unstable under strong ground motions due to the brittle failure of the particles and sliding displacement of coarse particles [5,6]. Therefore, the utilization and development of natural sandy gravel soils with high bearing strength to reduce risks caused by soil settlement and the amplification effect of seismic waves have attracted significant attention in recent years.

Several conventional methods, such as grouting reinforcement, dynamic compaction, and volume replacement methods, have been employed in high-risk seismic zones to mitigate geotechnical hazards and alleviate potential damage to structures. In the case of grouting reinforcement techniques, the voids in the ground are filled to increase the resistance against deformation. It has attracted considerable interest owing to its high performance and low cost, especially from the perspective of soil replacement efficiency. The cement grouting technique used in geotechnical engineering is a potential method that can enhance the cohesion, compressive strength, and lateral stiffness of soil with poor foundation conditions while considerably reducing sedimentation. These techniques can significantly improve the local soil conditions and seismic behavior of the profile. Additionally, an isolation seismic concept called GSI technology, which utilized natural geotechnical conditions, was proposed by Dhanya [7]. It improved the upper soil strength and stiffness while presenting the lower soil sliding isolation characteristics. Recently, the effectiveness of grouting methods to improve the bearing capacity and reduce the settlement of soils has been verified in practice by actual use of various engineering techniques such as shotcrete wall protection of tunnels [8–10] and strengthening natural soft foundations [11–13]. Several studies have demonstrated that the bearing capacity of natural foundations was improved by grouting reinforcement. For example, Akin et al. [14] investigated the soil properties in the compression zone after jet-grouting in sandy soils through standard penetration tests and observed a low shear strain. Santhoshkumar et al. [15] conducted a study on bentonite to improve the efficiency of cement grouting in coarse sands. Gallagher et al. [16] conducted a centrifuge modeling test to investigate the liquefaction and deformation resistance of liquefiable sands through colloidal silica treatment. Kumar et al. [10] verified that the bearing capacity of a soft soil foundation increased after grouting reinforcement. Meite et al. [17] studied the local ground motion amplification in densified soils through numerical analysis and observed that the frequency content of input waves propagating in densified soils was modified and it shifted towards higher frequencies. Several numerical studies [18–21] have been performed to evaluate the seismic behavior of site ground improvements for loose and liquefiable soils.

The abovementioned studies have focused on the improvement and reinforcement measures for soft soils or grouting materials and the improvement of bearing capacity and resistance to liquefaction for sand soil or liquefiable soil. However, the strength and stiffness of grouting reinforced foundation have changed after grouting behavior, and the natural period of soils has also changed correspondingly. Therefore, the mechanical behavior of grouted foundations under dynamic conditions is still unknown. Only a few studies have focused on the dynamic characteristics of foundations after grouting reinforcement. The potential implications of grouted foundations might lead to uncertainties or inaccuracies in the estimation of local site amplification effect and soil-structure interaction problems.

Shaking table tests, which can reproduce the motion of an earthquake, provide an effective technique to evaluate the dynamic response of soil or a structure. Several studies have adopted laminar shear boxes to simulate the dynamic behavior of soil foundation or the interaction between foundation soil and superstructure after grouting reinforcement under simulated seismic excitations. Zhang et al. [22] used a laminar shear box and conducted a shaking table test to evaluate the performance of microbially-treated calcareous sandy foundation. Banovic et al. [23] performed a shaking table test to investigate the efficiency of seismic base isolation using a natural stone pebble layer. The results demonstrated that the stone-pebble layer can significantly reduce the acceleration amplitude. However, it is only suitable for stone-pebble layers with a small thickness. Additionally, multiple shaking table tests have used laminar shear boxes to evaluate the performance of the soil-understructure system [24–27] or pile-soil-structure system [28–30]. Therefore, laminar shear boxes have been used in shaking table tests to study the soil foundation with and without grouting reinforcement.

In the present study, shaking table tests were conducted for sandy gravel foundations with and without grouting reinforcements. The tests were conducted to study the seismic response of the foundations under different seismic excitations and intensities. The amplification effect of ground motion, natural frequency, lateral displacement of soil layers, surface settlement, and stress−strain response of the two sandy gravel foundations were compared and discussed. The results can provide a reference for foundation treatment of sandy gravel foundation and an understanding of the dynamic behavior of grouted foundations prior to investigating soil-structure interaction problems.

