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Question a

Question b

Depending on the exact location and type of rock or soil encountered, the geological and geotechnical conditions along the tunnel's path may differ dramatically (Zhang, 2022). Due to the ordinary structural strength of volcanic rocks like granite, basalt, and limestone, which lets them to endure the momentous stresses placed on them by the tunnel short of failing disastrously, tunnels are regularly dug into these sorts of formations. Tunnel steadiness and structural veracity might be more tough to maintain whereas excavating through less cohesive constituents like gravel, sand, or clay. Engineers may infrequently determine that by means of grouting or shotcreting techniques as a form of tunnel reinforcement is essential to guarantee the constancy of the tunnel. The existence of water or other liquids, which can weaken the rock and upsurge the risk of erosion or flop, and the presence of faults or fractures in the rock, which can upsurge the possibility of collapse or instability, are two more issues that can distress the geology and geotechnical conditions along a tunnel course. The probable geology and geotechnical conditions along a tunnel route can be la-di-da by a number of variables, such as the setting, the sort of rock or soil, and the presence of any environmental or geological jeopardies (Maleki, 2021). Careful preparation and engineering can lead to the harmless and effective building of tunnels, even under tough situations.

Question c

Via the PHASES finite element program, the strains and distortions in the tunnel were calculated. This program makes it easier to examine non-linear deformation in rocks in a two-dimensional setting. Sturdier rock materials can be estimated by means of the Hoek-Brown criterion, while feebler rock materials can be examined by means of the Mohr-Coulomb failure criteria (Singh, 2020). The program utilizes the Hoek-Brown criteria as its fiasco criterion and makes use of a hydrostatic stress field. The PHASES software can automatically produce a mesh around the tunnel segment and conduct an elastoplastic examination to compute deformation brought on by applying static masses to the tunnel. To simulate the method of tunnel excavation in sandstone, limestone, and marl, three arithmetical models were created with similar mesh and tunnel forms but dissimilar material properties.

These are the models:

  1. A tunnel that passes through sandstone
  2. A limestone tunnel is moved through.
  3. The tunnel crosses the marl

We conducted a numerical study on all three models. It takes at least 396 triangular finite components to accurately depict the subsurface structure. These components all have a minimum of 230 nodes installed. The yield zone in the rock mass surrounding the tunnel and the induced displacements brought on by the excavation were found using the numerical model (PHASES). This made it possible to compare the displacements with those that will be measured at the location in the future. The diagram below shows the areas of yielding for various types of rock together with the highest cumulative displacements observed at the tunnel's walls, ceiling, and floor. These results came from a finite element analysis that was done on the tunnel. Less than 1 cm of movement in the surrounding rock mass was the result of the tunnel excavation procedure; this result was consistent across all models. Compared to the other portions, the failure zone surrounding the tunnel in Model III (Marl) is significantly greater. There is no yielding material or flexible zone surrounding the sandstone excavation.

Question d

For the following reasons, I will prefer the roadheader excavation method for tunneling excavation (Deshmukh et al., 2020):

  1. High production rates: Roadheaders are well known for their remarkable excavation rates, which far outpace those of conventional tunneling methods. This makes it possible to complete the excavation process more quickly and complete projects on time.
  2. Requires less labor; roadheaders are highly automated devices that require little in the way of human interaction. The abovementioned occurrence marks in a decline in the need for a noteworthy work force, which in turn produces economic profits and enhanced safety procedures by extenuating workers' exposure to hazardous settings.
  • Ecologically friendly: Compared to outmoded digging methods, roadheaders have a lesser carbon trail. Electric vehicles (EVs) are considered a more ecologically bearable alternative owing to their abridged energy usage and reduced pollution releases.
  1. Cost savings: In some circumstances, the roadheader excavation technique may attest to be more cost-effective, particularly when dealing with petite excavations or tunnels with intricate geometries. Reduced recruitment necessities and higher production are two things that contribute to general cost savings.
  2. Flexible: Roadheaders are extremely adaptive machinery that can work in a diversity of geological locations, including problematic terrains like soft earth, hard rock, and variable face conditions. These devices are flexible to different excavation requirements and can be easily altered to meet explicit project specifications.

