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It is very necessary to research the bearing characteristics of composite pile group foundations with long and short piles under lateral load in loess areas, because these foundations are used widely. But few people researched this problem in loess areas up to now worldwide. In this paper, firstly, an indoor test model of a composite pile foundation with long and short piles is designed and then employed to explore the vertical load bearing characteristics and load transfer mechanisms of a single pile, a four-pile group, and a nine-pile group under different lateral loads. Secondly, ANSYS software is employed to analyze the load-bearing characteristics of the test model, and for comparison with the experimental results. The results demonstrate the following. (1) The lateral force versus pile head displacement curves of the pile foundation exhibit an obvious steep drop in section, which is a typical feature of piercing damage. A horizontal displacement limit of the pile foundation is 10 mm and 6mm for the ones sensitive to horizontal displacement. (2) The axial force along a pile and frictional resistance do not coincide, due to significant variations and discontinuities in the collapsibility of loess; a pile body exhibits multiple neutral points. Therefore, composite pile groups including both long and short piles could potentially maximize the bearing capacity and reduce pile settlement. (3) The distribution of stress and strain along the pile length is mainly concentrated from the pile head to a depth of about 1/3 of the pile length. If the lateral load is too large, short piles undergo rotation about their longitudinal axis and long piles undergo flexural deformation. Therefore, the lateral bearing capacity mainly relies on the strength of the soil at the interface with the pile or the horizontal displacement of the pile head.

Pile foundation is one of the most common deep foundation forms employed for supporting superstructures in collapsible loess regions. Significant achievements have been made in the selection of pile foundations [

Research regarding composite pile foundation with long and short piles has typically focused on single pile deformation characteristics under vertical loading and has employed numerous research methods including theoretical analysis, field or laboratory test, and numerical simulation. However, the extent of research focused on pile groups is considerably less. S.C.Wong et al. [

This paper presents the design of an indoor composite pile foundation test model with long and short piles. The model was employed to explore the vertical load bearing characteristics and load transfer mechanism of pile groups composed of a single pile, four piles, and nine piles under different lateral loads. The ANSYS finite element software was employed to analyze the load-bearing characteristics of the test model, and comparisons verify the feasibility of applying composite pile foundations with long and short piles in loess areas. The findings of this study can provide guidance for pile foundation optimization in loess areas.

Experimental testing employed the cubic model enclosure illustrated in Figures

Physical parameters of loess.

| | | ^{3}) | |
---|---|---|---|---|

2.71 | 16.3 | 29.5 | 1.76 | 12.7 |

Plane arrangement of the test model.

Elevation arrangement of the test model.

Strain testing of the model piles was conducted using foil type resistance strain gauges. A pair of resistance strain gauges was symmetrically placed evenly along the length of the piles, beginning with the bottom, to ensure the accuracy of the measurement results. As illustrated in Figure

Arrangement of strain gauges on the short and long piles.

Short pile

Long pile

Testing was conducted using a pseudo-static loading test system. A 30 t load sensor was positioned on the top surface of each pile to measure the vertical load, and a 2 cm thick steel plate was placed over the load sensors on the top surfaces of the piles. In order to make level, cushion sandbags were placed between the load sensor and pile head. Vertical settlement and horizontal displacement of the pile top were measured by displacement sensors. A hydraulic jack with a digital display was employed for applying the vertical load. To guarantee the stability of the vertical load, testing was suspended momentarily to ensure an accurate loading due to the settlement of the pile foundation.

Horizontal load testing was conducted for a single pile, four piles, and nine piles using the apparatus shown in Figure

Image of testing facility.

Applied at the top of the pile under 0.8 times vertical ultimate bearing capacity, single pile (#2 and #7 piles), four-pile (#4, #5, #9, #10 piles), and seven-pile (#1, #3, #6, #8, #11~#13 piles) side sway displacement S of pile top change with horizontal thrust F curve is shown in Figure

Relations between the horizontal load

Single pile

Four-pile group

Seven-pile group

The displacements S of the pile head/s with respect to the applied horizontal load to the single pile, four-pile group, and seven-pile group are shown in Figure

We observed that the short piles within a pile group are damaged with increasing horizontal loading prior to the long piles, and the short piles may be under a normal load when they are damaged. Displacement is an important factor affecting the bearing capacity of pile foundations; however, testing was discontinued after the head of the short piles exceeded the 2 cm displacement limit, even though the long piles or the overall pile structure had suffered no damage. For loess areas that lack static load test of pile group level, in conjunction with the current “technology code for building pile foundations” (JGJ 94-2008), a horizontal displacement limit of 10 mm is recommended; that for horizontal displacement sensors is 6 mm. Therefore, big thickness of loess foundation and bearing capacity of pile foundation design are not only the design standards and should be combined with regional experiences. Pile foundation design shall provide an adequate pile length-diameter ratio according to the requirements of the upper structure and the tensile strength of piles with consideration for permissible pile displacement values. To control the horizontal displacement, crack width limited, the deformation of the upper part of the pile foundation must be reduced by various measures such as increasing the pile reinforcement and improving the strength of the concrete.