2 Test design and experimental methods

2.1 Model foundation material

The sandy gravel foundation used in this study was based on an actual engineering foundation, in which the bridge abutment of a long-span arch bridge was developed on a combined diaphragm-wall foundation surrounded by sandy gravel soil. The aim of the bridge abutment project was to improve the bearing capacity and seismic resistance of sandy gravel foundation using grouting methods. Therefore, this study focused on the effect of grouting reinforcement behavior on the seismic performance of sandy gravel foundations. It should be noted that the sandy gravel layer was simplified as a single layer of sandy gravel soil and the water content was neglected in the shaking table tests due to complex geological conditions.

The geological conditions around a river valley are relatively complex. In the deep stratum, the grain size of gravel soils is large (≥200 mm), which is difficult to simulate in a laboratory model foundation. In the shallow stratum, the particle size of gravel soils is relatively small and it consists of a huge volume of fine sands. In this study, a sandy gravel stratum in natural conditions was simplified, which was considered as a single homogeneous sandy gravel soil layer without considering the effect of groundwater level. Therefore, the test soil samples were configured according to the designed scale grading method based on the particle grading curve measured by sampling at a project site [31]. Soil samples with different particle sizes were mixed and controlled with a maximum particle size of approximately 60 mm. Finally, the scaled sandy gravel soil samples were used in the model test. The particle grading curve of the model soil is shown in Fig.1. The physical and mechanical parameters of the model soil are listed in Tab.1. Although the scaled soil sample has differences of strength and stiffness compared with the prototype soil, a qualitative conclusion is still reliable for the comparison before and after grouting reinforcement.

2.2 Grouting material and operation method

The strength and stiffness of the grouted foundation were affected by the particle size distribution and fine content of soils. The grouting materials and methods determine the mechanical properties of soil after grouting. To understand the injectability of grouting material in the sandy-gravel foundation prior to investigating model soil dynamic behavior in shaking table tests, a set of 5 groups sandy-gravel samples were investigated with different fine-grained contents (IM1–IM5) to grouting cement slurry ratio, and with different water-cement ratios of 0.6:1, 0.8:1, 1.0:1 in model cylinders through the pre-test, as shown in Fig.2. The injectability parameters of the sandy gravel foundation were obtained by pressurizing and injecting the grouting cement slurry from the bottom to top-soil layers. The cement slurry with a water-cement ratio of 1:1 and the soil configuration with a fine-grained content of 20% and coarse grain content of 80% (such that the particle grading curve of the test sandy gravel soil was close to the IM2 configuration) was selected in the shaking table test based on the test results. Grouting methods require high-pressure injection in practical engineering applications. However, the grouting method in this test was simplified as an injection process from the top to the bottom soil layers. Additionally, the sandy gravel soil used for the grouting test was scaled to fulfill the requirements of shaking table tests. The detailed parameters are described in Section 2.4.

2.3 Shaking table equipment and model box

The shaking table tests were performed using the servo-hydraulic shaking table device at Guangxi University. The size of the device was 3.0 m × 3.0 m. The permissible maximum acceleration of the device was 1.0g under the condition of a full load of 10 t. The detailed information of the test system is listed in Tab.2. The tests were conducted along the longitudinal direction of the table device and fulfilled the equipment requirements. The shaking table device was driven by an iterative controller due to the time delay of the vibration servo signal, which was dynamically compensated according to the hydraulic servo actuator signal. Therefore, the actual acceleration signal of the deck surface was in good agreement with the input signal. In addition, a laminar shear box was designed for the shaking table tests as shown in Fig.3. The length, width, and height of the model box were 1.5 m, 1.0 m, and 1.0 m, respectively. The model box consisted of 13 layers of steel frames. Each frame had a height of 100 mm and they were connected by four pulleys, which moved horizontally with low friction. The sandy gravel soil in the laminar box was subjected to a shear deformation similar to that in natural ground conditions. A rubber plate was used to effectively reduce the lateral boundary effect.

2.4 Test design

A set of two shaking table tests (with and without grouting sandy gravel foundation) were performed. Case 1 represented the non-grouted foundation, and Case 2 represented the grouted foundation. The test cases for the shaking table tests are listed in Tab.3.

