Maden galerilerinde püskürtme betonun yenilme sonrası performansının değerlendirilmesi
An assesment into post failure performance of shotcrete in mine galleries
Yazar: ERİM GÜÇLÜ
Danışman: DOÇ. DR. HAKAN TUNÇDEMİR
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Maden Mühendisliği Ana Bilim Dalı
Derece: Doktora, 2014
Konu: Maden Mühendisliği ve Madencilik = Mining Engineering and Mining

Özet:
Maden galerinde püskürtme beton sağlamlaştırma elemanı olarak sıklıkla kullanımaktadır. Püskürtme beton kaplaması mekanik olarak bir çok yenilme parametresine bağlı olarak tasarımlandırılmaktadır. Bu yenilme türleri tutunma yenilmesi, eğilme yenilmesi, doğrudan kesme yenilmesi, zımbalama sonucu kesme yenilmesi, basınç yenilmesi ve çekme yenilmesidir. Tez çalışması kapsamında sadece eğilme mekanizması sonucu yenilen püskürtme betonda oluşan çekme gerilmeleri kaplama performansının değerlendirilmesinde kullanılmıştır.
Püskürtme betonun eğilme mekanizması altında kırılma sonrası davranışını incelemek amacıyla farklı lif içerikleri ve karışımlarındaki püskürtme beton örneklerine panel testi uygulanmıştır. Literatürde püskürtme betonun eğilme davranışı panel testi sonucu elde edilen enerji yutma kapasitesi ile belirlenmektedir. Bu yaklaşımda kırılma öncesi ve kırılma sonrasındaki enerji yutma miktarları birlikte değerlendirilmektedir. Ancak bu çalışmada püskürtme betonun kırılma öncesi ve kırılma sonrası davranışı ayrı ayrı değerlendirilmiştir. Kırılma öncesi davranışı rijitlik parametresi temsil ederken, kırılma sonrası davranışı çalışmada önerilen süneklik indeksi temsil etmektedir.
Süneklik indeksi püskürtme betonun kırılma sonrası yuttuğu enerjinin yine kırılma sonrasındaki mükemmel sünek davranışta yutulan enerjiye oranı olarak tanımlanmıştır. Bu tanımlama ile püskürtme betonun kırıldıktan sonra ne kadar daha enerji yutabileceğini kestirmek mümkün olmaktadır. Çalışmada önerilen süneklik indeksi püskürtme betonun performasının değerlendirmesinde bir paramatre olarak kullanılmaktadır.
Tahkimat tasarımlandırmasında kullanılan bir çok yöntem mevcut olup, bunlardan en sık kullanılan ve Hoek ve Brown tarafından önerilen kaya tahkimat etkileşimi metodu çalışmada önemli yer tutmaktadır. Kaya tahkimat etkileşimi teorisi arazi tepkime eğrisi ve tahkimat karakteristik eğrisinin birlikte çözümlenmesi ile kaya ve tahkimat arasında basınç dengesinin kurulmasına dayalıdır.
Madencilik faaliyetleri gereği açılan bir galerinin yakınında yeni bir galeri açılması sıkça rastlanan bir durumdur. Böyle bir durumda gerilme ve deformasyon koşulları ağırlaşmaktadır. Kaya tahkimat etkileşimi teorisinde kullanılan tahkimat karakteristik eğrisi kırılma sonrası davranışı içermemektedir. Çalışmada püskürtme beton için kırılma sonrası davranışın kaya tahkimat etkileşimi içerisinde yer aldığı yeni yaklaşım getirilmiştir.
Arazi tepkime eğrilerinin belirlenmesi için deterministik ve nümerik metotlar bulunmaktadır. Deterministik metotlar bazı kabuller içerisinde çözüm sunmaktadır. Bu kabuller yeraltı açıklıklarının dairesel kesitli olması ve hidrostatik basınç koşullarının bulunmasıdır. Ancak çalışma sahasında farklı jeolojik birimlerin olduğu kesitlerde galeriler sürülmektedir. Aynı zamanda galeri kesitleri ise dörtgen şeklindedir. Bu nedenle nümerik modelleme yapılarak çalışma sahalarında arazi tepkime eğrileri belirlenmiştir.
Mevcut yöntemde püskürtme beton malzemesinin basınç dayanımı yenilme kriteri olarak kullanılmaktadır. Bu yöntem püskürtme betondaki basınç yenilmesi mekanizması için uygundur. Ancak dörtgen kesitli açıklıklarda püskürtme betonun eğilme yenilmesinin teorik olarak etkin bir rol oynadığı düşünülmektedir. Bu nedenle çalışmada normal yük altında eğilme mekanizması sonucu oluşan çekme dayanımı yenilme kriteri olarak seçilmiştir. Püskürtme betonun normal yük altında eğilmesini gerçekçi biçimde ortaya koyan panel testleri uygulanmıştır. Panel testi sonucu elde edilen yük – sehim eğrileri akma hattı teorisi kullanılarak çekme gerilmesi – sehim eğrilerine dönüştürülmüştür.
