seismic evaluation of multi-storeyed buildings on plain ground and curve slope ground

IJSRD - International Journal for Scientific Research & Development| Vol. 3, Issue 10, 2015 | ISSN (online): 2321-0613

All rights reserved by www.ijsrd.com 571

Seismic Evaluation of Multistoried Buildings on Plain Ground and Curve

Slope Ground Md Sadruddin

1 Prof. Amaresha

2

1M. Tech Student

2Assistant Professor

1,2Department of Structural Engineering

1,2Veerappa Nisty Engineering College, Shorapur, District Yadgir, Karnataka

Abstract— Most of the hilly regions of India are highly

seismic. Buildings on hill slopes differ in a way from other

buildings. The soft storeies are typical feature in modern

constructions specially in seismic areas which has been

experience by the previous studies and past earthquakes.

Due to verious type of structures on sloped ground

structures are comes under irregularity and asymmetricity.

Structures on slope leads to seismic cases.The damages to

the structures are determined and acceptable safety can be

provided. The linear-elastic analysis is not adequate in

highly seismic areas. Thus for the design of building in

seimic areas and sloped areas inelastic procedure is used. In

the present dissertation work, 3D analytical model of eleven

storeyed buildings on plain and curved ground have been

generated. Models are analyze using „„ETABS”to get the

behavior of structure due to change in column height in

ground story due to curved sloped ground. The analytical

model of the building includes all important components

that influence the mass, strength, stiffness and deformability

of the structure. To study the effect of infill, concrete shear

wall and concrete core wall during earthquake, seismic

analysis using both elastic and inelastic method of analyses

i.e., linear static (equivalent static method), linear dynamic

(response spectrum method) has been performed. The

deflections at each storey level has been compared by

performing equivalent static method, response spectrum

method. Storey drifts are within the permissible limit given

for linear static and linear dynamic method. Again contrary

to common practice, the presence of masonry infills,

concrete shear and concrete core wall may affect the overall

behavior of structure while subjected to earthquake forces.

Key words: ETABS, Plain Ground, Curve Ground, Seismic

Evaluation, Soft Storey, Infills, Shearwalls and Core Walls,

etc…

I. INTRODUCTION

A. General:

The structures which are design and construct as per earliear

code provision do not have satisfied requirements for

current earthquakes.Thus many of the structures in seismic

areas are suffering from hazards.Therefore the new code

provisions are made for such cases.

Multistoried R.C. framed buildings are getting

popular in hilly areas because of increase in land cost and in

unavoidable circumstances.Thus the structures in the hilly

areas should have adequate strength to avoid the failure of

structure during earthquakes.

Indian subcontinent has been experienced with

some of the most earthquakes in the world. The youngest

mountain series of Himalayas covers whole northeast

boundary regions of India. The tectonic activities are still

continuing which may result into severe earthquake in future

as anticipated by many scientists and researchers. More than

50% of our land is seismically prone and is being visited by

earthquakes time and again incurring socio-economic losses

in huge proportions and at the same time reminding us the

need of earthquake resistant design.

The latest seismic zoning map of BIS 1893:2002

shows that 12% of our land area is in zone V i.e., MSK IX

or more (it means that more than 50% of reinforced concrete

buildings would suffer large cracks, gaps in walls leading to

collapse of parts of buildings whereas masonry and adobe

structures may even collapse), 18% in zone IV i.e., MSK

VII and 27% in zone III i.e., MSK VII. All these are

damaging earthquake intensities and the structures coming

up in these regions has to have special earthquake resistant

features. Therefore it is essential to seismically evaluate the

many existing building structures as per code current

requirements. The buildings found inadequate for resisting

future earthquake needs to be retrofitted.

The coceptss of earthquake resist design needs

nonlinear analysis to get damages for different levelses of

earthquakes.In performance based ideas reactions of

building for different levels of motion are specified. In this

dissertation, hypothetical multistoried buildings (i.e., eleven

storeyed with concrete shear wall ,concrete core wall ,infill

and without infill) assumeded in zone v of medium soil site

analyzed and designed as for load combinationns given by

code.

B. Analysis Procedures:

There aretwo types of linear analysis procedures , linear and

nonlinear.Further the liner analysis is divided into

linearstatic and lineardynamic procedure and nonlinear

analysis is divided into nonlinearstatic and

nonlineardynamic procedure.