Figure

Relations between the axial forces acting on a pile with respect to location H along the length of the pile for various horizontal loads.

#2 pile (single pile)

#7 pile (single pile)

#5 pile (four-pile group)

#10 pile (four-pile group)

#1 pile (seven-pile group)

#8 pile (seven-pile group)

These results differ from the axial force distribution of an in situ uniform loess foundation. Under in situ conditions, the vertical and horizontal loads are simultaneously brought to bear at the top of the pile. Moreover, the stiffness of pile end soil is small, and pile modulus is bigger. As a result, a stress concentration is easily produced, and the contact areas between the pile and surrounding soil gradually form a plastic zone. The upper portion of the pile body is firstly deformed and produced downward displacement of soil. The relative displacement between the pile and surrounding soil produces a frictional resistance at the pile-soil interface. The process of load transmission downwards along the pile body overcomes the frictional resistance, and in the diffusion process of passing it to the soil, which results in a decreasing axial force along the depth of the pile. The rate of attenuation in the axial force acting on the pile is not uniform. An increasing frictional resistance of the surrounding soil causes a more rapid decay in the axial force. This is equivalent to the change in the transverse compactness of the artificial layered fill employed in the model experiments.

Comparing the long and short piles under different horizontal loads, the long piles bear the majority of the load, but, because the length-diameter ratio is greater than that of the short piles, smaller stiffness and inflection appear, and the stress is more complicated. Compared with the single pile cases, the axial force distributions of the pile groups under the application of a horizontal force and transfer are more complicated and involve interactions between the piles and the soil surrounding the piles. The horizontal bearing capacity is related to strength of materials, the lateral resistance of the soil and foundation forms, and other factors. For example, because the tensile strength of concrete is far lower than its compressive strength, with increasing horizontal load, the pull part of the pile side appears fracture damage caused by a lack of tensile strength. Therefore, there is the possibility of cross-sectional tensile damage under the condition of small displacements and angle displacement.

Figure

Relations reflecting the frictional resistance f between the piles and surrounding soil with respect to H for various horizontal loads.

#2 pile (single pile)

#7 pile (single pile)

#5 pile (four-pile group)

#10 pile (four-pile group)

#1 pile (seven-pile group)

#8 pile (seven-pile group)

In addition, although the magnitude of negative frictional resistance obtained from the test results is between 4 and 50 kPa, which is largely commensurate with the negative skin frictional resistance of collapsible loess obtained in field tests (14.2-54.0 kPa), our results present at least two neutral points of pile. If we continue to apply the experience that the largest depth of neutral point is the bottom depth of collapsible loess, obviously, it does not accord with our findings here. The filled soil in model enclosure is distributed in sandwich layers interactively, whose collapsibility is discountinuous, which is same as the actual situation. Especially there is possibility that the non-collasiblity of large thickness loess layer changes to collapsiblity, which caused by the reshape of the surrounding soil, leading to compressive deformation by pile driving or transmission of upper load. Therefore, pile lengths and pile foundation design should be taken seriously.

According to the strain measured by the test, the moments of each section of the piles can be obtained by using the bending theory of material mechanics, as shown in Figure

Moments along pile depth under the different horizontal load.

#2 pile (single pile)

#7 pile (single pile)

#5 pile (four-pile group)

#10 pile (four-pile group)

#1 pile (seven-pile group)

#8 pile (seven-pile group)

Figure

The composite pile foundation with long and short piles shown in Figure

Model parameters employed in finite element analysis.

| | | | ^{3}) | |
---|---|---|---|---|---|

Pile | 30,000 | 0.2 | - | - | 2,600 |

Soil layer | 70 | 0.34 | 35 | 24 | 1,700 |

3D model of the long-short pile composite foundation.

