Experimental Evaluation of Load Distribution between Piles in Case of Block Failure

Abstract

In this study, the load distribution of the piles in the pile group was investigated in the case of the pile raft foundations failure under the effect of vertical loads in cohesive soils. For this purpose, loading tests were carried out on model pile groups in the laboratory. In addition, the effects of these conditions on the load distribution between the piles were examined by changing the pile spacing and soil properties. As a result of the experiments, it was determined that the piles in the corner region carried more load than the ones in the center region in small settlement amounts as in the literature. However, it has been determined that as the amount of settlement in the pile foundation increases, the soil between piles behaves like a block and approaches failure, and the piles in the center region of the pile group carry more load. As a result of excessive settlement, a fracture surface formed around the block and therefore the corner piles of the block began to carry less load. It has been determined that failure analyses should be performed considering the load carried by the corner piles after failure due to excessive settlement.

1. Introduction

The basic requirements of engineering designs are economy and safety. For this reason, the calculations should be examined in more detail in order to design the piles more safely and economically. In the literature, there are many field measurements, model tests and numerical studies on the investigation of the bearing capacity and settlement behavior of single piles, pile groups and pile raft foundations. Moreover, as it is known, cohesive soils have lower bearing capacity compared to cohesionless soils [1,2]. For this reason, soil improvement is made in order to provide sufficient bearing strength in clayey soils. Pile foundations are used when soil improvement methods are not economical. However, despite their widespread use, studies on load distribution between piles in pile foundations are limited. Pile load distribution is one of the controversial issues among engineers even today. Some studies on this subject are summarized below.

Whitaker [3], who carried out the first studies on this subject, determined in his laboratory experiment on reconstructed clay soil that the pile loads gradually decreased from the center to the corner. Another example of the load difference between the corner and center piles was the Messeturm Tower. Katzenbach et al. [4] reported that the ratio of corner pile load measured on piles under the Messeturm Tower building in Frankfurt to the load of the center pile was 3.5. The engineers have designed the length of the corner and center piles differently due to the different load distribution between the piles. In this study, the length of the center piles was 34.9 m, and the length of the corner piles was 26.9 m since the settlement amount must be within acceptable limits. The reason for this design was that the corner piles carried more load in the piled raft foundations at the allowed settlement values. In these conditions, the loads carried by the center piles were smaller than the corner piles. Thus, the aim was to make the load distribution in the pile group more uniform.

Mandolini et al. [5] reported the corner/center pile load ratio (q_cor/q_cen) as 1.6 in the piles of the Garigliano Bridge that sit on clayey-silt and sand layers. De Sanctis and Russo [6] found load increases in the corner piles of circular tanks. Likewise, Shulyat’ev and Kharichkin [7] reported that the corner and center piles of the building in Moscow’s Pavshinsk River Valley did not carry an equal pile load. Researchers gave q_cor/q_cen as 2.4 for the foundation of a building resting on alluvial soil by the river. Dai et al. [8] carried out a loading test on nine piled foundations on a soil consisting of silty-clay and sand layers and reported that the corner pile loads were greater than the center one. Katzenbach and Moormann [9] determined that the pile at the corner of the foundation and the center pile carry different loads.

In addition, there are numerical investigations in the literature that calculate the load distribution of piles [10,11,12,13,14,15,16,17]. However, although formulas were suggested using the results obtained from these studies, most of these formulas remained at the research level. Therefore, in pile foundation projects, designers have to use finite-element-based programs to determine the load distribution between piles.

Ergun and Turkmen [18] conducted model experiments and analyzed the load distribution between piles. As a result of this study, they determined that the center piles carried more load than the corner piles when the foundation was loaded from the center. Singh and Singh [19] found that the amount of load carried by the center pile decreased as the number of piles and pile space increased by using FEM.

Importance of the Study

When the studies in the literature are examined, it has been seen that the behavior of the piles that settle within the limits of the allowed settlements has been examined in almost all of the studies. However, studies on the load distribution of collapsed pile groups are limited.

Within the scope of this study, the load distribution of the pile group which excessively settled was examined. In this study, the interaction between pile material and soil was not investigated. In this paper, settlements in case of failure were referred to as excessive settlements. The relationship between the amount of settlement in pile raft foundations and the load distribution (q_cor/q_cen) between corner and center piles has been determined. Thus, this study will contribute to the determination of the behavior of structures which suffered from excessive settlement.

There are very few articles on the causes and mechanism of block formation in pile groups. Additionally, in these articles, the cause of block formation has not been investigated in detail. In this study, the relationship of block formation with soil strength parameters and distance between piles was researched. In addition, the effect of this situation on the load distribution between piles was investigated.

