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 CHEMICAL ENGINEERING TRANSACTIONS  
 

VOL. 59, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Zhuo Yang, Junjie Ba, Jing Pan 
Copyright © 2017, AIDIC Servizi S.r.l. 
ISBN 978-88-95608- 49-5; ISSN 2283-9216 

Research on Damage Repair and Reinforcement of Deep 

Foundation Pit Support Structure Based on Fractal Dimension 

Theory 

Jun Li, Feng Jin, Yongzheng Ma 

School of civil and transportation engineering, Ningbo University of Technology, Ningbo 315211, China 

JunLi@126.com 

Foundation pit engineering refers to the excavation in the ground below the underground space and its 

supporting support system. The foundation pit support is used to ensure the excavation of the foundation pit, 

the smooth construction of the foundation and the safety of the surrounding environment. The support and 

reinforcement measures are also used for the side wall safety of the foundation pit and the surrounding 

environment. With the rapid development of China's high-rise buildings, deep foundation pit support is the 

current construction of a wide range of important applications. This has a direct impact on the safety and 

quality of construction. Therefore, it is of great significance to strengthen the research on the damage of deep 

foundation pit support. This paper introduces a kind of repair and reinforcement of deep foundation pit support 

which is based on fractal dimension theory. According to the complex environmental effects of foundation pit 

engineering, the reinforcement of foundation pit support should not only ensure the safety and stability of the 

foundation pit itself, but also effectively control the movement of the surrounding strata and protect the 

surrounding environment. 

1. Introduction 

The foundation pit engineering is an important research direction in the current foundation of our country. 

However, with the development of China's construction industry, the emergence of high-rise buildings in the 

city has greatly promoted the theory of deep foundation pit engineering design and the development of deep 

foundation pit engineering (Kayan et al., 2017). In the end of the 1980s, Construction technology continues to 

develop, but also has produced a large number of deep foundation pit support design and construction 

problems. A lot of engineering practice show that the most dangerous stages of many projects are not 

necessarily in the normal use stage, but in the construction stage and the aging stage (Sheng et al., 2017). 

Many engineering accidents often occur in the construction phase, the reason is that the construction quality is 

not guaranteed, the construction method of unreasonable changes, one of the important reasons is fit to the 

environment, geology, load and other factors. Because we lack of design, construction is caused by some 

mistakes and omissions.  

Deep foundation pit engineering is a comprehensive technology related to many factors, and it is also a 

systematic engineering problem (Ursyn, 2015). Deep foundation pit has a wealth of construction experience. 

Combined with the proposed site of the soil and the surrounding environment, it is closely related to site 

engineering survey, support structure design, construction excavation, foundation pit stability, precipitation, 

construction management, on-site monitoring and mutual construction of adjacent sites. Many complex 

problems are related to geological conditions, geotechnical properties, geotechnical properties, site 

environment, engineering requirements, climate change, groundwater dynamics, construction procedures and 

methods which are the comprehensive technical disciplines and theoretically perfect, mature (Boje et al., 

2016). The premise of guaranteeing stability is also an important problem of foundation pit. Therefore, in the 

foundation pit engineering design and construction, the need is rigorous, careful analysis and calculation. 

For decades, the existing foundation pit support frame structure is more and more reinforced by the relevant 

scientific research and engineering technical personnel attention, which has played a great role in promoting 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1759075

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Jun Li, Feng Jin, Yongzheng Ma, 2017, Research on damage repair and reinforcement of deep foundation pit 
support structure based on fractal dimension theory, Chemical Engineering Transactions, 59, 445-450  DOI:10.3303/CET1759075   

445



the development and application of frame structure reinforcement technology (Verdiere et al., 2014). At the 

same time, people are accustomed to the existing reinforcement method, and the foundation pit support 

structure reinforcement project is often on the matter, the lack of deeper theoretical research, so that the level 

of reinforcement technology helps to improve unhappy. Chinese foundation pit support frame structure 

reinforcement method has formed a more systematic, supporting the construction technology and technology. 

But in general, the construction technology and technology is still relatively backward (Barceló et al., 2015). 