The test preparation for Case 1 was performed by mixing the sandy gravel soil and laying it in the model box. The height of each layer was controlled by knocking the soil with a mass hammer to obtain a total filled height of 1.0 m. Finally, the shaking table test was performed. A sandy gravel soil with the same configuration was used to refill the box by the above method for Case 2. Additionally, the grouting method of the prototype project was performed using a sleeve-valve pipe which was inserted into the sandy gravel stratum to inject the slurry. This method is known as high-pressure grouting. Therefore, in this test, the soil in the middle of the model box was retained by a thin rigid sleeve while preset a sleeve-valve pipe was embedded into the model soil. Subsequently, the configured cement slurry was injected into the model soil through the sleeve-valve pipe and the injection process was maintained at a slow and uniform rate. The grouting nozzle was maintained at a fixed position (50 cm above the bottom level of the box). The cement slurry was poured into the grout pipe. The grouting nozzle was slowly raised during the grouting operation to obtain a uniform grouting flow in the required grouting zone of the sandy gravel foundation. The sleeve-valve pipe was removed after the grouting was completed. The grouted soil was allowed to solidify for 1 day. Subsequently, the rigid sleeve was removed and the soil was allowed to settle for 6 days. Finally, the shaking table test was performed. The details of the test diagram for the two shaking table tests are shown in Fig.4. The observation of the grouting zone before and after the test is shown in Fig.5.

2.5 Sensor arrangement

Accelerometers and displacement transducers were arranged in the model as shown in Fig.6. Accelerometers were used to measure the acceleration response of the different soil layers. Displacement transducers were used to measure the horizontal layered displacement and soil surface settlement. Two arrays of accelerometers were arranged along the height of model soils in Case 1 and the displacement transducers were fixed on an upright column outside the model box. A displacement transducer was arranged vertically on the surface (for Case 1, it represented soil settlement; for Case 2, it represented grouting zone settlement) to measure the settlement. An array of accelerometers was arranged near the strengthened soil and the second array was arranged at the non-grouting zone in model soil in Case 2.

2.6 Input waves and test cases

In order to investigate the seismic behavior of the sandy gravel foundations with and without grouting under general earthquakes, two typical natural seismic waves (El Centro and Kobe waves, as historical earthquake records) were selected. The El Centro wave was recorded in 1940 in the imperial valley in the United States. Kobe wave was recorded in Japan in 1995 along with a short characteristic period. The selected seismic waves were extracted from the Next Generation Attenuation project database (NGA-West2), the Pacific Earthquake Engineering Research Centre (PEER). The natural period of sandy-gravel soils was considered as a short period due to the high strength and stiffness of the sandy gravel soils. An artificial wave with a characteristic period closed to the natural period of the sandy-gravel soil was selected as the input signal to investigate the resonance effect. The seismic wave amplitude corresponding to three earthquake intensities of small, moderate, and rare intensity earthquakes were 0.15g, 0.3g, and 0.5g, respectively, which were measured using Seismosignal software. And the duration was scaled to 25 s. The time-history records and response spectra of input seismic waves are shown in Fig.7. Two shaking table tests were conducted to examine and compare the seismic behavior of sandy gravel foundations with and without grouting. The input seismic signals were fed to the shaking table deck to simulate bedrock motions. The details of the test cases are listed in Tab.4.

3 Test results and interpretation

3.1 Acceleration responses

The acceleration response of soil along the height represented the lateral resistance at different depths. The acceleration amplification ratio R was defined as the ratio of acceleration amplitude measured for each layer (A_i) by accelerometers to input seismic wave (A_{\mathrm{I}\mathrm{N}\mathrm{P}}) as Eq. (1).

(1)R=\frac{A_i}{A_{\mathrm{I}\mathrm{N}\mathrm{P}}}.