1) Linear Static Procedures:

In linear static procedures structure is modeled as equivalent

singledegreeof freedom system with linear static stiffness

and an equivalent viscouss damping. The inputis modeled

by an equivalent lateral forces to found same stresses and

strains as earthquake may gives. From first fundamental

frequency of structure using Rayleigh‟s method, spectral

acceleration Sa is calculated from the appropriate response

spectrum, whichis, multiply by mass of the building M,

results in the equivalent lateral force, V

-------- 1.1

The coefficient Ci takes into accounto issue order

effects, stiffness degradation also force reduction due to

inelastic behaviour. These lateral forces are distributed

along height of building.The internalforces and

displacements are determined using linear elastic analysis.

This procedure is used for design purposess and

Seismic Evaluation of Multistoried Buildings on Plain Ground and Curve Slope Ground

(IJSRD/Vol. 3/Issue 10/2015/120)


incorporated in more codes. Their expenditureis very less.

However their applicability is restricted to regular structure.

2) Linear Dynamic Procedures:

In linear dynamic procedure structureis modeled as a

multidegreeof freedom with linear elastic stiffness matrix

and equivalent viscous damping matrix. The input is

modeled as time history analysis. Time-history analysis

based on a time stepbystep evaluationof building

charecterstics by recording synthetic ground motion. In this

case internal forces and displacements are determined by

linear elastic analyses.

The scope of this procedure is highermodes can be

considered which makes it suitable for irregularstuctures.

3) Nonlinear Static Procedures:

In this procedure the modeled incorrporate directly to the

nonlinear forcedeformation characterstics of every part of

structure due to inelastic reaction of various parts of

structure. Several methods of nonlinear static procedure

exists (e.g. ATC 40, FEMA 273[9]).

Clearly, the advantage of these procedures with

respect to the linear procedures is that they take into account

directly the effects of nonlinear material response and hence

the calculated internal forces and deformations will be more

reasonable approximations of those expected during an

earthquake. However, only the first mode of vibration is

considered and hence these methods are not suitable for

irregular buildings for which higher modes become

important.

4) Nonlinear Dynamic Procedures:

In this procedure same modeled is used as in nonlinearstatic

procedure by directly introducing inelastic reaction using

finiteelements. The main differrence is seismicinput is

modeled using a timehistory analyses.

This method is most valuable to get internal forces

and displacements under seismic input but the calculated

responses are very sensitive to individual ground motion

used as seismic input.

II. LITERATURE REVIEW

A. General:

Several studies, experiments, and research works are carried

out since a long time to got the effect of seismic forces on

buildings. The concept of modeling and analysis used for

this purpose are getting improved day by day as

advancement of engineering improved.

B. Review:

Mohammad Umar Farooq Patel, et al., [2014], has studies

on “Seismic Evaluation Of RC Building On Scurved

Ground”. They studied behavior of frame on curved ground

with cncrtshear wall at different levels..A parametric study

is made on 8storey building including bareframe and

cncrtshear wall in seismic zone III.For comparisonthey

consider modeled on plainground with 5bays in Lgtd and

Trvs directions..Seismic analysis is done by E.S.Method and

R.S.Method.Based on E.S.Method building with cncrtshear

wall at centre and corner have 41.41% 60.50% respectively

lessdisplacement compared to bare frame on curved ground.

Based on R.S.Method they got that building have 24.60%,

39.10% lessdisplacement by bare frame modeled on curved

slopedground.From above studies he concluded building on

curveslope ground has more displacement the influence of

cncrtshear wall minimizes lateral displacement

considerably.