In the first step, only gravity was applied, without any other load. Then horizontal loading was separately applied to the single pile (#2 or #7), four-pile group (#4, #5, #9, and #10), and nine-pile group (#1-#3, #6-#8, and #11-#13) for different conditions, when a vertical load was forced that was 80% of the ultimate bearing capacity of the piles.

The strain contours of pile bodies are shown in Figure

Strain nephograms of piles under different horizontal loads.

#2 single pile

#7 single pile

Four-pile group

Nine-pile group

Owing to space limitations, we examine the displacement

Displacement S with respect to H for the nine-pile group under different horizontal loads.

#1 pile

#8 pile

Displacement comparison of pile between the numerical and experimental results

In conclusion, the material strength of the individual piles was eventually exceeded by the applied horizontal loading and produced lateral deformation. The interplay of lateral forces between the piles and their surrounding soil represents a complex interaction. As pile body deformation gradually increases with increasing horizontal load, the stress eventually exceeds the allowable limit or the surrounding soil loses its stability and yields. Even if the pile body strength was sufficient to accommodate the high-stress conditions, the loss of soil stability or pile displacement exceeding specifications would lead to pile foundation damage. Therefore, the horizontal bearing capacity is mainly controlled by the strength of the soil surrounding the piles or the extent of horizontal displacement of the pile head, which are more likely to occur in areas prone to collapsible loess. All these factors should be considered in the design, construction, and use of composite pile foundations with short and long piles.

Figure

Stress nephograms of piles under different horizontal loads.

#2 single pile

#7 single pile

Four-pile group

Nine-pile group

Axial force distribution with respect to H for the nine-pile group under different horizontal loads.

#1 pile

#8 pile

Axial comparison of Pile 1 between the numerical and experimental results

Axial comparison of Pile 8 between the numerical and experimental results

The results in Figures

(1) Under the application of different horizontal loads, the F-S curves of the pile foundation exhibited an obvious steep fall in the section, which is a typical feature of piercing damage. Short piles were observed to suffer damage with increasing horizontal loading prior to long piles. A horizontal displacement limit of the pile foundation is 10 mm and 6mm for the ones sensitive to horizontal displacement.

(2) The play of pile axial force and pile-soil interfacial frictional resistance with asynchrony: the pile-soil interfacial frictional resistance under different horizontal loads ranged from 30 kPa to 70 kPa. The magnitude of the negative skin frictional resistance ranged between 4 and 50 kPa. There are multiple nuetral points along pile bodies because the soil interlayers surrounding piles distribute interactively and the distribution of collapsibility is discountinous, which leads to the determination of the lower limit depth is complex in collapsible soil layer. So the design thought applying long-short composite pile foundation conforms to the principle of settlement reducing pile.

(3) Pile body stress and strain are mainly concentrated between the pile head and about one-third of the pile depth. Beginning at a particular depth along a short pile, the pile body will rotate about its longitudinal axis, and the integrity of the pile foundation will be reduced to below acceptable limits when the displacement becomes too large. For the long piles, the pile bodies undergo flexural deformation, and the pile body will suffer damage due to bending when the pile body displacement and bending moment increase beyond acceptable limits. The horizontal bearing capacity is mainly controlled by the strength of the soil surrounding the piles or the extent of horizontal displacement of the pile heads.

(4) The finite element analysis results of the pile foundation were in good agreement with the results of the experimental model testing. Especially the pile-soil contact surface is simulated with nonlinear shear spring elements, which can provide a useful example for future engineering design.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no financial and personal relationships with other people or organizations that can inappropriately influence their work; there is no professional or other personal interest of any nature or kind in any product, service, and/or company that could be construed as influencing the position presented in, or the review of, the paper entitled.

This work was supported by the National Science Foundation of China “Theoretical analysis and testing study on row pile supporting with pre-stressed anchors for deep foundation pit” (No. 51568042) and Program for Changjiang Scholars and Innovative Research Team in University (No. IRT_17R51). We thank LetPub (www.letpub.com) for its linguistic assistance during the preparation of this manuscript.

Supplementary Materials description: 1, e.g., #5: relations between the horizontal load F and the displacement of the pile heads S for the pile groups considered. 2, e.g., #6: relations between the axial forces acting on a pile with respect to location H along the length of the pile for various horizontal loads. 3, e.g., #7: relations reflecting the frictional resistance f between the piles and surrounding soil with respect to H for various horizontal loads. 4, Fig. 10: displacement S with respect to H for the nine-pile group under different horizontal loads. 5, e.g., #12: axial force distribution with respect to H for the nine-pile group under different horizontal loads.