The value of R along with the soil height (measuring A7-A11 side, as shown in Fig.6) of the two foundations under different intensities and seismic waves are represented in Fig.8. This figure was used to observe the R variation law of the sandy gravel foundation before and after grouting. It can be observed that the value of R along with the height of the non-grouted and grouted foundations under 0.15g excitation slightly increased. The value of R in Case 2 was lower than that in Case 1 for the same soil height. This indicated that the initial lateral stiffness of the grouted foundation was greater than that of the non-grouted foundation. A significant difference in the R distribution was observed with an increase in the seismic intensity, particularly for the upper soils under KB-2 and AT-2 excitations. This indicated that the grouting zone of the grouted foundation limited the acceleration amplification. However, different seismic excitations exhibited significant difference in the R distribution. The value of R without a foundation under KB-2 and AT-2 excitations exhibited a similar distribution under 0.3g excitations. The maximum value of R was approximately 1.24, but the values of R of the grouted foundation under the same conditions were approximately 1.03 and 1.18. This implied that ground motions with different spectral characteristics caused different acceleration consequences. This phenomenon was consistent for different types of soils such as soft soil or sawdust-mixed soil [25,32]. The value of R for the non-grouted foundation decreased at the bottom or upper soil under an excitation of 0.5g. Conversely, the value of R for the grouted foundation exhibited an acceleration amplification trend. It should be noted that the value of R in Case 2 was smaller than that in Case 1 under KB-2, but it was larger under KB-3 excitation. This indicated that grouting of the foundation might cause significantly opposite results under different earthquake intensities. In the case of a grouted foundation, the low intensity seismic excitations (0.15g and 0.3g) correlated with decreased values of R, whereas the high intensity seismic excitations (0.5g) enhanced the value of R compared with that of the non-grouted foundation.

It can be concluded that the difference between non-grouted and grouted foundations under dynamic conditions is dependent upon the seismic characteristics and intensity. The seismic characteristics cause different excitation characteristics, whereas the seismic intensity affects the mechanical properties of soil. Grouting might be effective for an acceptable range of seismic intensity.

To observe the difference between the free field and grouting zone of the two cases, the soil field included accelerometers (A2–A6) side was considered as the free field, whereas the grouting side (A7–A11) was considered as the grouting zone. This enabled the comparison of the grouting behavior on the acceleration response at different spatial distribution. The R distribution between the free field and grouting zone of the two cases is shown in Fig.9.

The R distribution at the bottom layer (–0.8−–0.4 m) for the two cases was similar under different waves. This indicated that the bottom layer was slightly affected by grouting and the amplification effect caused by seismic excitations. It should be noted that the R distribution in Case 2 significantly decreased at the bottom layer where it was not subjected to the effect of the grouting zone, indicating that the sandy gravel soil had a large shear deformation at the bottom layer. However, the upper layer (particularly the ground surface) behaved differently under AT-2, KB-3, and AT-3 excitations. The R distribution of the grouted foundation at the free field was larger than that at the grouting zone. However, this phenomenon did not occur in the non-grouted foundation. Additionally, a certain acceleration reduction effect was observed in the grouting zone in Case 2. A low R distribution for the non-grouted foundation was observed compared with that of the grouted foundation. Conversely, a uniform acceleration response was observed for Case 1 in the grouting zone or free field due to a homogeneous stress field distribution of the soil layers. However, the soil stiffness and lateral resistance in the grouting zone were improved for Case 2, resulting in different acceleration spatial distribution under strong ground motions. Therefore, it can be considered that the grouting behavior limited the grouting zone acceleration response causing a large free-field response. It should be noted that this analysis of the seismic amplification or reduction effect by grouting behavior might not be effective for earthquakes, in which the vertical acceleration component is dominant in relation to the horizontal component.

3.2 Response spectrum analysis

Considering the acceleration response spectrums, the variation in the predominant periods of motion was quantitatively defined as the change in the transmission precession from the bedrock to the ground surface. This enabled the understanding of the effect of grouting zone on the acceleration response of ground surface in terms of the safety of superstructure. The acceleration response spectrums at the bedrock and the surface of the two cases under different seismic waves are shown in Fig.10.

In the case of El Centro wave excitation, the predominant periods for Case 1 under EL-1, EL-2 and EL-3 were 0.10, 0.32, and 0.28, respectively. Correspondingly, the predominant periods for Case 2 were 0.10, 0.12, and 0.48, respectively. This indicated that the acceleration response of the grouted foundation increased, compared with that of the non-grouted foundation, in the high-frequency band (approximately 10 Hz) with an increase in the seismic intensity. Case 2 had a more significant frequency band concentration trend than that of Case 1. A comparison of the three different input waves demonstrated that the sensitive frequency band for the sandy gravel foundation was approximately 10 Hz even though the input seismic waves with different characteristic periods induced different acceleration responses. In particular, the amplification effect for KB-3 excitation was significant at approximately 10 Hz. Therefore, the high-frequency resonance phenomenon for both Case 1 and Case 2 was enhanced with an increase in the intensity of the earthquake.