Rayyan-Ul-Hassan and H.S Vidyadhara, [2013]

carried out “Analysis Of Earthquake Resisting Multistory

Multibay RC Frames.They Analyze Seismic Behavior Of

Bareframe, Building With Firstsoft Story (Infillwall In

Above Stories) With Presence Of Infill And Cncrt Shear

Wall At Corner”. They used fourbay 12storey building on

sloping ground situated in seismic zoneV.These buildings

are analysed by E.S.Method and R.S.Methods.Based on

E.S.Method they found reduce in displacement of modeled

with infill and cncrtshear wall at corner compare to

bareframe by almost 78.14% and 88.26% respectively and

from R.S.Method they noted almost 51.96% and 74.98%

respectively.Hence they found presence of infill and

cncrtshear wall reduces displacement considerably. It can be

observed that there is increase in baseshear due to influence

of cncrtshear wall when compare to bareframe. As per IS

1893 part (I) 2002code, the permissible storeydrifts are

restricted to 0.004 times the storyheight and they notice all

buiidings are under sufficient conditions.

Haroon Rasheed Tamboli and Umesh.N.Karadi,

[22] studied “Seismic Analysis Using E.S.Method For

Varied Rcframe Modeled Which May Have Bareframe,Infill

Walls And Soft Stories At Different Levels”. The Infill

walls should be considered in seismic regions because the

story drift of soft storey is much more compared to infill

storey which may leads to collaps of structures.The use of

infill walls may increases the strength and stiffness of

structure.

M C Griffth and A R Pinto, [6] have investigated

on the “Three Bay Four Story Building Including

Unreinforced Brick Masonry Walls”. The building was

expected to have maximum lateral deformation capacities

corresponding to about 2% lateral drift.The unreinforced

infill walls are being cracking at very small drift and

completey lost its load carrying capacity.

III. ANALYTICAL MODELLING

A. Description of The Sample Building:

The plan layout for building on a plain and on curved slope

ground models are shown in below figures. column hight of

each storey is 3m for all models

1) Model 1:

Building has nowalls in the firststorey and one fullbrick

infillmasonry walls (230mm) thick in the upper stories.

Building is modeled as bareframe .However, masses of the

walls are considered.

2) Model 2:


infillmasonry walls (230 mm thick) in the upper stories.

Stiffness and mass of the walls are considered.

3) Model 3:

Building has nowalls in the firststorey and halfbrick

infillmasonry walls (110 mm thick) in the upper stories..

Stiffness and mass of the walls are considered.

4) Model 4:

Building has one full infillmasonry wall (230 mm thick) in

all stories including the firststorey. The stiffness and mass of

the walls are included.




5) Model 5:


infillmasonry walls (230mm thick) in the upper stories and

L-shaped shear walls (230mm thick) are provided at the

corners.Stiffness and masses of the walls are considered.

6) Model 6:


infillmasonry walls (230mm thick) in the upper stories and a

central service concrete core wall (230mm thick) is

provided. Stiffness and masses of the walls are considered.

7) Model 7:


infillmasonry walls (230mm thick) in the upper stories, L-

shaped shear walls (230mm thick) are provided at the

corners and a central service concrete core wall (230mm

thick) is provided.Stiffness and masses of the walls are

considered.

Elevation of Building 3D view of Building

Fig. 3.1: Elevation and 3D view of Model-1.

Elevation of Building 3D-view of Building

Fig. 3.2: Elevation and 3D view of Model-5.

Elevation of Building 3-D view of Building

Fig. 3.3: Elevation and 3-D view of Model-3.

Elevation of Building 3D- view of Building

Fig. 3.4: Elevation and 3D view of Building Model-1 on

Curve Ground.

B. Design Data:

1) Material Properties:

Young‟s modulus of (M25) concrete, E= 25x106 kN/m²

Density of Reinforced (M25) Concrete= 25 kN/m³

Modulus of elasticity of brick masonry= 3500x10³ kN/m²

Density of brick masonry= 20 kN/m³

Upper Storey Height= 3.0 m

No. of Storeys= 11

2) Assumed Dead load intensities:

Floor finishes= 1.0 kN/m²

Live load intensities

Floor= 3.0 kN/m²

Roof= 0 kN/m²

3) Member properties:

Thickness of Slab= 0.125m

Column size= (0.4m x 0.7m)

Beam size= (0.3m x 0.45m)

Thickness of wall= 0.23m

Thickness of wall 2= 0.11m

Thickness of shear wall and core wall= 0.23m

4) Earthquake Live Load on Slab as per clause 7.3.1 and

7.3.2 of IS 1893 (Part-I)- 2002:

Roof (clause 7.3.2) = 0

Floor (clause 7.3.1) = 0.25x3.0=0.75kN/m2

IS: 1893-2002 Equivalent Static method

Design Spectrum

Zone –V

Zone factor, Z (Table2) – 0.36

Importance factor, I (Table 6) – 1.00

Response reduction factor, R (Table 7) – 5.00

Vertical Distribution of Lateral Load,

n

jjj hw

ii

Bi

hwVf

1

2

2

IS: 1893-2002 R.S.Method: Spectrum is applied

from fig.2 of the code corresponding to medium soil sites.