The evaluation of the condition of pile foundations after over-settlement (post-failure), the bearing capacity of their current condition, etc., is important in terms of determining the reinforcing methods to be applied to the system. Due to incorrect subsoil exploration, design defects or unpredictable conditions, excessive settled pile foundations may be encountered in the field. In this study, firstly, the load distribution mechanism between the piles of pile foundations sitting within the permissible limits was investigated.

Then, under the same conditions, the load distribution between piles in case of excessive settlement and a change of load distribution between settlement and piles were investigated. There was also determine the load-bearing mechanisms of pile foundations in the case of excessive settlement. So, it is thought that this study will be an example for the reinforcement of pile foundations or for the evaluation of bearing capacity after failure in similar conditions.

In most of the model experimental studies in the literature, cohesionless soils with a grain size smaller than 1mm were used [20,21,22,23,24,25,26,27,28,29,30]. However, in nature, the soils are mostly composed of clay and sand mixtures. For this reason, experiments were carried out on sand and clay mixtures which were consolidated with three different consolidation pressures in this study.

2. Test system and Properties of the Materials Used in Tests

2.1. Properties of Soils Used in Experiments

In order to determine the index properties of the soil, tests were carried out in accordance with ASTM C127-15, 2013; ASTM D 854-14, 2014; and ASTM D422- 63(2007)e2, 2007 standards [31,32,33]. Shear box tests were carried out on consolidated soils in accordance with ASTM D3080-03, 2004 Standard and the strength parameters of the soil were determined [34]. Experimental results are given in

Table 1. Index properties of the test soil.

Index Properties
Liquid Limit (%)	22%
Plastic Limit (%)	11%
Plasticity Index (%)	11%
D10 (mm)	0.35
D30 (mm)	0.018
D60 (mm)	0.19

and

Table 2. Index Properties and Strength Parameters of Soils Used in Experiments.

Parameters	Consolidation Pressure
	100 kPa	200 kPa	300 kPa
Density, γn (kN/m3)	16	16.5	17.2
Cohesion, c (kN/m2)	3	5	10
Angle of internal friction, φ (°)	33	36	38
Water content, w (%)	16.74	16.20	15.44

and in Figure 1.

2.2. Description of the Model Test System

In model tests, the dimensions of the test tank and the radius should be determined so that the boundary effects will have the least effect on the test results. In the literature, many studies have been carried out on the selection of the dimensions of the raft and the test tank in order to ensure semi-infinite medium conditions where the boundary effects do not change the experimental results. As a result of these studies, if there is a 2B (B is the dimension of the foundation) gap between the edge points of the foundation and the tank sides, the boundary conditions will not affect the test and thus semi-infinite conditions will be provided [20,21,24,25,35,36]. In this study, as seen in Figure 2, the dimensions of the test tank were determined by considering the boundary effects. Thus, the diameter of the raft foundation was determined as 12 cm, since the diameter of the experiment tank was 60 cm, in order to provide semi-infinite conditions.

Due to the stress-dependent soil properties, it is important to accurately model the prototype stress conditions in small-scale modeling experiments. One of the common ways to apply gravity (g) in model experiments is re-establish full-size stress levels. Details of the rules and modeling practice used in laboratory modeling can be found in Wood [37]. Information about the scaling laws used in this study is given in

Table 3. Scaling laws.

Physical Parameters	Scaling Factor (Model/Prototype)
Gravity (m/s2)	1
Force (N)	1/n3
Length (m)	1/n
Displacement (m)	1/n2-α
Area (m2)	1/n2
Stiffness (N)	1/n α
Strain	1/n1-α
Density (kg/m3)	1
Stress (kPa)	1/n
α	1

.

In this study, the in-plane strain condition of the test system was assumed. According to the scaling law given in Table 3, the dimensions of the test system were similar in all experiments with the exception of the foundation and soil types. While foundation and pile diameter were, respectively, 120 and 8 mm (the equivalent in the prototype was 12 and 0.8 m), the thickness of the soil layer was constant and 900 mm (the equivalent in the prototype was 90 m). The width of the system was 600 mm (the equivalent in the prototype was 60 m).

2.3. Test Tanks

Test tanks were designed in such a way that the consolidation and loading tests were carried out in the same tank. In the experiments, the aim was to examine the behavior of three types of piled raft foundations on consolidated soils at 3 different consolidation pressures. Details of the test tanks are shown in Figure 2.

2.4. Raft Foundations (Pile Caps)

Three different foundation types were used to examine the effect of pile spacing on the pile load distribution. Details of raft and pile spaces are shown in Figure 3. The manufactured piled raft foundations are seen in Figure 4a. A hydraulic piston with a capacity of 50 kN was used in the loading tests of the model foundations. The loading system consists of a loading frame fixed on 2 thread-adjustable rods and a unit in which the hydraulic piston was controlled. The loading speed in the experiment can be adjusted at the desired value using the control unit. Loading test system can be seen in Figure 4b.