Moreover, the characteristic period of the grouted foundation decreased, which indicated that the stiffness of the grouting zone improved. A single concentrated trend for the grouted foundation was distinct compared with that of the non-grouted zone. The resonance frequency of the grouted foundation was simplified at a specific frequency band. It was observed that the frequency composition of input waves transmitted to the ground surface was highly sensitive to the grouting zone depths, which modified propagation with a shift in the soil response harmonics towards higher frequencies in the grouting zone. This was observed because after the slurry changed the soil mass and compactness of the gravel foundation after grouting. The difference between the contact stiffness of the grouting and non-grouting zones increased with a decrease in the contact friction. The shear stiffness between the grouting and non-grouting zones slightly changed, and the seismic excitation became difficult to transmit to the upper soil. Therefore, the compressive and shear strength of the foundation was improved. Therefore, the grouting operation changed the natural period characteristics of the natural sandy gravel foundation and prevented the possibility of a severe resonance interaction between the soil and superstructure.

3.3 Lateral displacement response

Lateral displacement can be defined as the lateral resistance of the grouting zone that can be obtained by investigating the lateral displacement response of different soil heights. The displacement sensors, which were fixed on a vertical rod moving with the shaking table deck during the test, were used to measure the lateral displacement of the floor frame of the model box. Hence, the measured displacement response was the relative lateral displacement. In addition, the displacement sensor might not separately obtain the displacement of the grouting or non-grouting zones for Case 2 and it might only measure the overall displacement of the different sandy gravel soil layers. It indirectly represented the change in soil displacement for the two cases under different seismic excitations. The lateral displacement amplitudes of the two cases under different seismic waves excitation are shown in Fig.11.

It can be observed that the lateral displacement amplitude increased with an increase in the soil height for the three seismic waves under different seismic intensities. The displacement amplitude of the two foundations under EL-3 excitation was smaller than that of under KB-3 and AT-3 excitations. The amplitude of the grouted foundation at ground surface was 2.5 mm under EL-3. However, it was 11.7 and 17.6 mm under KB-3 and AT-3 excitations. This implied that the sandy gravel foundation was more sensitive to the El Centro wave than that to the Kobe waves or AT waves. This was related to the frequency characteristics of input waves even though a few differences were observed between non-grouted and grouted foundations. Additionally, the lateral displacements of Case 2 under different seismic waves were smaller than those of Case 1 with an increase in the seismic intensity. This indicated that the grouting improved the lateral resistance of the foundation. However, in the case of high-intensity earthquakes, it was observed that the lateral displacement of Case 2 under an artificial wave was greater than that in Case 1. This might be due to the slight separation between the grouting zone and surrounding soil due to a stable motion under strong ground motions. This result was consistent with the previous acceleration response results.

3.4 Ground surface settlement

Ground surface settlement is an intuitive index used to evaluate the effect of grouting. The ground surface settlement of the two cases under different seismic excitation was observed during the tests and its time-history response is depicted in Fig.12.

The settlement amplitude of the two foundations was correlated with the seismic intensity and lateral displacement by comparing the test results. Moreover, the settlement exhibited a nonlinear increasing trend with an increase in the seismic intensity. The grouting behavior significantly reduced the surface settlement, particularly under strong ground motions. Although the occurrence of settlement is related to the seismic wave shape, the settlement was accompanied by a sudden settlement of a single peak of the input wave. The significant settlement corresponded to the peak of the seismic wave, and there is almost without settlement under a smaller peak-wave. In the case of the non-grouted foundation, the unsteady nonlinear settlement might be caused by the particle sliding friction and gravel breakage. In the case of the grouted foundation, the compressive and lateral resistance of upper sand-gravel soils were improved. The settlement of the grouted foundation might be caused by the sliding of the lower non-grouted soil layer of the foundation. The settlement of Case 2 with a uniform and slight settlement that occurred under strong ground motions was attenuated compared with that of Case 1. Therefore, the grouting of the sandy gravel foundation improved the foundation settlement for static or dynamic conditions.