The spectrum is applied in the Lgtd and Trvs directions.

C. Calculations:

1) Natural periods:

For model 1,

Fundamental Natural period, longitudinal and transverse

direction, Ta=0.075*350.75

=1.079 sec

For model 2, 3, 4, 5,6,7:




Fundamental Natural period, longitudinal direction,

Ta=0.09x35 / ( =0.63sec

Fundamental Natural period, transverse direction,

Ta=0.09x35 / ( =0.704sec

MODEL NO EQX (KN) EQY (KN)

MODEL 1 2110.8096 1994.5560

MODEL 2 6113.0321 4606.9972

MODEL 3 4804.0486 3743.7886

MODEL 4 7702.1604 7702.1604

MODEL 5 7552.9334 7552.9334

MODEL 6 7459.8769 7459.8769

MODEL 7 7645.9898 7645.9898

Table 3.1: Base shear for models on plain ground

LEVEL VX(KN) VY(KN)

11 231.9026 219.1305

10 461.8628 436.4255

9 379.3229 358.4316

8 304.9016 288.1090

7 238.5991 225.4582

6 180.4152 170.4787

5 130.3499 123.1709

4 88.4035 83.5346

3 54.5755 51.5698

2 28.8665 27.2766

1 11.2759 10.6549

PB LEVEL 0.3341 0.3157

Table 3.2: Distribution of lateral seismic shear forces for

building on plain ground for Model 1.

LEVEL VX(KN) VY(KN)

11 835.5064 651.1090

10 976.3714 760.8849

9 801.8831 624.9064

8 644.5577 502.3029

7 504.3949 393.0744

6 381.3951 297.2206

5 275.5579 214.7420

4 186.8836 145.6381

3 115.372 89.9092

2 61.0232 47.5553

1 20.1591 15.7100

PB LEVEL 0.9442 0.7358


building on plain ground for Model-3

LEVEL VX(KN) VY(KN)

11 1226.5649 1226.5649

10 1556.9433 1556.9433

9 1278.7005 1278.7005

8 1027.8259 1027.8259

7 804.3193 804.3193

6 608.1810 608.1810

5 439.4108 439.4108

4 298.0087 298.0087

3 183.9747 183.9747

2 97.3090 97.3090

1 30.1855 30.1855

PB LEVEL 1.5098 1.5098


building on plain ground for Model-5

MODEL NO EQX (KN) EQY (KN)

MODEL 01 2319.3089 2106.6816

MODEL 02 7073.3196 7073.3196

MODEL 03 5323.7196 5323.7196

MODEL 04 7114.7196 7114.7196

MODEL 05 7249.0856 7249.0856

MODEL 06 7138.4393 7138.4393

MODEL 07 7314.2053 7314.2053

Table 3.5: Base shear for models on curve slope ground

LEVEL VX(KN) VY(KN)

10 255.1863 231.7916

9 508.2353 461.6418

8 417.4081 379.1414

7 335.5147 304.7557

6 262.5551 238.4849

5 198.5294 180.3288

4 143.4375 130.2876

3 97.2795 88.3611

2 60.0551 54.5495

1 31.7647 28.8526

PB LEVEL 8.0916 7.3498

Table 3.6: Distribution of lateral seismic shear force for

building on curve slope ground for model-1

IV. RESULTS AND DISCUSSION

A. Natural Periods:

Model

No. CODAL

Fundamental natural Periods T

(Sec)

ANALYSIS

Building On

Plain Ground

Building On

Curved Slope

Ground

Eleven Storeyed Building

1 1.079 2.009 1.839

2 0.63 0.870 0.448

3 0.63 0.816 0.500

4 0.63 0.512 0.446

5 0.63 0.864 0.455

6 0.63 0.868 0.472

7 0.63 0.864 0.481

Table 4.1: Codal and Analytical Fundamental N.P for

different building modeled along Lgtd direction

Model

No. CODAL

Fundamental natural Periods T(Sec)