Such as carbon fibre as the representative of the new material in the reinforcement project has not yet 

universal application, and its related design, construction, there are still many problems. Secondly, compared 

with foreign developed countries, China's testing equipment, the technical level is relatively low, in the 

detection software and equipment systems, there is a big gap (Ai, 2016). Therefore, the theory of 

reinforcement and damage of foundation damage is also of great practical significance. 

2. Research on foundation support based on fractal dimension theory 

The method of meta-fractal dimension has more research on geomorphic features, but less in damage of 

foundation pit structure. In this paper, the method of elemental fractal analysis is introduced into the degree of 

repair and reinforcement of the damage of foundation pit. The basic starting point of the element fractal model 

is that for each spatial element of the fractal object (Shao, 2016). The closer the spatial nature is, the more 

similar. In the process of damage repair and repair of the foundation pit structure, the closer the distance is, 

the more the choice of travel choice is. In order to describe the change of the damage of the foundation pit 

structure, the local difference of the research target and the continuity of the whole dimensional model of the 

analytical ideas are necessary (Xu et al., 2012). In the development of the elemental fractal dimension theory, 

the expression of the "sliding window" theory evolution grid is divided into the square grid with the length of r 

along the x and y axes according to the projection area within the land use research. The object of this paper 
is not limited to the target itself, but rather to the surrounding area adjacent to the target which is also included 

in the scope of the study. 

First, the range is divided into the square grid with the length of r, and the grid is used as the local object (the 
grid), and the characteristic value of the object is represented by the feature of the neighboring grid (Xiao et al., 

2016). The degree of damage to the foundation pit structure of each grid is related to the grid which adjacent 

to its surroundings, using the repair degree of damage to the foundation pit structure of the adjacent grid of the 

target grid. 

 

  
(a)                                                                            (b) 

Figure 1 Mesh area and edge area of the grid calculation 

3. Model establishment 

3.1 Stability analysis of foundation pit 

In the excavation of the foundation pit, due to the excavation of the soil in the pit, the stress field and the 

deformation field of the foundation are changed, which may lead to the instability of the foundation pit. So the 

overall pit or local landslide, foundation pit uplift and piping lead to engineering accidents (Otto et al., 2015). 

Therefore, in the design of foundation pit support, the need to check the stability of the foundation pit, if 

necessary, should take appropriate measures to strengthen the prevention, so that the stability of the 

foundation pit has a certain degree of security (Chen et al., 2015). We can ensure the safety of the entire 

excavation process. 

Horizontal rib configuration gives us the horizontal ribs minimum rate requirements.  

%1.030027.124.024.0 
yty

fff
  (1) 

446

https://www.ncbi.nlm.nih.gov/pubmed/?term=Xu%20Y%5BAuthor%5D&cauthor=true&cauthor_uid=22238682
http://www.mitpressjournals.org/author/Otto%2C+A+Ross


When h ≥ 800mm, and s=200mm, so Asv=565mm2 

Table 1: Reinforcement Chart See 

Type of reinforcement Level The real value of steel Calculated area (mm2/m) 

Longitudinal reinforcement in HRB335 D25@150 3272[2593] 

Longitudinal reinforcement out HRB335 D25@150 3272[2593] 

Horizontal reinforcement HRB335 D12@200 565 

Tie bar HPB235 d6@100 283 

3.2 Foundation stability of the anti-uplift 

The bottom surface of the wall as the ultimate bearing capacity of the reference plane, slip line shape see the 

calculation diagram, with reference to Prandtl foundation bearing capacity formula. Regardless of the size of 

the foundation pit (Liu et al, 2015). 

Figure 2 for the calculation and analysis of the diagram: 

 

H
D

B

A

B

D

q

τ

  

Figure 2: For the calculation and analysis of the diagram: 

Calculation and analysis diagram is shown as follows. 

qDH

cNDN
K

c






)(
1

q2



  (2) 

D - Wall depth (m); H - Excavation depth (m); 𝛾1,𝛾2 - Wall lateral and bottom soil gravity (kN/); 

q - Bottom Overload (kN /m); Nc, Nq - The coefficient of foundation bearing capacity. 