Furthermore, a comparison of the accumulated vertical settlement of the two foundations obtained by the shaking table tests is listed in Tab.5. The maximum seismically induced settlement response of the grouted foundation exhibited a reduction of greater than 34.9% compared with that for the non-grouted foundation, under strong ground motions (0.5g). This can be attributed to the increase in the compressive strength of the grouted zone when the coarse-grained content was used along with cement slurry in the grouted zone.

3.5 Dynamic shear stress-strain relationship

The dynamic shear stress and strain relate to the relationship between dynamic characteristics and energy dissipation capacity of the foundation soil under seismic excitation. The reliability and effectiveness of grouting for the enhancement of the seismic resistance were evaluated by comparing the dynamic shear stress and strain in non-grouted and grouted foundations. However, it was difficult to directly measure the dynamic shear stress of soils during the shaking table tests. A linear inversion method [33] based on the shear beam model can be indirectly used to obtain the dynamic shear stress by acceleration conversion and integrating the acceleration over the different depths of the soil above the required position, as shown in Fig.13.

The dynamic shear stress was calculated using Eq. (2) and correspondingly the dynamic shear strain was calculated using Eq. (3) based on the acceleration and horizontal displacement time-history records at different heights of the model soil. The displacement in Eq. (3) was obtained by the measured layer horizontal displacement in the test. During the processing of the acceleration data, the acceleration and displacement signal records in high-frequency noise contents were filtered and the baseline was corrected before calculation to eliminate the error caused by signal zero drift. It was noted that the grouting zone of Case 2 was represented for the central soil and not for the upper soil layer. Hence, obtaining the horizontal displacement of the grouting area was difficult. Therefore, the measured horizontal displacement cannot correspond to the horizontal displacement of the grouting zone. Hence, the corresponding hysteretic curve based on the proposed method only represented the layer soil of the grouting zone.

(2){\tau }_i\left(t\right)=\sum _{k=1}^i\rho \frac{a_k\left(t\right)+a_{k-1}\left(t\right)}{2}\mathrm{\Delta }{\mathit{\text{z}}}_k,(i=1,2,3,\dots ),

(3)\begin{array}{rl}{\gamma }_i\left(t\right)=& \frac{1}{\mathrm{\Delta }{\mathit{\text{z}}}_{i+1}+\mathrm{\Delta }{\mathit{\text{z}}}_i}\\ & \cdot \left[\frac{\left(u_i\left(t\right)-u_{i-1}\left(t\right)\right)\mathrm{\Delta }{\mathit{\text{z}}}_{i+1}}{\mathrm{\Delta }{\mathit{\text{z}}}_i}+\frac{\left(u_{i+1}\left(t\right)-u_i\left(t\right)\right)\mathrm{\Delta }{\mathit{\text{z}}}_i}{\mathrm{\Delta }{\mathit{\text{z}}}_{i+1}}\right],\end{array}

where {\tau }_i\left(t\right) is the time-history of the dynamic shear stress at the i soil layer of model soil, \rho is the mass density of model soil, a is the time-history record of acceleration, a_0 is the time history record of acceleration at the soil surface, u is the horizontal displacement relative to the shaking table (recorded displacement histories by each measuring point), \mathrm{\Delta }{\mathit{\text{z}}}_i is the vertical distance between two adjacent soil layers with accelerometers in the {\mathit{\text{z}}}_i direction (in this study, \mathrm{\Delta }{\mathit{\text{z}}}_i=0.2\mathrm{m}).

The dynamic stress–strain relationship of the two foundation soils under different earthquakes are shown in Fig.14. The nonlinearities of the sandy gravel soil were considered using the elastic-plastic model to account for the dynamic strain response. The hysteretic loop of the two types of foundation soils increased with an increase in the seismic intensity, and the seismic energy dissipation was gradually highlighted. The development curves of the hysteretic loops were compared for the two foundations under 0.15g earthquake excitation and it was observed that the stress-strain behavior of the soil was dominated by coarse soil and it was linear and without stiffness degradation. However, the hysteretic loop area gradually increased under an earthquake excitation of 0.3g and 0.5g. It can be observed that the hysteretic loop of Case 1 was smaller than that of Case 2, indicating that the energy dissipation of the grouting zone was not obvious. Although the stiffness of Case 2 described by the gradient line was greater than that of Case 1, the grouting foundation under strong ground motions maintained an elastic status. However, the shear modulus of grouting reinforcement was larger and the total input seismic energy of Case 2 was lower than that in Case 1 under an input wave with insensitive spectrum. This indicated that the grouting enhanced the lateral stiffness of the grouting zone. However, the grouting zone might severely affect the dissipation of the seismic energy. It should be noted that the grouting foundation changed the natural period of the soil, which usually exhibits a foundation with short-period characteristics, resulting in an increasing natural period of the soil.

