Underground Excavation problems

Greetings!
This post contains the brief lecture notes on the topic "Underground Excavation problems".

There are three types of underground excavation problems, which we come across in general:

1. Stability of excavation
2. Dewatering
3. Effect on the adjoining structures

In my previous post, I discussed the first part of this topic, i.e. Stability of Excavation. In this post, I will take up the second part, i.e. Dewatering.

Dewatering:

Dewatering is required for deep construction excavations, such as power houses, pumping stations, bridge foundations and so on. Practically any foundation below water table will require dewatering, however, if the soil has got low permeability i.e. less the 10^(-6) cm/sec, much problem due to seepage of water is not posed, because the discharge is small. 

However, if the discharge  is more, that is case of permeable soils having permeability more than 10^(-5) cm/sec, dewatering is essentially required. Extent of dewatering will depend upon characteristics of soil, presence of water bearing stratas, aquifer parameters and the field permeability.

 The dewatering job is to estimate the rate seepage of water, for this a central circular well is constructed, and the rate of discharge is estimated for a fully penetrating well. 

The rate of discharge will depend upon the geometry and extent of excavation and the desired level of lowered ground water table. 

A no. of wells are placed around the periphery of excavation and the water is pumped out simultaneously out of the wells.

There are three methods of dewatering:

1. Sump Pumping
2. Deep well pumping
3. well point dewatering.

Sump Pumping: If the soil is cohesive, having low permeability, shallow trenches are dug along outer edges of the excavation to collect water and to pump it out through the pumps. It is particularly suitable in clayey and silty clay, where the rate of seepage is low.

This method is inexpensive and easy to operate. The greatest depth upto which this method can be adopted is 5 to 6 m below the pump level.

Deep Well Pumping: Deeps wells are installed along the sides of excavation and water is continuously pumped out. This method is suitable for highly permeable soils such as sand and silty sand. A group of wells is installed, then the effect of pumping is observed, if sufficient control is not achieved, additional wells or pumps may be added. 

Deep wells must be constructed in such a way that they remove the large quantity of water, without allowing the silt to enter into the well casing.

Well Point Pumping: It consist of installation of nos. of well points around usually excavation. The vertical raiser pipes are connected to the header main on ground. The water is drawn into the riser pipe and discharged by the header pipe. The distance between the well points is 1 to 1.5 m. 

Thanks!

Consolidation Test (IS 2720- part 15 - 1986 )

AIM: This test is performed to determine the consolidation properties of a given soil as listed below:

1. Co-efficient of compressibility
2. Co-efficient of volume change
3. Co-efficient of consolidation Cv
4. Compression Index
5. Pre-consolidation Pressure, Cc
6. Co-efficient of permeability, K

STANDARD REFERENCE: IS: 2720(part 15) - 1986 - Determination of consolidation properties.

THEORY: Consolidation is the process of removal of pore water present in the soil gradually due to the application of sustained static load. Because of consolidation, there will be decrease in volume of soil mass.

SIGNIFICANCE: The consolidation data of soil is used to predict the rate and amount of settlement of structure founded on clay primarily due to volume change. In addition, the following information can be obtained for foundations resting on clay using consolidation data.

1. Total settlement of foundation under any given load.
2. Time required for total settlement due to primary consolidation.
3. Settlement for any given time and load.
4. Time required for any percent of total settlement or consolidation.
5. Pressure due to which soil already has been consolidation or compressed.

APPARATUS REQUIRED: 

1. Consolidometer
2. Loading device (Jack or lever system)
3. Ring of non-corrosive material
4. Porous stone
5. Water reservoir
6. Soil trimming tool like wire saw, knife or spatula etc.
7. Balance (0.01 gm sensitivity)
8. Dial gauge (0.01 mm accuracy)
9. Oven
10. Desiccators
11. moisture content cans
12. Stopwatch.
13. Scale ( 0.5 mm least count)

PROCEDURE: 