With Prandtl formula, Nc, Nq respectively means in forma (3). 

















 

tg

N
N

etgN

q
c

tg

q

)1(

)
2

45(
02

 (3) 

Using this method to check the anti-uplift safety factor, the requirement is Ks≥1. 10~1.20. Note: The safety 
factor from the "construction pit engineering technical specifications". 

Calculation process is as follows. 

mH 4.17  mD 9.11  kPaC 4.33  
0

1.24
  

0
1.2402

)
2

1.24
45(

tg

q
etgN



61.9  (4) 

447



0
1.24

1

tg

N
N

q

c




 25.19   (5) 

When the anti-uplift safety factor is checked by this method, it is assumed that the outer side of the wall and 

the bottom of the pit are heavy and due to the shearing strength 𝛾1 = 𝛾2 = 30𝑘𝑃𝑎 of the AB surface. 

Solutions have to satisfy with K=4.48>1.10~1.20. 
We can fulfill requirements. 

3.3 Estimation and control of foundation pit damage by fractal dimension theory 

Deep excavation should not only ensure the safety and stability of the foundation pit itself, but also effectively 

control the displacement of the foundation around the foundation pit and ensure the surrounding environment. 

The ground pit around the traffic is busy, and the geological conditions are poor, it is necessary to do strict 

control of the deformation of the foundation pit, that is, deformation estimation and deformation control. 

The excavation depth of the foundation pit is 17.4m. 

1) Horizontal displacement estimation 


DB

LH

10

2

 8.0
8.09.1110

604.17
2





 mm65.152

  
(6)

 

H—Depth of excavation; B—Wall thickness; D—Retaining wall depth; L—Section excavation length; δ –
Displacement wall factor, selection is 0.8 

2) Estimation of foundation pit uplift 

According to the actual situation, using Tongji University proposed simulation test empirical formula: 

  54.004.0
5.0

3.55.12167.017.29












  tgc

H

D
H

  (7) 



P
HH 

  (8) 

δ- foundation pit uplift; H - depth of excavation; P - the bottom of the pit is overloaded; 

c,φ,γ - cohesion of soil, internal friction angle, bulk density D - continuous wall depth. 

δ=-29.17-0.167×18.1×18+12.5×1.21+5.3×18.1×0.86×1.54=61.43mm  

4. Results and discussion 

In the construction project, the foundation pit support frame structure is one of the relatively wide application 

forms. From the middle of the last century, the frame structure has been widely used. The purpose of 

strengthening the existing frame structure is used to improve the strength, stiffness, ductility, stability and 

durability of the frame structure. And the existing foundation pit support frame structure helps to take the 

corresponding reinforcement measures which can reduce a lot of infrastructure investment and bring huge 

economic social benefits (Maksimović et al., 2017). At the present stage, with the deepening of the research 

on the structural reinforcement of the building, the method of strengthening the foundation pit frame structure 

is more. The reinforcement method commonly used in the project is as follows. 

1) Increased section reinforcement method 

Increasing the cross-section reinforcement method is a reinforcement method to increase the cross-sectional 

area of the support structure of the foundation pit or to increase the bearing capacity to improve its bearing 

capacity and to meet the normal use or to change its natural frequency. In this way, while the bearing capacity 

of the component is improved, the original strong beam weak column is changed to strong column weak beam 

to a certain extent. The results show that the increase of one or two closed stirrups in the core area will 

effectively reduce the cracking of the foundation pit support in the joint area, and it will also improve the 

seismic capacity of the joints. At the same time, the ductility of the components can be improved by the 

treatment of the encryption zone. To a certain extent, the cross-sectional size will use the space to reduce, 

and sometimes also be subject to restrictions on the use. 

2) Outsourcing steel reinforcement method 

Outer steel reinforcement method refers to the foundation pit support column or internal perfusion adhesive to 

achieve the overall force of a reinforcement method. Compared with the large section reinforcement method, 

the steel cladding method can make the original parts section basically unchanged, and the construction is 

convenient, but the bearing capacity of the foundation pit support can be greatly improved. 