2.5. Model Piles

The main purpose of this study was to determine the load distribution ratio between the piles. In this study, the interaction between pile material and soil was not investigated. In the literature, St37 class steel was used as the material for modeling piles and raft plates in the experiments. The diameter of the piles used in the experiments is D = 8 mm and their length was L = 280 mm.

2.6. Experimental Procedure

The soil used in the pile raft foundation tests was prepared at a water content of 33% (w = 1.5xw_L), filled into tanks. The purpose of preparing the test soil with a water content of 33% was to form the mixture homogeneously and to obtain a slurry (fluid) consistency and place it in the test tanks without air bubbles. Then, the soils placed in the tanks were consolidated under pressure of 100, 200, 300 kPa. Thus, 3 soils with different strength parameters were obtained. The consolidation process was carried out by transferring the air pressure to the inner tube and expanding the inner tube with the effect of pressure. As shown in Figure 5, this inner tube, placed between the lid of the test tank and the consolidation piston, consolidates the soil by creating pressure. As a result of the consolidation, the pressure of the inner tubes began to decrease due to the settlement on the soil. In order to prevent this situation, the pressure of the inner tube was kept constant with the air regulator.

In field applications, piles are driven into the soil using diesel hammers, vibro hammers that apply vibration or pistons that apply hydraulic pressure, depending on the diameter or cross-section shape of the pile. In the experimental study, the piles were pushed into the soil at a rate of 1.5 mm/min as shown in Figure 6.

In order to determine the load distribution between piles, strain gauge was installed on each pile and half Wheatstone bridge was used to connect to the datalogger. Strain gauges were fixed on the piles as shown in Figure 7a and calibrated in the unconfined compression test equipment. The loads on the piles were measured and recorded using 6 strain gauges in all experimental stages. The placement of strain gauges on the foundations can be seen in Figure 7b. As can be seen in Figure 7b, strain gauges were installed on all piles in symmetrical condition and the load carried by each pile was measured. The loads obtained from these strain gauges were compared with the total load measured with the s-type load cell and the proportional load carried by each pile was determined as in Equation (1).

$${\mathrm{Total} \mathrm{Load} }_{(\mathrm{measured} \mathrm{by} \mathrm{S}-\mathrm{type} \mathrm{load} \mathrm{cell})}{=\mathrm{S}1+\mathrm{S}2+\mathrm{S}3+\mathrm{S}4+\mathrm{S}5+\mathrm{S}6+\mathrm{S}2}^{’}{+\mathrm{S}3}^{’}+\mathrm{S}4’$$

(1)

Here, S1, S2 … S6 are the loads measured with strain gauges as seen in Figure 7b, and since S2′, S3′, S4′ are symmetrical to S2, S3, S4, these values are considered the same.

After the piles were driven, the leveling condition of the model foundation was checked so that the vertical loads would not affect the foundation eccentrically, and the load distribution between the piles was determined by applying static vertical loads to the foundation. During the experiment, data obtained from 6 strain gauges, 2 LVDTs and 1 S-type load ring were recorded via data logger. During the loading tests, LVDTs were used in order to measure the settlements occurring on the pile raft foundation. Pile loading speed was applied as 1.5 mm/min in all experiments.

3. Results Obtained from Experiments

When the data obtained as a result of the experiments were examined, the load distribution between piles in small settlement, similar to the results of the studies in the literature, as seen in Figure 8a, showed that corner piles carried more load compared to the center piles. In the case of excessive settlement conditions, the corner piles carried less load than the center piles, as in Figure 8b.

The load settlement graph obtained as a result of loading the piled raft foundation is as in Figure 9. In this figure, as a result of loading, the bearing capacity of the piled raft foundation and the failure point is clearly seen. The variation of the q_cor/q_cen ratio with the settlement amount is as shown in Figure 10. As seen in the figure, corner piles carried a higher load than the center pile at small settlement values. However, as the settlement value increases, this situation was reversed. The graph in Figure 10 was obtained by taking the average of the q_cor/q_cen ratio obtained as a result of the experiments performed on all foundation types and soils used in the study.

The q_cor/q_cen ratio obtained from other studies in the literature and the q_cor/q_cen ratio obtained as a result of this study are given in

Table 4. Comparison of the q_cor/q_cen ratio of this study and the other studies.