Bu dönüştürme işlemi sonucunda farklı püskürtme beton örnekleri için elde edilen çok sayıda çekme gerilmesi – sehim eğrisi doğrusal olmayan regresyon yöntemi ile modellenmiştir. Regresyon işleminde yakınsama algoritması olan Levenberg – Marquardt yöntemi kullanılmıştır. Model parametreleri ile kırılma anındaki sehim, maksimum çekme gerilmesi ve süneklik indeksi arasında ilişkiler tespit edilmiştir.
Önerilen süneklik indeksi ve model sayesinde püskürtme beton kullanıcıları püskürtme betonu ne zaman püskürtebilecekleri öngörebilmektedirler. Aynı zamanda bir galeri yakınında açılan yeni bir galerinin ağırlaştırdığı gerilme ve deformasyon altında kullandıkları püskürtme betonun kırılma sonrası davranışını, püskürtme betonun kullanılabilirği açısından değerlendirebilecekdir.

Abstract:
Shotcrete is widely used as reinforcement material in mine galleries. It is preferable because of its easy application and time saving operation. Failure mechanisms of shotcrete is generally classified as adhesion failure, bending failure, direct shear failure, shear failure under punching, compressive failure and tensile failure. In this thesis study, tensile stress on failed shotcrete panels induced by bending mechanism was used for evaluating performance of shotcrete lining.
There are several methods to design supports in mines. Hoek and Brown were proposed rock and support interaction method in 1980 which was is still widely used for this purpose. In this study, evaluations were based on rock support interaction method. The method is based on balancing ground pressure and support pressure by interpretation of ground reaction curves and support characteristic curves together.
Rock – support interaction theory is commonly used to design of support in underground mine openings. Compressive strength of shotcrete lining is used as failure parameter in the theory (Hoek and Brown, 1980). Theory is also based on circular cross – sectional opening and hydrostatic stress conditions. But nonhomogeneous geological formations and rectangular cross – section are existing in study area. In this case, bending behavior of shotcrete linings anchored with rock bolts become more important than other failure types of shotcrete. 
Panel tests were performed in order to determine bending behavior of shotcrete lining. Also post failure behavior of shotcrete lining is not included in current rock – support interaction theory. A new gallery can be driven near an existing one during mining operations. Stress and deformations conditions is getting harder in this situation and shotcrete lining starts to fail. Support reaction curve in rock support interaction theory does not include post crack behavior. But secondary stress and deformation conditions may cause shotcrete to fail and post crack behavior is getting more important in this situation. In this study, a new approach was presented which post crack behavior of shotcrete was included in rock support interaction theory.
An important result of panel tests showed that shotcrete was still carrying considerable load if it includes additives such as fiber and steel mesh. So that, post failure energy absorption level of shotcrete panel is much more than energy absorbed at pre failure according to panel tests results.
Panel tests were performed on shotcrete samples having different fiber amounts and different mix compositions in order to investigate post crack failure of shotcrete in bending mechanism. Bending behavior of shotcrete is determined by panel tests in terms of energy absorption capacity. Pre failure energy and post failure energy is evaluated together in literature. In this study, post crack behavior and pre failure behavior of shotcrete was evaluated separately. Stiffness is representing pre failure behavior and proposed ductility index is representing post crack failure of shotcrete.
Ductility index is defined as a ratio, which is calculated by dividing energy absorbed by shotcrete after failure to energy absorbed in perfectly ductile behavior. This definition allows users to estimate how much energy can be absorbed by shotcrete after failure. Proposed ductility index is used to evaluate post crack performance of shotcrete.
It was found out that the change in deflection is more effective on ductility index than the change in load. Ductility index is directly related with energy absorption capacity. So the support design chart of Papworth published in 2002 was revised by adding ductility index axis.
Tensile stress – deflection curves in bending mechanism should be scattered in order to evaluate shotcrete lining in rock – support interaction theory. Energy formed by normal load applied to panel tests generates tensile stress. Yield line theory was used for determining tensile stress through failure patterns on shotcrete panels. Fibers in shotcrete samples assist ductile behavior of shotcrete as cracks propagate. Hence, tensile stress – deflection curves of shotcrete samples were achieved by cumulative energy formed under normal loading conditions in yield line analysis. These curves were named as shotcrete characteristic curves in thesis study.
Shotcrete characteristic curve was modelled by nonlinear regression method using tensile stress – deflection curves of several shotcrete samples including different fiber amounts and having different mixture compositions. Levenberg – Marquardt algorithm was used in nonlinear regression analysis. Relationship between model parameters and deflection at failure of shotcrete, maximum tensile stress of shotcrete and ductility index were examined. So, shotcrete users can specify the model parameters and their magnitudes in order to obtain suitable shotcrete characteristic curve for his/her prior design. The relationship between model parameters and mechanical parameters mentioned above is valid only for lower and upper limits given in this study. Panel tests with different shotcrete compositions should be performed for further prediction beyond these limits.