1. Clean the ring and weigh it empty.
2. Measure the height and diameter of the consolidation ring.
3. For undisturbed soil specimen, insert the ring in the soil mass by pressing with hand and remove the material around the ring.  The soil specimen so cut should project about one centimeter on either side of the ring.
4. Trim the specimen to flush it with the top and bottom of the ring.
5. Remove any soil sticking outside of the ring and weight the ring with the soil specimen.
6. For remoulded specimen, compact the soil in the ring to the desired density and weigh it.
7. Determine the moisture content of the extra soil removed from outside the ring.
8. Assemble the consolidometer with the ring having the soil specimen and saturated porous stones on top and bottom of the specimen. Place the filter paper between the soil specimen and the porous stone.
9. Mount the assembly on the loading frame and the dial gauge is set in position in such a way that the dial is at the beginning of its release run.
10. Connect the system to a reservoir with the same level as that of specimen. Allow the water to flow into the sample till its saturation is achieved.
11. After saturation, note initial reading of the dial gauge.
12. Apply the normal load to give the desired pressure intensity of 2.5 N/cm^2 on the soil specimen. 
13. Not the dial gauge reading at elapsed times of o, 0.25, 1.0, 2.25, 4, 9, 16, 25, 36, 49, 64, 81, 100, 169, 256, 361, 600, 1440 - minutes from the instant of  application of load. The dial gauge readings are taken until 90% consolidation is reached or atleast for 24 hours.
14. Increase the normal load to give the doubled pressure intensity of the previous pressure or 5 kN/cm^2.
15. On successive days, apply the loads to give the pressure of 10, 20, 40 and 80 N/cm^2 for the desired pressure intensity.
16. After the last load is applied, decrease the load 1/4 th the value of the last laod i.e. 20 N/cm^2 and allow to stand for 24 hours.
17. Note the dial gauge reading after 24 hours.
18. Further reduce the load in steps of 1/4th the previous load and repeat the observations.
19. If data for repeated loading is required, the load intensity is increased and observations are repeated.
20. Finally reduce the load to the initial setting load, keep for 24 hours and final dial gauge reading is recorded.
21. Dismantle the consolidation ring and weigh it after gently removing any surface water present.
22. Dry the specimen in the oven for 24 hours and weigh the dry soil specimen.
23. Draw graphs between:

               (a) Dial gauge reading versus under root of time on normal graph sheet and determine t90 for all the pressure by square root of time fitting method.

               (b) Dial gauge reading versus root of time on semi log graph sheet and determine t50 for all pressure by logarithm of time fitting method.

               (c) Void ratio 'e' versus pressure curve.

               (d) Void ratio 'e' versus load of pressure on semi-log graph sheet.

Square root time fitting method

RESULTS AND COMMENTS: 

Average value of the co-efficient of compressibility =

Average value of co-efficient of consolidation, Cv = 

Average value of co-efficient of volume compressibility =

Average value of co-efficient of permeability, K = 

Compression Index, Cc = 

Forced vibrations of Single Degree Freedom System.

Greetings!
In previous article we discussed about the Free vibrations with the viscous damping, in which we discussed three different cases when the system is overdamped, critically damped and underdamped.

In today's article we will discuss about the forced vibrations of single degree freedom system. There are cases when vibrations caused by the rotating parts of machines cause steady state periodic exciting forces in the system.  This exciting force can be written as follows:

                          F(t) = F*.sin(w.t)

The equation of motion for a SDOF having a damping of 'C' subjected to such an exciting force can be written as follows:
                         m.z'' + C.z' + K.z = F(t)
 
The equation is a linear, 2nd order differential, nonhomogeneous equation. The solution of this equation consists of two parts, namely: (i) complementary function, and (ii) particular integral. Complementary function is obtained by considering no forcing function.
Therefore its equation can be written as follows:
                       m.z'' + C.z' + K.z = 0

the solution for the above equation has already been discussed in the previous article. Now the particular integral can be found by assuming an exciting force F(t), under action here.
                   m.z'' + C.z' + K.z = F(t)

This can be shown for the particular integral, that the system will vibrate harmonically with the same frequency as that of the exciting force.

The complete solution is obtained by adding the complementary function and the particular integral. The complementary function is an exponentially decaying function and will die out soon, and the motion will be described by only the particular integral. There the system as a whole will vibrate harmonically with the same frequency as the forcing.

Let, F` be the amplitude of the exciting force;
 K is the spring constant, and
Az is the amplitude of the displacement,  then it can be shown that

Az = Magnification factor * (F`/K)
 F`/K describes the static state amplitude, while magnification factor will depend upon the frequency ratio and the damping ratio of the system.

Free Vibrations with Damping of SDOF system

Greetings!
In previous article we discussed about the undamped free vibrating system. In this article we are going to talk about the free vibrations with damping for a SDOF(Single Degree of Freedom) system.
For such a system, the excitation force F(t) is kept zero, while the viscous damping is available.

The differential equation of motion for such a system can be written as follows:

m.z'' + C.z' + K.z = 0  [ F(t) = 0]

Here, 'C' is the damping constant or force per unit velocity.  The solution of the above equation gives us a value of 'z' with which we can interpret the following results:

1. Case 1:  (C/2m) > K/m

In this case the motion of the system is not exponential but is an exponential subsidence. Because of the relatively large damping, so much energy is dissipated by the damping force that there is not sufficient kinetic energy left to carry the mass and pass the equilibrium position. Physically this means a relatively large damping and the system is said to be over damped.