The interface between the grouting and non-grouting zones was decoupled to minimize the intensity of the strong ground motions transmitted into the grouting zone. This implied that the non-grouted foundation was dominated by the cumulative deformation energy in gravel soils, whereas the grouted foundation was dominated by the kinematic energy in the grouting zone. In the case of strong ground motions, the relative reduction of shear strain amplitudes and damping ratio between grouted and non-grouted foundations was substantial. Hence, the soil damping reduction effects overcame the site de-amplification of shear waves in the grouting zone. Therefore, the response of the grouted foundation could be substantially increased compared with that of the non-grouted foundation under strong ground motions, particularly while remediating sandy gravel layers at greater depth which might contribute to dissipation of seismic energy. Furthermore, the seismic response of the grouting zone exhibited a slight dynamic behavior for seismic waves with long-period characteristic, which is favorable for the seismic capacity of the system.

4 Conclusions

In the present study, shaking table tests of non-grouted and grouted reinforced foundation soil were performed based on a scaled foundation soil model. The amplification effect of the ground acceleration, the horizontal displacement response of soil layers, and the stress-strain relationship between the foundation soil were analyzed. The main conclusions are as follows.

1) The grouted foundation with a grouting zone and natural isolation soil layer resulted in a favorable dynamic response in the behavior of the natural sandy-gravel foundation. The grouting of the foundation might provide different results under different earthquake intensities. The acceleration amplification factor of the grouting foundation system was smaller, which indicated that the grouting reinforcement behavior improved the lateral resistance of soils. However, the grouting behavior might only be effective within an acceptable seismic intensity. Additionally, the grouting operation changed the natural period characteristics of the natural sandy gravel foundation, which can prevent a severe resonance interaction between the soil and superstructure. The grouting operation limited the grouting zone acceleration response causing a large free-field response. Therefore, the grouting behavior improved the lateral resistance of the sandy gravel foundations.

2) The resonance frequency of the grouting foundation was simplified at a specific frequency band. It was observed that the frequency composition of input waves transmitted to the ground surface was highly sensitive to the grouting zone depths, which was modified by propagating with a shift of soil response harmonics towards higher frequencies in the grouting zone.

3) The settlement of the grouted foundation might be caused by the sliding of the lower non-grouting soil layer of the foundation. The grouting of the sand-gravel foundation improved the foundation settlement under both static and dynamic conditions.

4) The stress-strain response of the two types of foundation soils demonstrated that the natural sandy gravel soil entered the plastic deformation stage during the earthquake and dissipated energy by cumulative deformation of the soil. The non-grouted foundation was dominated by the cumulative deformation energy in gravel soils and the grouted foundation was dominated by the kinematic energy. Since the natural period of a grouted system changes, the total input energy into the grouting foundation is smaller than that into the without grouted system. Therefore, the seismic performance of the sandy gravel foundation can be significantly improved by grouting. A sandy gravel layer can be considered as a sufficiently efficient low-technology seismic base isolation method. However, firm conclusions require further research.

This study provides a basis for an understanding of grouting behavior of foundations and offers a comprehensive insight into the differences between the grouted and non-grouted foundations under seismic excitation. It should be noted that limited by the working conditions of the shaking table tests, the results of this study are a qualitative evaluation of individual grouting parameters and depths. Consideration of factors such as grouting materials and grouting density, different grouting depths and reinforcement methods, as well as the grouting improvement measures for other site soil, and even the dynamic interaction between foundation and superstructure after grouting, provide opportunity for further investigation. Nevertheless, the conclusions of this paper provide insights into grouting reinforcement and improvement of the seismic performance of natural foundations.

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