Studies in the Literature	Analysis Method	qcor/qcen
Katzenbach et al., [4]	Experimental and numerical	3.50
Mandolini et al., [5]	Experimental	1.60
Sanctis and Russo, [6]	Experimental	2.10
Shulyat’ev and Kharichkin, [7]	Experimental and numerical	2.40
Dai et al., [8]	Experimental	3.10
Katzenbach and Moormann, [9]	Numerical	2.10
Small and Zhang, [13]	Numerical	1.70
Hamderi, [15]	Numerical	4.40
This Study	Experimental	1.25

at small settlement values.

Corner and center pile load-bearing ratios (q_cor/q_cen) are shown in detail in Figure 7b and Figure 11 in cases where the settlement amount increases. In Figure 11, the corner pile (S1) started to carry a higher load than the center pile (S6) in the initial state where the settlement values were small. However, as the amount of settlement with the load increased, the foundation failure and the center pile (S6) started to carry more load compared to the corner pile (S1).

As can be seen from the test results, as the soil consolidation pressure increased, the corner piles started to carry more load than the center piles at small settlement amounts. However, when the settlements after failure were examined, it was observed that the corner piles started to carry less load than the center piles.

In the experiments, it has been observed that the soil between the piles behaves like a block and moves as if it is a single piece in the soil. As seen in Figure 12, there are studies in the literature in which the block effect was detected (Taylor et al., 2013).

After loading, a fracture surface forms around the block, and this causes the soil between the piles to behave like a block. This fracture surface become evident when the piled foundation begins to experience excessive settlement. Therefore, no fracture surface is formed around the block before the failure and the corner piles carry a higher load than the center ones. As seen in Figure 13a, it has been observed that no blocks are formed in the pile foundations that settle within the allowable limits and the piles can be withdrawn without breaking the soil. However, in the case of excessive settlement, it was determined that the block was formed, and a fracture surface was formed around the pile as seen in Figure 13b. While the piles were being pulled out of the soil, the block fracture surface formed around the piles was checked and this situation was clearly observed (Figure 13c). Due to this fracture surface formed around the block, the bearing capacity of the corner piles is reduced compared to the center piles.

As the consolidation pressure increases, the water content of the soil decreases and the soil becomes more friable (brittle, solid) and loses its elasticity. For this reason, the soil behaves more brittle under load, and at low deformations, the fracture surface is formed and collapse occurs. As a result of consolidation, the soil’s strength increases as the water content of the soil decreases, and it carries more load at lower deformations. However, due to the solidified soil, the effect of the block behavior in piled foundations increases and the q_cor/q_cen ratio decreases as the settlement increases, inversely proportional to the settlement amount.

This situation is clearly visible in Figure 14. Depending on the increase in consolidation pressure in each foundation type, soil strength parameters have improved, the settlement amount of the pile foundation has decreased and the total bearing capacity has increased.

In the case of excessive settlement, as the total bearing capacity of the foundation increased, the bearing capacity of the corner piles decreased due to the block effect, while the bearing capacity of the center piles increased (for these reasons q_cor/q_cen ratio decreased).

In all experiments, nine piles were used, and the experiments were carried out by changing only the distance between the piles. For this reason, as the distance between the piles increased, this caused an increase in the block volume. Thus, the total bearing capacity of the foundation increased. However, in the case of excessive settlement, as the distance between the piles increased, the q_cor/q_cen ratio decreased. As pile space increased from 2D to 4D, the q_cor/q_cen ratio decreased by 18.6%. The change of the pile space and the q_cor/q_cen ratio is as shown in Figure 15.

4. Conclusions

In this study, similar to previous studies, it was determined that corner piles carry more load than center piles at small settlement values.

In pile raft foundations, as the settlement amount increases, center piles start to carry more load compared to corner piles.

In the experiments, it has been observed that the soil between the piles behaves like a block and acts as a single piece in the soil. This block is caused by a fracture surface formed around the pile group after loading. This fracture surface becomes evident when the pile foundation starts excessive settlement.

In pile raft foundations after excessive settlement, failure occurs first in the corner piles. Therefore, in allowable settlement conditions, the pile raft foundations should be designed by taking the bearing capacity of the corner piles into consideration.

After failure caused by excessive settlement, the load carried on the corner piles should be taken into consideration and failure analyses of the structure should be carried out accordingly.

Another result is that the center piles have a higher bearing capacity than the corner piles in case of failure due to excessive settlement.

As the consolidation pressure increases in cohesive soils, the soil becomes brittle; therefore, failure occurs at smaller settlement values in soils consolidated under high pressure.

Similar to other studies in the literature, for soils which consolidated at low pressures, center piles carry more load compared to the corner piles in allowable settlement limits. However, as the consolidation pressure increases, corner piles start to carry more loads than the center piles.

As the space between piles increases in case of excessive settlement, the amount of load carried by the center pile increases. However, the effect of the increase in the space between the piles on the q_cor/q_cen ratio decreases after a certain value.