Question e

The subsequent ground behavior groupings are expected:

  1. Cohesive soils, that have a high clay content and a propensity to combination. When excavation is done without enough support, it can lead to problems and possibly instability.
  2. Granular soils: Excavation in soils with sand and gravel tends to be easier than in soils with cohesive characteristics. Nevertheless, stability-related problems can still arise if they are not adequately maintained.
  • Rock: The composition of the rock determines how easy or difficult it is to excavate. When performing excavations in more durable rock formations, such granite, the usage of specialized equipment may be judged necessary.

Question f

Python code was used to calculate the curve.

Equation code line

def u_el_calc(p0,nu,pi,Ep,a):

 ep = Ep*1000

u_el=(1+nu)/ep*(p0-pi)*a*100 #cm return u_el

Yielding point calculation

def cot(j):

_cot_ = 1/np.tan(j)


def Rp_calc(pi,p0,fi_r,fi_p,cr,cp,Nr,

Rp = a*((p0+cr*cot(fi_r)-(p0+cp*cot(fi_p))*np.sin(fi_p))/(pi+cp*cot(fi_p)))**(1/(Nr-1))

return Rp def p_cr_calc(p0,cp,Np): 

p_cr = 2*(p0-cp*np.sqrt(Np))/(1+Np) #kPa

return p_cr

Calculating tunnel plastic behavior

Def u_pl_calc(Rp,pi,Ep,Er,p0,fi_p,cp,fi_r,cr,nu,Np,Nr,a): 

ep = Ep*1000 #kPa

 er = Er*1000 #kPa

 sum_1= (1+nu)/ep*(p0+cp*cot(fi_p))*np.sin(fi_p)*(Rp**2)/a

sum_2 = (1+nu)/er*(1-2*nu)*((p0+cr*cot(fi_r))*((Rp**2)/a-a)-(pi+cr*cot(fi_r))/(a**(Nr-

1))*((Rp**(Nr+1))/a-a**Nr)) u_pl = (sum_1+sum_2)*100 #cm return u_pl


def groun_reaction_calc(fi_p,fi_r,Np,Nr,cp,cr,nu,a,Ep,Er,p0):

 # pressure lists

p = np.arange(p0,0,-1)

 # critical pressure

p_cr = p_cr_calc(p0,cp,Np)

print("Critical pressure [kPa] = ",float(round(p_cr,0)))

 data = []

 for pi in p:

 l = 1-pi/p0

 Rp = np.nan

 if pi>=p_cr:

# elastic settlement calculation

u = u_el_calc(p0,nu,pi,Ep,a)


# plastic radius calculation

Rp = Rp_calc(pi,p0,fi_r,fi_p,cr,cp,Nr,a)

 #plastic settlement calculation

 u = u_pl_calc(Rp,pi,Ep,Er,p0,fi_p,cp,fi_r,cr,nu,Np,Nr,a)


 df = pd.DataFrame(data = data, columns = ['p [kPa]','$\lambda$ [-]','u [cm]','Rp [m]'])

 return df

Question g

The following are typical rock sizes and shapes for tunneling:

Boulders: It is occasionally possible to identify larger boulders, especially in difficult geological formations. The length of these measurements could vary from a few meters to several tens of meters. Although rare, large stones do occasionally appear.

Rock chips: When tunneling, debris or rock chips are frequently produced. These materials have smaller physical dimensions than waste. These measurements could range from centimeters to millimeters.

Blocks of rock: Larger rock fragments are also produced by tunneling. These blocks can differ in scope and shape from a few millimeters to many meters. The topographies of the land being crossed and the specific technology used in tunnel building are taken into thought while determining a tunnel's exact size.

Small debris: Excavations often leave behind minute remains of rock or other debris. These substances could be wherever in size from a few centimeters to a few decimeters.