448



3) Change the structure of the force system reinforcement method 

Change the structure of the force system reinforcement method that the middle part of the structural 

components to add fulcrums, joists or multi-span simple beam into a continuous beam and other methods. In 

the frame structure, the method is actually through the appropriate parts of the additional shear wall, the 

original frame structure into a framework - shear wall structure. The method of adding shear wall is a kind of 

reinforcement method which is widely used at present. When using this method, two aspects should be 

considered first. On the one hand, the position and quantity of the shear wall are determined, and then the 

new shear wall and the original frame structure. 

4) Pre-stressed reinforcement method 

Pre-stressed reinforcement method is the use of external pre-stressed steel rod or steel brace, so that the 

original structure or component of the force to improve or adjust the indirect reinforcement method. Reinforced 

frame beams with pre-stressing are already subjected to reinforcement and have been cracked before 

reinforcement. After the reinforcement of the pre-stressed rod, the crack of the original beam is reduced or 

even closed, and the original frame beam is generated to reverse the load deflection of the part of the original 

beam, thus improving the mechanical performance of the frame beam structure. 

5) Bonded steel reinforcement method 

Bonded steel reinforcement method is the use of high-performance steel structure which is bonded to the 

surface of the foundation support components, so that steel and foundation pit support helps to form a whole, 

we can strengthen and enhance the original structure of the effective improvement and bearing capacity. This 

reinforcement method construction period is short, sticky steel space is very small, almost no change in the 

original shape of the component (Yang, YY., 2015). The technology is mainly used in foundation pit support 

broken beam, broken column, shock absorption and lifeline building seismic reinforcement. 

6) Sticky carbon fiber cloth reinforcement method 

Carbon fiber reinforcement method is a new, high-tech structural reinforcement method. Carbon fiber strength 

is generally ten times the strength of ordinary steel, elastic modulus is several times the steel, is an excellent 

structural reinforcement material. So you can use high-performance structural adhesive to the carbon fiber 

material paste and the original component surface, to the original structural components of the reinforcement 

and improve the original components of the seismic performance. At the same time, carbon fiber 

reinforcement method has the characteristics of high strength and high efficiency, thin material, light weight, 

convenient construction and durable corrosion resistance. However, the use of carbon fiber reinforced method 

of adhesive performance requirements are relatively high, whether it is carbon fiber cloth or adhesive with a 

major dependence on foreign imports, the corresponding high cost, such as large-scale promotion of this 

method there are still some difficulties. 

7) Foundation pit support replacement technology 

When the beam, plate or column and other components of the foundation pit support strength can not m eet 

the design requirements or a lot of difference, can not meet the quality requirements of the pit support chisel, 

replaced with the requirements of the new pit support, for Beam plate as long as the set of templates and 

support, while adjusting the steel is easier to achieve. However, for the column, the whole root or a region, 

especially when it has been built above the multi-layer pillars, the pit support replacement is very difficult. So 

must do a good job supporting the design to meet the strength requirements at the same time should meet the 

requirements of stable deformation, the construction process must be monitored to ensure the absolute safety 

of the reinforcement process. And the replacement of the foundation pit support should be compared with the 

original building foundation pit support strength level, while the use of micro-expansion of the pit support. 

5. Conclusion 

Deep foundation pit is based on the construction of wide applications and its complex, variability. In the 

construction program which is not considered, it can easily lead to sudden problems, to the property and 

personnel security to bring a greater threat. This requires engineering staff according to the actual conditions, 

which is combined with engineering experience, the various possible support programs have to compare and 

optimize. In order to ensure the safety and applicability of the support structure in engineering applications, 

deep foundation pit excavation and support belongs to the underground structure of the construction 

mechanics category, the program design involves engineering structure, construction knowledge, and rely on 

experience which has technology and theory between the close combination. There are many ways to 

reinforce and repair the existing frame structure. The choice of reinforcement method should be based on the 

results of reliability identification and the characteristics of structure. The factors such as reinforcement effect, 

construction simplicity and economy should be taken into account. At the same time, the identification and 

reinforcement of the building is a long way to go, do a good job of each reinforcement project design and 

449



construction, to ensure the quality of reinforcement works, we engaged in building identification and 

reinforcement workers duty-bound. 

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