Theoretical solutions

In the past few decades, several practitioners and researchers have developed the predictive models for the estimation of frictional jacking forces based on the experiments or field monitoring data.

Scherle (1977) established the interface friction coefficients between concrete and asbestos cement pipes and various soil types based on data collected at field investigation. He classified the interface friction coefficients into three categories representing the state of motion of the pipeline: static friction, sliding friction and fluid friction (Dietrich Stein, 2005) and asserted that the frictional component of the jacking force was a function of the interface friction coefficient, multiplied by the unit weight of the soil, multiplied by the cover depth to the springline of the pipe, times a factor that was based on the state of stress in the soil. Values for the interface friction coefficient as established by Scherle are shown in Table 1.1.

Table 1.1 Interface friction coefficients summarized by Stein et al. (1989)

Pipe Material and Soil at Interface

Static Friction Interface Friction

Coefficient, μ

Sliding Friction Interface Friction

Coefficient, μ

Fluid Friction Interface Friction

Coefficient, μ Concrete Pipe on Gravel

or Sand 0.5 ~ 0.6 0.3 ~ 0.4 0.1 ~ 0.3

Concrete Pipe on Clay 0.3 ~ 0.4 0.2 ~ 0.3 0.1 ~ 0.3 Asbestos Cement Pipe on

Gravel or Sand 0.3 ~ 0.4 0.2 ~ 0.3 0.1 ~ 0.3

Asbestos Cement Pipe on

Clay 0.2 ~ 0.3 0.1 ~ 0.2 0.1 ~ 0.3

Weber (1989) established a calculation model that provided an upper bound for the interface friction value, using an interface friction value of 0.46, corresponding to an interface friction angle of 24.7 degrees, regardless of pipe material or soil type to provide a conservative value for predicted jacking forces. He also published a table of jacking stresses related to skin friction that were categorized by soil type (Staheli, 2006).

These values for jacking stresses were calculated post-construction from several microtunneling projects as shown in Table 1.2.

Table 1.2 Frictional jacking stresses for various soil types (Weber & Hurtz, 1981)

Soil Type Jacking Stress due to Skin Friction, kN/m²

Jacking Stress due to Skin Friction, tons/ft²

Gravel, sand 8.4 ± 2 0.087 ± 0.02

Loamy sand 9.3 ± 1 0.097 ± 0.01

Loam 7.3 ± 1 0.076 ± 0.01

Loam, stones 5.7 ± 4 0.060 ± 0.04

With the measurements of the normal loads on the pipes from the contact stress transducers, Milligan and Norris determined the soil-pipe interface friction angle at each of the sites.

The International Society for Trenchless Technology formed a working group in 1992 entitled Working Group No.3, which conducts technical research on microtunneling. At the time, the research statement was developed, the “type” was undetermined, and a statistical analysis of data from 398 projects was undertaken to find similarities in order to group the data by a “common variable.” The variables included machine type, soil type, soil removal system type, pipe diameter, cover depth, jacking length, and so on.

However, because all of the projects were analyzed together and none of the records were analyzed for construction problems or case history anomalies, the range of data scatter was extremely large and few conclusions could be obtained from the past study (Staheli, 2006). In 1999, Chapman and Ichioka (1999) revisited the work done by the ISTT working group and re-evaluated the data. They separated the microtunneling case histories into three categories by soil type: clay, sand, and sand with gravel. Then, they developed an equation for frictional resistance, P, which they related to the diameter of the pipe by the following equation:

𝑃 = 𝑎 + 0.38𝐷 Eq. 1.15

where, P – frictional resistance, tons/m²; a – intercept value for each soil type;

D – pipe diameter.

Table 1.3 shows the intercept value for predictive model proposed by Chapman.

Table 1.3 Intercept values “a” for Chapman and Ichioka predictive model

Soil Type Intercept value “a” for Chapman and Ichioka predictive model.