Question h

The RMR value, which arrays from 0 to 100, is computed by the RMR system by means of a set of five constraints. The following are the parameters which are being taken to account (Somodi et al., 2021):

The uniaxial compressive strength (UCS), a measure of the unbroken rock material's mechanical strength. Via laboratory testing, the UCS value is ascertained. Uniaxial Compressive Strength (UCS) values amid 0 and 10 MPa are scored by means of a scale that runs from 0 to 20 in the Rock Mass Rating (RMR) scheme. An RMR score in the range of 80 to 100 is provided for UCS values larger than 100 MPa.

The notch of jointing and breakage inside a rock mass is determined by the Rock Quality Designation (RQD). The length of intact rock rubbles inside a drill core is used to find the Rock Quality Designation (RQD). For Rock Quality Designation (RQD) values below 25%, the Rock Mass Rating (RMR) scheme uses a grading scale running from 0 to 20, whereas RQD values over 75% are given a score in the RMR scheme between 80 and 100.

The extent of the spatial parting of jointspaces and crevices inside a rock mass is recognized as the spacing of discontinuities (S). For S values greater than 300 cm, the RMR uses a marking scheme with a array of 0 to 20, and for S values lesser than 10 cm, it allocates a score between 80 and 100.

The condition of discontinuities (C) measures how far the rock mass's joints and cracks have been infilled, weathered, and changed. For C values greater than 20%, the Relative Match Ratio (RMR) allocates a score between 0 and 20, while for C values less than 5%, it allocates a score between 80 and 100.

The groundwater circumstances (G) measure the quantity of water that has leaked into the fundamental geological formation. For G values above 10 liters per minute per 10 meters of tunnel, the RMR uses a marking system that varies from 0 to 20, and for G values less than 1 liter per minute per 10 meters of tunnel, it allocates a score between 80 and 100.

The Q value, which is between 0 and 100, is computed by the Q system using six parameters. The following are the constraints that are painstaking:

  1. Uniaxial compressive strength (UCS)
  2. Discontinuity spacing (S)
  • Discontinuity condition (C)
  1. Conditions at groundwater (G)
  2. The Rock Quality Index (RQI), a statistic similar to the Rock Quality Designation (RQD) of the Rock Mass Rating (RMR) scheme that is used to assess the notch of assembly and breaking inside a rock mass (Sebbeh-Newton, 2021). However, joint alignment and fracture persistence are assessed as part of the RQI procedure. The Q system makes use of a scoring method that gives RQI (Relative Quality Index) values below 10 a score in the range of 0 to 30, and RQI values beyond 50 a score in the range of 70 to 100.
  3. Stress conditions (σ); a measure of the rock mass's insitu stress condition. For σ values below 5 MPa, the Q system uses a numerical scale from 0 to 10, and for σ values beyond 50 MPa, it assigns a score between 90 and 100.

Question j

The equation that follows can be used to determine the shotcrete design thickness:t = (K * P * L) / (f * D) is one way to write the equation above, where t stands for variable, K for constant, P for parameter, L for factor, f for additional factor, and D for divisor.Where is it? The shotcrete thickness is represented by the variable t. Barrett and McCreath's research indicates that the coefficient represented by the letter K is related to the particular type of shotcrete. The pressure applied when shotcrete is applied is represented by the variable P. The span, or separation between the supports, is denoted by L. The shotcrete's flexural strength is represented by the variable "f". The deflection limit is represented by the variable D. In order to illustrate the intended example, hypothetical values for K, P, L, f, and D must be established because exact values for these variables are missing.

We will utilize the following measurements for our tunnel:



L= 70 feet

F= 500 psi D= 0.25 inches t = (0.8 * 1500 * 10) / (500 * 0.25) t = 960 inches

Therefore, based on the aforementioned theoretical calculations and the guidelines provided by Barrett and McCreath, the shotcrete's calculated design thickness is 960 inches.