ANALYSIS

Building On

Plain Ground

Building On

Curved Slope

Ground

Eleven Storeyed Building

1 1.079 2.009 1.839

2 0.704 0.870 0.448

3 0.704 0.816 0.500

4 0.704 0.512 0.446

5 0.704 0.864 0.455

6 0.704 0.868 0.472

7 0.704 0.864 0.481




Table 4.2: Codal and Analytical Fundamental N.P for

different building modeled along Trvs direction

B. Lateral Displacement For Models On Plain Ground:

ST0REY

NO

BUILDING MODELS ON PLAIN

GROUND

E.S.METHOD R.S.METHOD

Ux Uy Ux Uy

12 42.3 43.8 30.4 31.8

11 41.1 42.8 29.7 31.2

10 39.1 40.9 28.5 30.1

9 36.4 38.1 26.8 28.4

8 32.9 34.5 24.6 26.2

7 28.8 30.4 22.0 23.6

6 24.2 25.8 19.0 20.6

5 19.4 21.0 15.6 17.2

4 14.4 15.9 11.8 13.4

3 9.3 10.8 7.9 9.3

2 4.6 5.7 4.0 5.1

1 1.0 1.3 0.8 1.1

Table 4.3: Lateral Displacements (mm) along Lgtd and Trvs

direction for model-1

Fig. 4.1: Displacements of Models on plain ground along

Longitudinal direction (Analysis cases: Equivalent Static

Method)


Transverse direction (Analysis cases: Equivalent Static

Method)


Transverse direction (Analysis cases: Response Spectrum

Method)

Fig. 4.4: Displacements of Models on Curve slope ground

along Transverse direction (Analysis cases: Equivalent

Static Method)

C. Lateral Displacement for Models on Curve Slope

Ground

ST0REY

NO

BUILDING MODELS ON CURVE SLOPE

GROUND

E.S.METHOD R.S.METHOD

Ux Uy Ux Uy

11 38.9 40.9 27.0 29.3

10 37.6 39.9 26.2 28.7

9 35.5 37.9 24.8 27.4

8 32.5 34.9 22.9 25.6

7 28.6 31.2 20.5 23.3

6 24.2 26.9 17.7 20.5

5 19.2 22.1 14.4 17.3

4 14.0 17.1 10.7 13.7

3 8.7 11.8 6.8 9.7

2 3.8 6.5 3.0 5.5

1 0.6 3.3 0.5 2.9

Table 4.4: Lateral Displacements (mm) along Lgtd and Trvs

direction for model-1

0

20

40

60

80

100

120

S1

S2

S3

S4

S5

S6

S7

S8

S9

S1

0

S1

1

S1

2

DIS

PL

AC

EM

EN

TS

(M

M)

STO REY NUMBER

M7

M6

M5

M4

M3

M2

M1

0

10

20

30

40

50

60

70

80

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

S11

S12D

ISP

LA

CE

ME

NT

S (

MM

)

STO REY NUMBER

M7

M6

M5

M4

M3

M2

M1





along Longitudinal direction (Analysis cases: Equivalent

Static Method)


along Transverse direction (Analysis cases: Equivalent

Static Method)


along Longitudinal direction (Analysis cases: Response

Spectrum Method)


along Transverse direction (Analysis cases: Response

Spectrum Method)

D. Storey Drifts for Models On Plain Ground:

Fig. 4.9: Storey Drifts of Models on Plain ground along


Method)



Method


Longitudinal direction (Analysis cases: Response Spectrum

Method)



Method)

0

10

20

30

40

50

60

70

80

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10S11

DIS

PL

AC

EM

EN

TS

(M

M)

STO REY NUMBER

M7

M6

M5

M4

M3

M2

M1

0

10

20

30

40

50

60

70

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11

DIS

PL

AC

EM

EN

TS

(M

M)

STO REY NUMBER

M7

M6

M5

M4

M3

M2

M1

0

0.5

1

1.5

2

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

S11

S12S

TO

RE

Y D

RIF

TS

(M

M)

STO REY NUMBER

M1

M2

M3

M4

M5

M6

M7

0

0.5

1

1.5

2

2.5

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12

ST

OR

EY

DR

IFT

S (

MM

)

STOREY NUMBER

M1

M2

M3

M4

M5

M6

M7




E. Storey Drifts for Models on Curve Slope Ground:



Method)



Method)


Longitudinal direction (Analysis cases: Response Spectrum

Method)



Method)

V. CONCLUSIONS

1) As the infills, cncrt shear and cncrt core walls are

provides which leads to reduces in fundamental natural

periods.