Deterministic and numerical methods are used for determining ground reaction curves. Deterministic methods are introducing solutions with some assumptions such as circular cross sections of opening and hydrostatic stress conditions. However galleries having rectangular cross-sections were driven in study area and complex geological conditions were existing. For that reason, numerical method were preferred in order to determine ground reaction curves.
In this study, a numerical method called "load reduction method" is used. Load reduction is a stepwise method. Support stress against ground stress is equal to ground stress at first step. For each step, a reduction factor is applied and support stress become zero at last step. Maximum total displacement and mean stress values of each step were used to plot ground reaction curves.
Ground reaction curves and shotcrete characteristic curves were examined together in this study. Effect of distances between galleries on stress and deformation conditions were investigated. It was found out that stress and deformations start to decrease after a certain distance between galleries. Five different gallery was examined in terms of stress and deformation distribution in numerical analysis. Galleries were named as 745XCS Giris, 640XCS, 745XCS, 745FWCN09 and 760XCS. For 745XCS Giris gallery, two galleries were affected between each other if they were closer more than 10 m. This limit is at least 15 m for 640XCS, 745XCS and 745FWNC09 galleries. It is 7.5 m for 640XCS gallery.
The worst stress and deformation conditions were around 640XCS gallery. In numerical analysis, it was found that stress and deformation conditions were getting better 745FWCN09, 745XCS, 745XCS Giris and 760XCS galleries, respectively. Shotcrete characteristic curves of different composition were evaluated with ground reaction curves. Shotcrete samples including steel fiber, PP22 and PP23 (PP refers to shotcrete mixture including polipropylene fiber) were high performance mixtures in terms of ductility index and maximum tensile stress whereas shotcrete sample without fiber were underperformer.
Ground reaction curves for five different galleries driven in different geological cross-sections were gathered by numerical analysis. Effect of distance between two galleries on ground reaction curves were also investigated for different distances. The reason for this investigation was that strength of shotcrete lining was exceeded in different stress and deformation conditions. When strength of shotcrete lining was exceeded, post failure behavior should be taken into consideration.
In this scope, shotcrete characteristic curves and ground reaction curves were examined together considering post failure behavior of shotcrete. There were some important parameters used in analysis. One of them is minimum displacement which should be occurred in gallery in order to apply shotcrete. The other one was stress and deformation values at failure of shotcrete. These two parameters were referred to pre failure behavior. For post failure behavior, there were three main parameters used. One of them was proposed ductility index. Second one is stress and deformation values at intersection points between shotcrete characteristic curves and new ground reaction curves related to different stress and deformation conditions. Third one is critical distance between galleries where shotcrete lining was not out of use.
Minimum displacements, which should be occurred in gallery in order to apply shotcrete, were compared for each gallery. Lower and upper limits of these values varied between 130 mm and 168 mm for 640XCS, 92 mm and 115 mm for 760XCS, 80 mm and 100 mm for 745XCS Giris, 81 mm and 113 mm for 745XCS and 25 mm and 39 mm for 745FWCN09, respectively.
PP22 and PP23 showed the highest performances in all galleries. Post failure and pre failure parameters used in analysis were mentioned above.
Relationships were found out between ductility index and deflection values where shotcrete characteristic curves intersected to new ground reaction curves representing new stress and deformation conditions. As the ductility index increases, shotcrete characteristic curve intersects to ground reaction curve earlier in post failure media.
In conclusion, shotcrete users can predict application time of shotcrete and the conditions which shotcrete continue carrying load by evaluating its performance using rock – support interaction theory and post failure behavior. However the important point is to measure in situ displacements in mine galleries. Without in situ measurements, this methodology may cause unexpected situations. Because real formation data may not be exactly the same with the data in model used. Displacement measurements should confirm the model analyzed. If current displacements are decreasing and shotcrete lining does not lose its load bearing capacity much after failure, solution can be provided by repairing shotcrete lining. If deformations are increasing continuously, shotcrete user should remove the lining and apply a new design for that gallery.
Some of the future works were suggested in order to develop the methodology related to usage of post failure behavior of shotcrete in rock – support interaction theory. The change in mechanical properties of shotcrete with time should be integrated with shotcrete characteristic curve. Investigations for relationship between energy absorption capacities of different shotcrete samples having various thickness were presented literature. The effect of sample thickness should be taken place in proposed methodology. In this study, 60 cm × 60 cm × 10 cm shotcrete panels were tested. Furthermore, post failure behavior of shotcrete lining with rock bolt system should be numerically analyzed in different conditions and geometries. Fiber effect in shotcrete mixture was also investigated in literature. These studies should be evaluated systematically and effect of fibers should be examined in rock – support interaction concept.