Question k

The order in which excavation should be done is (Gao, 2020);

  1. Ground improvement measures: ought to be taken into account in the event that the pilot tunneling or site inspection reveal unfavorable ground conditions. Depending on the particular situation, a variety of techniques like grouting, stabilizing the soil, or ground freezing may be applied. The purpose of ground improvement is to stabilize the excavation zone and improve the mechanical qualities of the nearby soil.
  2. Utilized is the New Austrian Tunneling Method (NATM) or Sequential Excavation Method (SEM). The strategy that is being suggested involves gradually excavating the tunnel in smaller sections and then acting quickly to fortify the ground that has been exposed. Excavation should be done in separate sections so that better control and observation of the existing ground conditions are possible. Shotcrete, rock nuts and bolts, steel ribs, and other appropriate techniques can all be used to provide quick help.
  • It is strappingly advised to monitor the ground in order to generate a thorough system that shelters every phase of the excavation process. To guarantee the unceasing monitoring of ground dislocations, deformations, and steadiness, a variety of instruments, such as inclinometers, extensometers, and settlement gauges, are used. Regular monitoring is essential for recognizing unusual ground behavior and permits prompt alterations to the excavation order.
  1. Tactics for contingencies should be formed in case the ground conditions turn out to be less auspicious than originally expected. Other excavation techniques, additional ground improvement strategies, and, if essential, the redirecting of the tunnel's course must all be involved in the planned designs. By havign contingency plans into place, the venture may lessen potential delays and uphold a high level of protection by guaranteeing that it can respond to unexpected blockades in an effective manner.
  2. Expert Consultation: It is suggested to integrate highly competent geotechnical engineers and tunneling specialists at various stages of the project to take benefit of their extensive expertise and skill. An individual's skill can be used to assess the terrain's condition, find potential dangers, and make endorsements for the most effective order of excavation events. By taking in these experts, the venture can benefit from their specific knowledge, which decreases the likelihood of significant distractions caused by poor ground conditions.

The venture team may trail the recommended tunnel excavation order to reduce the potential effect of uncomplimentary ground conditions. It permits for improved risk control, early discovery of possible problems, and remedial action to promise the tunneling project's ultimate accomplishment.


Deshmukh, S., Raina, A. K., Murthy, V. M. S. R., Trivedi, R., & Vajre, R. (2020). Roadheader–A comprehensive review.  Tunnelling and Underground Space Technology ,  95 , 103148.

Gao, C., Zhou, Z., Li, Z., Li, L., & Cheng, S. (2020). Peridynamics simulation of surrounding rock damage characteristics during tunnel excavation.  Tunnelling and Underground Space Technology ,  97 , 103289.

Maleki, Z., Farhadian, H., & Nikvar-Hassani, A. (2021). Geological hazards in tunnelling: the example of Gelas water conveyance tunnel, Iran.  Quarterly Journal of Engineering Geology and Hydrogeology ,  54 (1), qjegh2019-114.

Sebbeh-Newton, S., & Zabidi, H. B. (2021). Application of artificial intelligence techniques for identifying rock mass quality in an underground tunnel.  International Journal of Mining and Mineral Engineering ,  12 (2), 132-148.

Singh, A., Ayothiraman, R., & Rao, K. S. (2020). Failure criteria for isotropic rocks using a smooth approximation of modified Mohr–Coulomb failure function.  Geotechnical and Geological Engineering ,  38 , 4385-4404.

Somodi, G., Bar, N., Kovács, L., Arrieta, M., Török, Á., & Vásárhelyi, B. (2021). Study of Rock Mass Rating (RMR) and Geological Strength index (GSI) correlations in granite, siltstone, sandstone and quartzite rock masses.  Applied Sciences ,  11 (8), 3351.

Zhang, W., Han, L., Gu, X., Wang, L., Chen, F., & Liu, H. (2022). Tunneling and deep excavations in spatially variable soil and rock masses: A short review.  Underground Space ,  (3), 380-407.

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