2) Storey drifts are found within the specified limit.

3) The masonry infill walls increases the behaviour of

structure during earthquake.

4) The influence of masonry infills may reduces the

displacement of structure.

5) The strength of structure can be increases by avoiding

soft stories.

6) The presence of central concrete core wall and

concrete shear wall at corners has not affected much on

behavior of the object, While action of lateral forces

comes into contact, as compared to other models.

ACKNOWLEDGEMENT

My heart full thanks to PROF. AMARESHA my beloved

guide, for their valuable Suggestions and Last but not the

least I am indebted to my Parents, Brother, Friends and my

colleagues for their support and supplications.

REFERENCES

[1] Krawinkler Helmut and Seneviratna G. D. P. K. :

“Earthquake resistant design of structures”, Prentice-

Hall of India Private Limited, New Delhi, India.

[2] An experimental study on cyclic tests on RC frames

[Murthy and Jain, 2000]. “Seismic Response of RC

Frame Buildings with Soft First Storeys”, Proceedings

of the CBRI Golden Jubilee Conference on Natural

Hazards in Urban Habitat, New Delhi, 1997.

[3] Applied Technology Council (1996): Seismic

Evaluation and Retrofit of Concrete Buildings, ATC-

40, Vol. 1.

[4] Elnashai, [2001]: e-conference proceedings, January

28; 2002.

[5] IS: 1893 (Part-I) 2002 (2002): Criteria for Earthquake

Resistant Design of Structures, Part-I General

Provisions and Buildings, Fifth Revision, Bureau of

Indian Standards, New Delhi.

[6] (Kabeyasawa, 1993; Eberhard and Sozen 1993)

“Seismic Performance of Conventional Multi-storey

Buildings with Open Ground Storey for Vehicular

Parking”, Indian Concrete Journal, February 2004.

[7] Lee, H.S., and Woo, W.S., “Effect of masonry infills

on seismic performance of a 3-storey RC frame with

non-seismic detailing”, John Wiley & Sons Ltd., 2001.

[8] Murthy, C.V.R., and Jain, S.K., “The Beneficial

Influence of Masonry Infill Walls on the Seismic

Performance of RC Framed Buildings”, Indian

Institute of Technology, Kanpur, 12th World

Conference on Earthquake Engineering, January 2000;

Auckland, New Zealand.

[9] Jack Moehle, Yousef Bozorgnia and T.Y.Yong. “The

Effect of Concrete Core Wall on Tall Buildings” .

[10] Ravi Sinha et al. “Earthquake Resistant Capacity of

Reinforced Concrete Frame Buildings”, Technical

Project Report, Vol. 2: Indian Institute of Technology,

Bombay.

0

0.5

1

1.5

2

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10

S11

S12ST

OR

EY

DR

IFT

S (

MM

)

STOREY NUMBER

M1

M2

M3

M4

M5

M6

M7

0

0.5

1

1.5

2

2.5

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12

ST

OR

EY

DR

IFT

S (

MM

)

STOREY NUMBER

M1

M2

M3

M4

M5

M6

M7




[11] David, M. Scott, “Some Recent Key Developments in

the Design of Tall Buildings”, Proceedings of National

Workshop on High Rise Buildings; Hyderabad 2008.

[12] Santha Kumar, A.K., “Design of Ductile Shear Walls

for Tall Buildings”.

[13] Mahesh Tandon and Vinay Gupta, Prerna Sohal,

“Recommendations for the seismic design of high rise

buildings”.

[14] ATC-72. Proceedings of Workshop on Tall Building

Seismic Design and Analysis Issues.

seismic evaluation of multi-storeyed buildings on plain ground and curve slope ground

Education