• Case 2:   (C/2m)^2 = K/m

In this case the system is called critically damped system. It is similar to the previous case, but the difference is that the amplitude may become negative as shown in the figure. 

The damping constant obtained from this case is known as critical damping constant and the ratio of the actual damping to the critical damping constant is known as the damping ratio.

• Case 3:     (C/2m)^2 < K/m

In this case the solution for displacement 'z' can be written in a sinusoidal form, and the frequency of therefore damped system is known as damped frequency.

From above discussions we can say the a freely vibrating SDOF with viscous damping is over damped if damping ratio is greater than one, critically damped if equal to one and underdamped when less than one.

Thank you!

Undamped Free Vibrations

Greetings!
In previous article we had an introduction with the system with the single degree of freedom, in this article we are going to study behavior of the system with the 1 degree of freedom which is undamped and is free to vibrate, without any external exciting force.

For undamped free vibrations, the damping force and the exciting force are equal to zero. Therefore the equation of motion of the system becomes

m.z'' + K.z = 0

or  z'' + (K/m).z = 0  ---------eqn.(1)

The solution of the equation can be obtained by substituting

z= A1. cos.Wn.t + A2. sin.Wn.t

Where A1 and A2 are both constants and Wn is the undamped natural frequency.

when we substitute this value into the above eqn. (1), we get
 
   Wn = (K/m)^(1/2)

It can be shown the final equation for the displacement will be again a sinusoidal wave with a phase angle at the start of the curve, i.e. at t=0.

Fundamentals of Vibrations: SDOF systems

Greetings!

In real scenarios, structural foundations have to bear many kind of dynamic loadings, such as the loading due to the earthquakes, blastings, wind loads, pile driving, machine works, quarrying and fast moving moving traffic.
The characteristics of the dynamic load is that, they varies with time. Purely dynamic loads do not occur in nature. Loads are the combination of the static and dynamic load. Static loads are caused by the dead weight of the building itself, while the dynamic loads may occur due to the causes mentioned above.
The pattern of variation of a dynamic load with respect to time may either be periodic or transient. The periodical motions can be resolved into sinusoidally varying components e.g. vibrations in the case of reciprocating machine foundations. Transient vibrations may have very complicated non-periodic time history e.g. vibrations due to earthquake and quarry blasts.

The structures subjected to dynamic loads may vibrate along its extension, shearing, bending and may be along torsional deformation of the structure. The form of vibration mainly depends of the mass, stiffness distribution and end conditions of system.
To study  the response of a vibratory system, in many cases it is satisfactory to reduce it to the idealized system of lumped parameters. The simplest model consists of mass, spring and dashpot.

First of all we must know, what a Degree of freedom means, well!, the number of independent coordinates which are required to define the position of a system during vibration, is called the degrees of freedom  of the system. In order to understand the motion of the systems with the multi degrees of freedom, we should first analyse the single motion with the single degree of freedom.

A simple harmonic motion can be described by a simple sinusoidal function, having a time period of T.  In this article we are going to discuss the vibrations of a single degree of freedom system shown in fig.3 above, consisting of a rigid mass m supported by a spring  and dashpot.
Damping in this system is represented by the dashpot, and the resulting damping force is proportional to the velocity. The system is subjected to an external time dependent force F(t).

Figure above, shows the free body diagram of the mass m at any instant during the course of vibrations. The forces acting on the mass m are:

1. Exciting force, F(t): It is the externally applied force that causes the motion of the system. 
2. Restoring force, Fr: It is the force exerted by the spring on the mass and tends to restore the mass to its original position. For a linear system, restoring force is equal to K.z, where K is the spring constant and indicates the stiffness. This force always acts towards the equilibrium position of the system.
3. Damping force, Fd: The damping force is considered directly proportional to the velocity and is given by C.z' where C is called the co-efficient of viscous damping; this force always opposes the motion.
4. Inertia force, Fi: It is due to the acceleration of the mass and is given by m.z''. This force can be justified by the De-Alembert's principle.

The equation of equilibrium for the mass m is given as:

m.z'' + C.z' + K.z = F(t)

Thank you!

Construction Problems with the Underground Structures

Greetings!
Here are Lecture notes on the construction problems related to the construction of the underground structures.
The major problems which we come across while underground excavation and construction of underground structures are classified into following 3 groups:

1. Stability of Excavation
2. Dewatering
3. Effect on adjoining structures

In this post, I am going to discuss only the introduction of the first part, i.e. stability of excavation. In the subsequent posts, I shall discuss it in details and other parts as well.