Clay Soils 0.153

Sand 0.243

Sand and Gravel 0.343

A series of field tests were conducted by the US Army Corps of Engineers in which instrumented test beds were constructed of four soil types, based on which Bennett (1998) developed a model for predicting jacking forces in both cohesive and granular soils, by considering the concept that the total jacking force is a function of the surface area of the pipe multiplied by a normal force and a friction coefficient. However, the normal force is not based on depth, but rather on the diameter of the pipe and the effective unit weight of the soil. In order to simplify, Bennett introduced an arching reduction factor, Ca, that is multiplied by the effective unit weight and the diameter and also the friction reduction factor, Cf, was introduced to relate the interface friction factor, μ, to the residual friction angle of soil, and then the upper bound, best-fit, and lower bound values were established for the arching and friction reduction factors for use in his proposed model. The Bennett’s predictive model can be expressed by the following equation:

𝐹_𝑟 = 𝐶_𝑎𝛾^′𝑑_𝑝𝑡𝑎𝑛 (𝐶_𝑓𝜙_𝑟)𝐴_𝑝𝐿 Eq. 1.16 where, Fr - frictional jacking force; γ′- effective soil unit weight; dp - pipe diameter; φr - residual soil friction angle; Ap - pipe circumference, and L - jacking length. One final distinction that makes Bennett’s model unique is that he separates the drive into two individual segments. The first segment of the microtunneling drive Bennett terms the

“initial dewatered, non-lubricated interval” followed by the “lubricated non-dewatered interval.” Each of these segments has different recommended values for the arching and friction reduction values (Staheli, 2006).

Pellet -Beaucour and Kastner (2002) developed a predictive jacking force equation based on the geomechanical phenomenon of soil arching effect, which was observed by Terzaghi (1951). The model postulated that the normal stresses acting on the outer surface of the

pipeline resulted from ground overburden pressure. The soil stresses acting normal to the tunnel crown are relaxed because of the arching effect, which causes the reduction of contact stresses on the outer surface of jacked pipes. Therefore, the model presented by Pellet -Beaucour and Kastner (2002) is shown as the following equation:

𝐹 = 𝜇𝐿𝐷_𝑒𝜋

2[(𝜎_𝐸𝑉+𝛾𝐷_𝑒

2 ) + 𝐾₂(𝜎_𝐸𝑉+𝛾𝐷_𝑒

2 )] Eq. 1.17

𝜎_𝐸𝑉 =𝑏(𝛾 − 2𝐶 𝑏⁄ )

2𝐾𝑡𝑎𝑛𝜑 (1 − 𝑒^{−2𝐾(ℎ 𝑏⁄ )𝑡𝑎𝑛𝜑}) Eq. 1.18 where, F is the total frictional jacking force; L is the jacking distance; De is the outer pipe diameter; σEV is the vertical soil stress at the pipe crown; γ is the unit weight of soil;

K is the lateral earth pressure coefficient; K2is the thrust coefficient of soil acting on the pipe with a suggested value of 0.3; C is soil cohesion, φ is the soil internal friction angle, b

= De[1+2tan(π/4-φ/2)] is the influencing soil width above the pipe and μ= tanφ is the coefficient of the pipe-soil friction.

Within the Japan Microtunneling Association, Osumi (2000) studied 49 pipe jacking projects and developed a method for calculating the frictional component of jacking forces, based the interface friction coefficient between the pipe and the soil on the internal friction angle of the soil. He assumed that regardless of pipe material, the interface friction coefficient, μ′, was equal to the tangent of half of the interface friction angle (tan(φ/2)), whose equation for the frictional component of the jacking force is as follows:

𝐹₀= 𝛽(𝜋𝐵_𝑐𝑞 + 𝑤)𝜇^′+ 𝜋𝐵_𝑐𝐶^′ Eq. 1.19 where, F0 - frictional component of jacking force; β - jacking force reduction factor; Bc - outer diameter of pipe; q - normal force; w - weight of pipe; and C′- adhesion of pipe and soil, 8kN/m² for N<10 and 5kN/m² for N>10. In addition, Osumi performed a statistical analysis to determine the jacking force reduction factor, β, of various soil type as shown in Table 1.4.

Table 1.4 Jacking force reduction factors, β (Osumi, 2000)

Soil types Jacking force reduction factor, β

Cohesive soil 0.35

Sandy soil 0.45

Gravel 0.60

Solid soil 0.35

The Japan Sewage Association (JSA) has proposed several empirical prediction equations of thrust when using the pipe jacking method. These equations are given by theoretically considering the frictional resistance between soil and the pipes (Japan Sewage Association , 2000). Firstly, the common prediction equation that was proposed by the Japan Sewage Association can be expressed as follows：