1) Stability of Excavation: Excavation is done manually or by chemical means depending upon the quantity of earth work involved. In case of manual excavation, the size of foundation is limited. The mechanical excavators and haulers can be used for gentle side slopes such as in road construction, thus the area involved will be larger.

Sloped excavation - for underground construction

Depending upon the space availability at the construction site, the excavation with a side slope as shown in figure, or a braced cut can be adopted, however the sloped excavation can be adopted only for a stable slope & free space in vicinity of the structure.

If, however there is an existing building in close vicinity, then excavation with the side slopes will not be feasible and economic. 

There in built up & crowded areas, braced cut is a viable proposition. Braced cuts consist of making the vertical walls in the soil and suitably propping them by driving steel struts as the excavation is proceeded.

Excavation with Braced Cut

At the final excavation level, the foundation is cast and the soil is backfilled to restore the original ground level, as the struts are successively pulled up. 

For shallow footings and raft foundations, the depth seldom exceeds 2 m and hence, no extensive supporting system is required, because earth pressure is not much. If however, heterogeneous soil exist near ground surface, side protection can be applied using timber planks or small struts may be used. 

Deep excavations exceeding 2 basements i.e. excavation depth greater than 6 m, will require thick, adequate lateral support by using diaphragm walls or continuous bored  piles and struts. 

In case of large excavation widths, it is not possible to have horizontal struts, because they may bend under their own weight. 

In such cases, inclined props or struts may be provided in between the diaphragm wall and base.  Also, a series of H-pile(Heavy I -sections) may be driven throughout the excavation at close intervals. The inclined props support the diaphragm wall in the wide cuts.

To be continued to next post.... 

Thank you!

The Foundations in Expansive Soils

Greetings! Here are the lecture notes for the next lecture of Advanced Foundation Engineering.

The following methods can be used for the construction of foundations on expansive soils:

• A) Designing the structure as a solid structure to withstand the effects of swelling & shrinkage of strata.
• B) Eliminating the swelling by:
• i) stabilizing the moisture.
• ii) Loading the soil more than the swelling pressure.
• iii) Treating the soil, so that its behavior changes.
• iv) Replacing the soil by non-swelling soil.
• C) Isolating the structure by taking down the foundation to a stratum, which is not affected by swelling.

A) Strengthening the structure beyond a certain limit is not economic, however, reinforcement bands can be provided at different levels, such as plinth, lintel and beams.

 Heavily reinforced rafts can also be provided, but the flexible structures are not practical.

B) Taking down the foundation to a level where no volume changes or water content change occur, pre-wetting techniques may also be required. For isolated structures it may not be possible.

• Loading the foundation with more than swelling pressure has shown better performance, but quantification of suitable load is not practical, as the factors affecting are many.
• Stabilization of an expansive soil by lime is well known but mixing of soil and compacting it in layers is problematic and sometimes un-economical too. Usually 2 to 8% lime decreases the liquid limit(LL) and Swelling; increases the OMC and strength of expansive soil. This method is more practical for roads. For deeper treatments lime slurry may be injected, but it is not a common practice.

Thank you!

Under Reamed Piles

Greetings!

The under reamed piles are the most common and appropriate type of foundation used in expansive soils. In this case the superstructure of the building is supported over beams, which are clear off the ground surface, and span over the piles anchored at the depth where the soil has nearly constant water content. This depth is usually found to be 3.5 m in India.

Length of Under reamed Pile:

The length of pile varies from 3.5 m to 4.0 in deep deposits of black cotton soils, and pile is carried to non expansive soil layer up to a depth of at least 0.6 m. 

Spacing of Piles:

Depending upon bearing capacity, spacing of piles varies from 1.5 m to 3.0 m. A pile is to be provided under every wall junction or where a point load is acting on the plinth beam. 

Diameter of pile shaft:

It varies from 200 to 500 mm, and the ratio of the diameter of the bulb to shaft i.e. Du/D varies from 2 to 3. In case of multi-reamed piles, the first bulb should be at minimum depth of 2.Du, below the ground level.  

Center to center distance between 2 bulbs may vary from 1.25 to 1.5.Du. The pile is reinforced throughout its length to take care of tensile stresses. Steel reinforcement should be sufficient to take care of shrinkage effects when the pile acts as the column, so 0.8 to 6% (IS: 456-2000) of reinforcement, which we provide for the columns should be provided at least to make it as a column.

As per IS:2911-1980(part 3), the ultimate bearing capacity of the soil can be calculated and a factor of Safety(FOS) of 2 to 2.3 is applied to calculate the safe load/allowable load.

Thanks for your kind visit!