𝐹 = 1.31𝜋𝐵_𝑐𝑁 + [(𝜋𝐵_𝑐𝑞 + 𝑊)𝜇^′+ 𝜋𝐵_𝑐𝐶′]𝐿 Eq. 1.20 where, Bc - outer diameter of the pipe, m; N - N-value obtained by the standard penetration test; q - load action on the surface of pipes, kN; μ′ - coefficient of kinematic friction between soil and pipe (μ′=tan(φ/2); L - jacking distance, m; W - unit weight of pipe, kN/m; C′ - cohesion between soil and pipe, kPa; and φ - internal friction angle of soil. Secondly, the prediction equation as applied to the pipe-jacking method that uses lubricant can be expressed as follows:

F = 𝜋(𝑃_𝑒+ 𝑃_𝑤)(𝐵_𝑐/2)² + 𝜋𝐿𝐵_𝑐{𝐶_𝑎+ 𝜇′′[𝛽𝑞 + 2𝑊/(𝜋²(𝐵_𝑐 − 𝑡))]} Eq. 1.21 where, Pe - initial thrust per unit cross section (=150kPa); Pw - slurry pressure, kPa; t - thickness of pipe, m; Ca - cohesion resistance between soil and pipe, kPa and β - empirical constant. Based on the JSA’s empirical prediction model, Shimada et al.

(2004a) established an improving prediction equation of jacking force for well-lubricated jacking pipes. It was concluded that the initial thrust was dependent on the slurry pressure, and the frictional resistance around the pipes should be implemented as the value between the mud slurry and the pipes. Consequently, the proposed prediction equation can be derived:

𝐹 = 𝑃_𝑤(𝐵_𝑐⁄ )2 ²𝜋 + 𝜋𝐵_𝑐(𝜇𝑃_𝑤 + 𝐶)𝐿 Eq. 1.22

In the standard of ASCE (ASCE27-00, 2000), calculation of jacking load is based on experimental values for each soil type, as shown in Table 1.5. It is stated that lubrication may reduce the required jacking force by more than 50%, but more commonly, the average reduction may be about 30%. Also, in case of jacking operation stoppage, in some soils, the resistance may increase significantly. Jacking force increases of 20-50%

can be expected after delays of as little as 8 hours.

Table 1.5 Frictional jacking resistance for various ground conditions (ASCE27-00, 2000)

Ground condition Frictional Resistance, psi Frictional Resistance, kPa

Rock 0.3 ~ 0.4 2 ~ 3

Bounder clay 0.7 ~ 2.6 5 ~ 18

Firm clay 0.7 ~ 2.9 5 ~ 20

Wet clay 1.4 ~ 2.2 10 ~ 15

Silt 0.7 ~ 2.9 5 ~ 20

Dry loose sand 3.6 ~ 6.5 25 ~ 45

Fill Up to 6.5 Up to 45

In the German code DWA ATV A-125 (Röhner & Hoch, 2010), the face pressure, frictional resistance and misalignment are taken into account. In addition, jacking stoppage and lubricant effects are considered similarly as the ASCE 27 standard. The total maximum required jacking force F can be estimated by the following equation:

𝐹 = 𝑓_𝑘𝐾𝛾𝐻 [1 + 𝑘₂ 2 (𝜋𝐷²

4 + 𝜋𝐿𝐷𝑡𝑎𝑛𝛿)] Eq. 1.23

where, and k2 present the earth pressure condition over and blow pipe crown, respectively, according to ATV-A 161E; K - Silo effect according to Terzaghi; fk - factor for the consideration of curvature.

In Chapter 4 of this thesis, the parametric study will be conducted according to various conditions by using numerical approaches. Similarly, the comparative analysis is performed between numerical and theoretical results, which is not only for validation of the numerical simulations, but also for the prediction of jacking force and the determination of intermediate jacking station under various geological conditions. The

common-used predictive equations of jacking force within the unfrozen soil is not suitable for the pipe jacking in frozen ground. Because, there are many stoppages happening during jacking process, such as lifting new pipe in launch shaft, overnight or weekend stoppage and so on. Therefore, restart jacking loads induced by stoppages should overcome the static frictional force rather than sliding frictional force between concrete pipe and frozen soil. Moreover, with pore water partly being frozen, ice crystal becomes a bonding agent to increase the bond strength between concrete pipe and adjacent ground. So, the effect of ground temperature must be taken into consideration in the jacking force of slurry pipe jacking in frozen ground. In the Chapter 5, a calculation model for prediction of jacking force in frozen ground under different ground temperatures was proposed based on the results of a series of numerical simulations under different contact conditions between concrete pipes and frozen ground.